Average Error: 0.0 → 0.0
Time: 6.2s
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 r131 = 0.5;
        double r132 = re;
        double r133 = sin(r132);
        double r134 = r131 * r133;
        double r135 = 0.0;
        double r136 = im;
        double r137 = r135 - r136;
        double r138 = exp(r137);
        double r139 = exp(r136);
        double r140 = r138 + r139;
        double r141 = r134 * r140;
        return r141;
}
↓
double f(double re, double im) {
        double r142 = 0.5;
        double r143 = re;
        double r144 = sin(r143);
        double r145 = r142 * r144;
        double r146 = 0.0;
        double r147 = im;
        double r148 = r146 - r147;
        double r149 = exp(r148);
        double r150 = exp(r147);
        double r151 = r149 + r150;
        double r152 = r145 * r151;
        return r152;
}

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 +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))))