Average Error: 0.0 → 0.0
Time: 9.9s
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 r32741 = re;
        double r32742 = exp(r32741);
        double r32743 = im;
        double r32744 = cos(r32743);
        double r32745 = r32742 * r32744;
        return r32745;
}
↓
double f(double re, double im) {
        double r32746 = re;
        double r32747 = exp(r32746);
        double r32748 = im;
        double r32749 = cos(r32748);
        double r32750 = r32747 * r32749;
        return r32750;
}

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)))