Average Error: 0.0 → 0.0
Time: 5.4s
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 r31459 = 0.5;
        double r31460 = re;
        double r31461 = sin(r31460);
        double r31462 = r31459 * r31461;
        double r31463 = 0.0;
        double r31464 = im;
        double r31465 = r31463 - r31464;
        double r31466 = exp(r31465);
        double r31467 = exp(r31464);
        double r31468 = r31466 + r31467;
        double r31469 = r31462 * r31468;
        return r31469;
}
↓
double f(double re, double im) {
        double r31470 = 0.5;
        double r31471 = re;
        double r31472 = sin(r31471);
        double r31473 = r31470 * r31472;
        double r31474 = 0.0;
        double r31475 = im;
        double r31476 = r31474 - r31475;
        double r31477 = exp(r31476);
        double r31478 = exp(r31475);
        double r31479 = r31477 + r31478;
        double r31480 = r31473 * r31479;
        return r31480;
}

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 2020064 +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))))