Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\sin re \cdot \left(e^{0.0 - im} + e^{im}\right)\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\sin re \cdot \left(e^{0.0 - im} + e^{im}\right)\right)
double f(double re, double im) {
        double r12704 = 0.5;
        double r12705 = re;
        double r12706 = sin(r12705);
        double r12707 = r12704 * r12706;
        double r12708 = 0.0;
        double r12709 = im;
        double r12710 = r12708 - r12709;
        double r12711 = exp(r12710);
        double r12712 = exp(r12709);
        double r12713 = r12711 + r12712;
        double r12714 = r12707 * r12713;
        return r12714;
}
↓
double f(double re, double im) {
        double r12715 = 0.5;
        double r12716 = re;
        double r12717 = sin(r12716);
        double r12718 = 0.0;
        double r12719 = im;
        double r12720 = r12718 - r12719;
        double r12721 = exp(r12720);
        double r12722 = exp(r12719);
        double r12723 = r12721 + r12722;
        double r12724 = r12717 * r12723;
        double r12725 = r12715 * r12724;
        return r12725;
}

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 associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019294 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))