Average Error: 0.0 → 0.0
Time: 6.8s
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 r81386 = 0.5;
        double r81387 = re;
        double r81388 = sin(r81387);
        double r81389 = r81386 * r81388;
        double r81390 = 0.0;
        double r81391 = im;
        double r81392 = r81390 - r81391;
        double r81393 = exp(r81392);
        double r81394 = exp(r81391);
        double r81395 = r81393 + r81394;
        double r81396 = r81389 * r81395;
        return r81396;
}
↓
double f(double re, double im) {
        double r81397 = 0.5;
        double r81398 = re;
        double r81399 = sin(r81398);
        double r81400 = r81397 * r81399;
        double r81401 = 0.0;
        double r81402 = im;
        double r81403 = r81401 - r81402;
        double r81404 = exp(r81403);
        double r81405 = exp(r81402);
        double r81406 = r81404 + r81405;
        double r81407 = r81400 * r81406;
        return r81407;
}

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 2020060 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))