Average Error: 0.0 → 0.0
Time: 24.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\sqrt{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5} \cdot \sin re\right) \cdot \sqrt{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(\sqrt{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5} \cdot \sin re\right) \cdot \sqrt{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5}
double f(double re, double im) {
        double r794794 = 0.5;
        double r794795 = re;
        double r794796 = sin(r794795);
        double r794797 = r794794 * r794796;
        double r794798 = 0.0;
        double r794799 = im;
        double r794800 = r794798 - r794799;
        double r794801 = exp(r794800);
        double r794802 = exp(r794799);
        double r794803 = r794801 + r794802;
        double r794804 = r794797 * r794803;
        return r794804;
}
↓
double f(double re, double im) {
        double r794805 = 0.5;
        double r794806 = im;
        double r794807 = exp(r794806);
        double r794808 = r794805 / r794807;
        double r794809 = r794807 * r794805;
        double r794810 = r794808 + r794809;
        double r794811 = sqrt(r794810);
        double r794812 = re;
        double r794813 = sin(r794812);
        double r794814 = r794811 * r794813;
        double r794815 = r794814 * r794811;
        return r794815;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-*r*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))