Average Error: 0.0 → 0.0
Time: 26.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r15890 = 0.5;
        double r15891 = re;
        double r15892 = sin(r15891);
        double r15893 = r15890 * r15892;
        double r15894 = 0.0;
        double r15895 = im;
        double r15896 = r15894 - r15895;
        double r15897 = exp(r15896);
        double r15898 = exp(r15895);
        double r15899 = r15897 + r15898;
        double r15900 = r15893 * r15899;
        return r15900;
}
↓
double f(double re, double im) {
        double r15901 = 0.5;
        double r15902 = re;
        double r15903 = sin(r15902);
        double r15904 = r15901 * r15903;
        double r15905 = 0.0;
        double r15906 = exp(r15905);
        double r15907 = r15904 * r15906;
        double r15908 = im;
        double r15909 = exp(r15908);
        double r15910 = r15907 / r15909;
        double r15911 = r15904 * r15909;
        double r15912 = r15910 + r15911;
        return r15912;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]
  4. Using strategy rm

  5. Applied exp-diff0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\frac{e^{0.0}}{e^{im}}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  6. Applied associate-*r/0.0

    \[\leadsto \color{blue}{\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  7. Final simplification0.0

    \[\leadsto \frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))