Average Error: 0.0 → 0.0
Time: 11.2s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{\cos re}{e^{im}} \cdot 0.5 + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \cos re\right)\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{\cos re}{e^{im}} \cdot 0.5 + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \cos re\right)\right)
double f(double re, double im) {
        double r71826 = 0.5;
        double r71827 = re;
        double r71828 = cos(r71827);
        double r71829 = r71826 * r71828;
        double r71830 = im;
        double r71831 = -r71830;
        double r71832 = exp(r71831);
        double r71833 = exp(r71830);
        double r71834 = r71832 + r71833;
        double r71835 = r71829 * r71834;
        return r71835;
}
↓
double f(double re, double im) {
        double r71836 = re;
        double r71837 = cos(r71836);
        double r71838 = im;
        double r71839 = exp(r71838);
        double r71840 = r71837 / r71839;
        double r71841 = 0.5;
        double r71842 = r71840 * r71841;
        double r71843 = sqrt(r71839);
        double r71844 = r71841 * r71837;
        double r71845 = r71843 * r71844;
        double r71846 = r71843 * r71845;
        double r71847 = r71842 + r71846;
        return r71847;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied add-sqr-sqrt0.0

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

  8. Applied associate-*l*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))