Average Error: 0.0 → 0.0
Time: 12.6s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]
e^{re} \cdot \cos im
↓
\cos im \cdot e^{re}
double f(double re, double im) {
        double r1211015 = re;
        double r1211016 = exp(r1211015);
        double r1211017 = im;
        double r1211018 = cos(r1211017);
        double r1211019 = r1211016 * r1211018;
        return r1211019;
}
↓
double f(double re, double im) {
        double r1211020 = im;
        double r1211021 = cos(r1211020);
        double r1211022 = re;
        double r1211023 = exp(r1211022);
        double r1211024 = r1211021 * r1211023;
        return r1211024;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{re} \cdot \cos im\]

  2. Final simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))