Average Error: 0.0 → 0.0
Time: 4.7s
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 r69735 = 0.5;
        double r69736 = re;
        double r69737 = sin(r69736);
        double r69738 = r69735 * r69737;
        double r69739 = 0.0;
        double r69740 = im;
        double r69741 = r69739 - r69740;
        double r69742 = exp(r69741);
        double r69743 = exp(r69740);
        double r69744 = r69742 + r69743;
        double r69745 = r69738 * r69744;
        return r69745;
}
↓
double f(double re, double im) {
        double r69746 = 0.5;
        double r69747 = re;
        double r69748 = sin(r69747);
        double r69749 = r69746 * r69748;
        double r69750 = 0.0;
        double r69751 = im;
        double r69752 = r69750 - r69751;
        double r69753 = exp(r69752);
        double r69754 = exp(r69751);
        double r69755 = r69753 + r69754;
        double r69756 = r69749 * r69755;
        return r69756;
}

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 2019346 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))