Average Error: 0.0 → 0.0
Time: 2.7s
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 r40302 = re;
        double r40303 = exp(r40302);
        double r40304 = im;
        double r40305 = cos(r40304);
        double r40306 = r40303 * r40305;
        return r40306;
}
↓
double f(double re, double im) {
        double r40307 = re;
        double r40308 = exp(r40307);
        double r40309 = im;
        double r40310 = cos(r40309);
        double r40311 = r40308 * r40310;
        return r40311;
}

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 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))