Average Error: 0.0 → 0.2
Time: 15.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(0.5 \cdot e^{im} + \log \left(e^{\frac{0.5}{e^{im}}}\right)\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(0.5 \cdot e^{im} + \log \left(e^{\frac{0.5}{e^{im}}}\right)\right)
double f(double re, double im) {
        double r256770 = 0.5;
        double r256771 = re;
        double r256772 = sin(r256771);
        double r256773 = r256770 * r256772;
        double r256774 = 0.0;
        double r256775 = im;
        double r256776 = r256774 - r256775;
        double r256777 = exp(r256776);
        double r256778 = exp(r256775);
        double r256779 = r256777 + r256778;
        double r256780 = r256773 * r256779;
        return r256780;
}
↓
double f(double re, double im) {
        double r256781 = re;
        double r256782 = sin(r256781);
        double r256783 = 0.5;
        double r256784 = im;
        double r256785 = exp(r256784);
        double r256786 = r256783 * r256785;
        double r256787 = r256783 / r256785;
        double r256788 = exp(r256787);
        double r256789 = log(r256788);
        double r256790 = r256786 + r256789;
        double r256791 = r256782 * r256790;
        return r256791;
}

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

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

  4. Applied add-log-exp0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019151 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))