Average Error: 0.0 → 0.0
Time: 3.3s
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 r20360 = 0.5;
        double r20361 = re;
        double r20362 = sin(r20361);
        double r20363 = r20360 * r20362;
        double r20364 = 0.0;
        double r20365 = im;
        double r20366 = r20364 - r20365;
        double r20367 = exp(r20366);
        double r20368 = exp(r20365);
        double r20369 = r20367 + r20368;
        double r20370 = r20363 * r20369;
        return r20370;
}
↓
double f(double re, double im) {
        double r20371 = 0.5;
        double r20372 = re;
        double r20373 = sin(r20372);
        double r20374 = r20371 * r20373;
        double r20375 = 0.0;
        double r20376 = im;
        double r20377 = r20375 - r20376;
        double r20378 = exp(r20377);
        double r20379 = r20374 * r20378;
        double r20380 = exp(r20376);
        double r20381 = r20374 * r20380;
        double r20382 = r20379 + r20381;
        return r20382;
}

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 2020024 +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))))