Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[e^{re} \cdot \cos im\]
e^{re} \cdot \cos im
↓
e^{re} \cdot \cos im
double f(double re, double im) {
        double r31451 = re;
        double r31452 = exp(r31451);
        double r31453 = im;
        double r31454 = cos(r31453);
        double r31455 = r31452 * r31454;
        return r31455;
}
↓
double f(double re, double im) {
        double r31456 = re;
        double r31457 = exp(r31456);
        double r31458 = im;
        double r31459 = cos(r31458);
        double r31460 = r31457 * r31459;
        return r31460;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))