Average Error: 0.0 → 0.0
Time: 5.9s
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 r128 = 0.5;
        double r129 = re;
        double r130 = sin(r129);
        double r131 = r128 * r130;
        double r132 = 0.0;
        double r133 = im;
        double r134 = r132 - r133;
        double r135 = exp(r134);
        double r136 = exp(r133);
        double r137 = r135 + r136;
        double r138 = r131 * r137;
        return r138;
}
↓
double f(double re, double im) {
        double r139 = 0.5;
        double r140 = re;
        double r141 = sin(r140);
        double r142 = r139 * r141;
        double r143 = 0.0;
        double r144 = im;
        double r145 = r143 - r144;
        double r146 = exp(r145);
        double r147 = exp(r144);
        double r148 = r146 + r147;
        double r149 = r142 * r148;
        return r149;
}

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 2020025 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))