Average Error: 0.0 → 0.0
Time: 24.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r607529 = 0.5;
        double r607530 = re;
        double r607531 = sin(r607530);
        double r607532 = r607529 * r607531;
        double r607533 = 0.0;
        double r607534 = im;
        double r607535 = r607533 - r607534;
        double r607536 = exp(r607535);
        double r607537 = exp(r607534);
        double r607538 = r607536 + r607537;
        double r607539 = r607532 * r607538;
        return r607539;
}
↓
double f(double re, double im) {
        double r607540 = im;
        double r607541 = exp(r607540);
        double r607542 = re;
        double r607543 = sin(r607542);
        double r607544 = r607541 * r607543;
        double r607545 = r607543 / r607541;
        double r607546 = r607544 + r607545;
        double r607547 = 0.5;
        double r607548 = r607546 * r607547;
        return r607548;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))