Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r8850 = 0.5;
        double r8851 = re;
        double r8852 = sin(r8851);
        double r8853 = r8850 * r8852;
        double r8854 = 0.0;
        double r8855 = im;
        double r8856 = r8854 - r8855;
        double r8857 = exp(r8856);
        double r8858 = exp(r8855);
        double r8859 = r8857 + r8858;
        double r8860 = r8853 * r8859;
        return r8860;
}
↓
double f(double re, double im) {
        double r8861 = 0.0;
        double r8862 = exp(r8861);
        double r8863 = 0.5;
        double r8864 = re;
        double r8865 = sin(r8864);
        double r8866 = r8863 * r8865;
        double r8867 = r8862 * r8866;
        double r8868 = im;
        double r8869 = exp(r8868);
        double r8870 = r8867 / r8869;
        double r8871 = r8869 * r8866;
        double r8872 = r8870 + r8871;
        return r8872;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied exp-diff0.0

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

  8. Applied associate-*l/0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))