Average Error: 0.0 → 0.0
Time: 21.2s
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 r180590 = 0.5;
        double r180591 = re;
        double r180592 = sin(r180591);
        double r180593 = r180590 * r180592;
        double r180594 = 0.0;
        double r180595 = im;
        double r180596 = r180594 - r180595;
        double r180597 = exp(r180596);
        double r180598 = exp(r180595);
        double r180599 = r180597 + r180598;
        double r180600 = r180593 * r180599;
        return r180600;
}
↓
double f(double re, double im) {
        double r180601 = im;
        double r180602 = exp(r180601);
        double r180603 = re;
        double r180604 = sin(r180603);
        double r180605 = r180602 * r180604;
        double r180606 = r180604 / r180602;
        double r180607 = r180605 + r180606;
        double r180608 = 0.5;
        double r180609 = r180607 * r180608;
        return r180609;
}

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 2019151 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))