Average Error: 0.0 → 0.0

Time: 13.0s

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 r736960 = re;
        double r736961 = exp(r736960);
        double r736962 = im;
        double r736963 = cos(r736962);
        double r736964 = r736961 * r736963;
        return r736964;
}

↓

double f(double re, double im) {
        double r736965 = im;
        double r736966 = cos(r736965);
        double r736967 = re;
        double r736968 = exp(r736967);
        double r736969 = r736966 * r736968;
        return r736969;
}

Error

The X axis uses an exponential scale — Bits error versus `re`

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[e^{re} \cdot \cos im\]
Final simplification0.0
\[\leadsto \cos im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))