Average Error: 0.0 → 0.0
Time: 18.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{0.5 \cdot \cos re}{e^{im}}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{0.5 \cdot \cos re}{e^{im}}
double f(double re, double im) {
        double r5682794 = 0.5;
        double r5682795 = re;
        double r5682796 = cos(r5682795);
        double r5682797 = r5682794 * r5682796;
        double r5682798 = im;
        double r5682799 = -r5682798;
        double r5682800 = exp(r5682799);
        double r5682801 = exp(r5682798);
        double r5682802 = r5682800 + r5682801;
        double r5682803 = r5682797 * r5682802;
        return r5682803;
}
↓
double f(double re, double im) {
        double r5682804 = im;
        double r5682805 = exp(r5682804);
        double r5682806 = 0.5;
        double r5682807 = re;
        double r5682808 = cos(r5682807);
        double r5682809 = r5682806 * r5682808;
        double r5682810 = r5682805 * r5682809;
        double r5682811 = r5682809 / r5682805;
        double r5682812 = r5682810 + r5682811;
        return r5682812;
}

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

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(e^{im}, 0.5 \cdot \cos re, \frac{0.5 \cdot \cos re}{e^{im}}\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

    \[\leadsto \color{blue}{e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{0.5 \cdot \cos re}{e^{im}}}\]

  5. Final simplification0.0

    \[\leadsto e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{0.5 \cdot \cos re}{e^{im}}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))