Average Error: 0.0 → 0.0
Time: 12.0s
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 r24348 = re;
        double r24349 = exp(r24348);
        double r24350 = im;
        double r24351 = cos(r24350);
        double r24352 = r24349 * r24351;
        return r24352;
}
↓
double f(double re, double im) {
        double r24353 = re;
        double r24354 = exp(r24353);
        double r24355 = im;
        double r24356 = cos(r24355);
        double r24357 = r24354 * r24356;
        return r24357;
}

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