Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r71364 = 0.5;
        double r71365 = re;
        double r71366 = sin(r71365);
        double r71367 = r71364 * r71366;
        double r71368 = 0.0;
        double r71369 = im;
        double r71370 = r71368 - r71369;
        double r71371 = exp(r71370);
        double r71372 = exp(r71369);
        double r71373 = r71371 + r71372;
        double r71374 = r71367 * r71373;
        return r71374;
}
↓
double f(double re, double im) {
        double r71375 = 0.5;
        double r71376 = re;
        double r71377 = sin(r71376);
        double r71378 = r71375 * r71377;
        double r71379 = 0.0;
        double r71380 = im;
        double r71381 = r71379 - r71380;
        double r71382 = exp(r71381);
        double r71383 = r71378 * r71382;
        double r71384 = exp(r71380);
        double r71385 = r71378 * r71384;
        double r71386 = r71383 + r71385;
        return r71386;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]

  4. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2020083 +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))))