Average Error: 0.0 → 0.0

Time: 3.3s

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 r640648 = re;
        double r640649 = exp(r640648);
        double r640650 = im;
        double r640651 = cos(r640650);
        double r640652 = r640649 * r640651;
        return r640652;
}

↓

double f(double re, double im) {
        double r640653 = im;
        double r640654 = cos(r640653);
        double r640655 = re;
        double r640656 = exp(r640655);
        double r640657 = r640654 * r640656;
        return r640657;
}

Error

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

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Out

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Derivation

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

Reproduce

herbie shell --seed 2019156 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))