Average Error: 0.0 → 0.0
Time: 16.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\frac{\sin re}{e^{im}} + e^{im} \cdot \sin re\right) \cdot 0.5
double f(double re, double im) {
        double r1162620 = 0.5;
        double r1162621 = re;
        double r1162622 = sin(r1162621);
        double r1162623 = r1162620 * r1162622;
        double r1162624 = 0.0;
        double r1162625 = im;
        double r1162626 = r1162624 - r1162625;
        double r1162627 = exp(r1162626);
        double r1162628 = exp(r1162625);
        double r1162629 = r1162627 + r1162628;
        double r1162630 = r1162623 * r1162629;
        return r1162630;
}
↓
double f(double re, double im) {
        double r1162631 = re;
        double r1162632 = sin(r1162631);
        double r1162633 = im;
        double r1162634 = exp(r1162633);
        double r1162635 = r1162632 / r1162634;
        double r1162636 = r1162634 * r1162632;
        double r1162637 = r1162635 + r1162636;
        double r1162638 = 0.5;
        double r1162639 = r1162637 * r1162638;
        return r1162639;
}

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. Taylor expanded around inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))