Average Error: 0.0 → 0.0
Time: 8.2s
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 r1390278 = re;
        double r1390279 = exp(r1390278);
        double r1390280 = im;
        double r1390281 = cos(r1390280);
        double r1390282 = r1390279 * r1390281;
        return r1390282;
}
↓
double f(double re, double im) {
        double r1390283 = im;
        double r1390284 = cos(r1390283);
        double r1390285 = re;
        double r1390286 = exp(r1390285);
        double r1390287 = r1390284 * r1390286;
        return r1390287;
}

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 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))