Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r82755 = 0.5;
        double r82756 = re;
        double r82757 = sin(r82756);
        double r82758 = r82755 * r82757;
        double r82759 = 0.0;
        double r82760 = im;
        double r82761 = r82759 - r82760;
        double r82762 = exp(r82761);
        double r82763 = exp(r82760);
        double r82764 = r82762 + r82763;
        double r82765 = r82758 * r82764;
        return r82765;
}
↓
double f(double re, double im) {
        double r82766 = 0.5;
        double r82767 = re;
        double r82768 = sin(r82767);
        double r82769 = r82766 * r82768;
        double r82770 = 0.0;
        double r82771 = im;
        double r82772 = r82770 - r82771;
        double r82773 = exp(r82772);
        double r82774 = exp(r82771);
        double r82775 = r82773 + r82774;
        double r82776 = r82769 * r82775;
        return r82776;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))