Average Error: 0.0 → 0.0
Time: 5.0s
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 r26277 = 0.5;
        double r26278 = re;
        double r26279 = sin(r26278);
        double r26280 = r26277 * r26279;
        double r26281 = 0.0;
        double r26282 = im;
        double r26283 = r26281 - r26282;
        double r26284 = exp(r26283);
        double r26285 = exp(r26282);
        double r26286 = r26284 + r26285;
        double r26287 = r26280 * r26286;
        return r26287;
}
↓
double f(double re, double im) {
        double r26288 = 0.5;
        double r26289 = re;
        double r26290 = sin(r26289);
        double r26291 = r26288 * r26290;
        double r26292 = 0.0;
        double r26293 = im;
        double r26294 = r26292 - r26293;
        double r26295 = exp(r26294);
        double r26296 = r26291 * r26295;
        double r26297 = exp(r26293);
        double r26298 = r26291 * r26297;
        double r26299 = r26296 + r26298;
        return r26299;
}

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 2020033 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))