diff --git a/evm/src/bn254_pairing.rs b/evm/src/bn254_pairing.rs
index fc470e9b..9c4956c2 100644
--- a/evm/src/bn254_pairing.rs
+++ b/evm/src/bn254_pairing.rs
@@ -129,8 +129,14 @@ pub fn invariance_inducing_power(f: Fp12) -> Fp12 {
     t.frob(3) * t_a2.frob(2) * t_a1.frob(1) * t_a0
 }
 
-/// Given an f: Fp12, this function computes the triple
+/// Given an f: Fp12, this function computes
 ///     T^a2, T^(-a1), T^(-a0)
+/// by first computing
+///     T^a4, T^a2, T^a0
+/// where a1 is given by
+///     a1 = a4 + 2a2 - a0
+/// thus what remains is inverting T^a0 and returning
+///     T^a2, T^a4 * T^a2 * T^a2 * T^(-a0), T^(-a0)
 fn get_powers(f: Fp12) -> (Fp12, Fp12, Fp12) {
     const EXPS4: [(usize, usize, usize); 64] = [
         (1, 1, 0),
@@ -308,7 +314,8 @@ fn get_powers(f: Fp12) -> (Fp12, Fp12, Fp12) {
     }
     y0 = y0 * sq;
 
-    (y2, y4 * y2 * y2 / y0, y0.inv())
+    let y0_inv = y0.inv();
+    (y2, y4 * y2 * y2 * y0_inv, y0_inv)
 }
 
 // The curve is cyclic with generator (1, 2)
diff --git a/evm/src/cpu/kernel/asm/curve/bn254/curve_arithmetic/tate_pairing.asm b/evm/src/cpu/kernel/asm/curve/bn254/curve_arithmetic/tate_pairing.asm
index 2557d882..fe46a9e7 100644
--- a/evm/src/cpu/kernel/asm/curve/bn254/curve_arithmetic/tate_pairing.asm
+++ b/evm/src/cpu/kernel/asm/curve/bn254/curve_arithmetic/tate_pairing.asm
@@ -1,18 +1,8 @@
 /// def tate(P: Curve, Q: TwistedCurve) -> Fp12:
 ///     out = miller_loop(P, Q)
-///
-///     inv = inv_fp12(out)
-///     out = frob_fp12(6, out)
-///     out = mul_fp12(out, inv)
-///
-///     acc = frob_fp12(2, out)
-///     out = mul_fp12(out, acc)
-///
-///     pow = invariance_inducing_power(out)
-///     out = frob_fp12(3, out) 
-///     out = mul_fp12(out, pow)
-///
-///     return out
+///     out = out.frob(6) / out
+///     out = out.frob(2) * out
+///     return final_power(out)
 
 global tate:
     // stack:                        ptr, out, retdest
diff --git a/evm/src/cpu/kernel/tests/bn254.rs b/evm/src/cpu/kernel/tests/bn254.rs
index 5985b404..18a7eb4a 100644
--- a/evm/src/cpu/kernel/tests/bn254.rs
+++ b/evm/src/cpu/kernel/tests/bn254.rs
@@ -208,7 +208,6 @@ fn test_inv_fp12() -> Result<()> {
 fn test_tate() -> Result<()> {
     let ptr: usize = 300;
     let out: usize = 400;
-
     let inputs: Vec<U256> = vec![
         CURVE_GENERATOR.x.val,
         CURVE_GENERATOR.y.val,