Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)
double f(double re, double im) {
        double r17491 = 0.5;
        double r17492 = re;
        double r17493 = sin(r17492);
        double r17494 = r17491 * r17493;
        double r17495 = 0.0;
        double r17496 = im;
        double r17497 = r17495 - r17496;
        double r17498 = exp(r17497);
        double r17499 = exp(r17496);
        double r17500 = r17498 + r17499;
        double r17501 = r17494 * r17500;
        return r17501;
}
↓
double f(double re, double im) {
        double r17502 = 0.5;
        double r17503 = -1.0;
        double r17504 = im;
        double r17505 = r17503 * r17504;
        double r17506 = exp(r17505);
        double r17507 = exp(r17504);
        double r17508 = r17506 + r17507;
        double r17509 = re;
        double r17510 = sin(r17509);
        double r17511 = r17508 * r17510;
        double r17512 = r17502 * r17511;
        return r17512;
}

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

    \[\leadsto \color{blue}{0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)\]

Reproduce

herbie shell --seed 2020018 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))