Average Error: 0.0 → 0.1
Time: 34.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(0.5 \cdot e^{im} + \frac{\sqrt{0.5}}{\frac{\sqrt{e^{im}}}{\frac{\sqrt{0.5}}{\sqrt{e^{im}}}}}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(0.5 \cdot e^{im} + \frac{\sqrt{0.5}}{\frac{\sqrt{e^{im}}}{\frac{\sqrt{0.5}}{\sqrt{e^{im}}}}}\right)
double f(double re, double im) {
        double r904735 = 0.5;
        double r904736 = re;
        double r904737 = sin(r904736);
        double r904738 = r904735 * r904737;
        double r904739 = 0.0;
        double r904740 = im;
        double r904741 = r904739 - r904740;
        double r904742 = exp(r904741);
        double r904743 = exp(r904740);
        double r904744 = r904742 + r904743;
        double r904745 = r904738 * r904744;
        return r904745;
}
↓
double f(double re, double im) {
        double r904746 = re;
        double r904747 = sin(r904746);
        double r904748 = 0.5;
        double r904749 = im;
        double r904750 = exp(r904749);
        double r904751 = r904748 * r904750;
        double r904752 = sqrt(r904748);
        double r904753 = sqrt(r904750);
        double r904754 = r904752 / r904753;
        double r904755 = r904753 / r904754;
        double r904756 = r904752 / r904755;
        double r904757 = r904751 + r904756;
        double r904758 = r904747 * r904757;
        return r904758;
}

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-sqr-sqrt0.0

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

  5. Applied associate-/l*0.0

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

  7. Applied add-sqr-sqrt0.1

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

  8. Applied associate-/l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019155 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))