Average Error: 0.0 → 0.0
Time: 4.8s
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 r71662 = 0.5;
        double r71663 = re;
        double r71664 = sin(r71663);
        double r71665 = r71662 * r71664;
        double r71666 = 0.0;
        double r71667 = im;
        double r71668 = r71666 - r71667;
        double r71669 = exp(r71668);
        double r71670 = exp(r71667);
        double r71671 = r71669 + r71670;
        double r71672 = r71665 * r71671;
        return r71672;
}
↓
double f(double re, double im) {
        double r71673 = 0.5;
        double r71674 = re;
        double r71675 = sin(r71674);
        double r71676 = r71673 * r71675;
        double r71677 = 0.0;
        double r71678 = im;
        double r71679 = r71677 - r71678;
        double r71680 = exp(r71679);
        double r71681 = exp(r71678);
        double r71682 = r71680 + r71681;
        double r71683 = r71676 * r71682;
        return r71683;
}

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 2020100 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))