Average Error: 0.0 → 0.2
Time: 22.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{im} + e^{0.0 - im}\right)}^{3}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{im} + e^{0.0 - im}\right)}^{3}}
double f(double re, double im) {
        double r19373 = 0.5;
        double r19374 = re;
        double r19375 = sin(r19374);
        double r19376 = r19373 * r19375;
        double r19377 = 0.0;
        double r19378 = im;
        double r19379 = r19377 - r19378;
        double r19380 = exp(r19379);
        double r19381 = exp(r19378);
        double r19382 = r19380 + r19381;
        double r19383 = r19376 * r19382;
        return r19383;
}
↓
double f(double re, double im) {
        double r19384 = 0.5;
        double r19385 = re;
        double r19386 = sin(r19385);
        double r19387 = r19384 * r19386;
        double r19388 = im;
        double r19389 = exp(r19388);
        double r19390 = 0.0;
        double r19391 = r19390 - r19388;
        double r19392 = exp(r19391);
        double r19393 = r19389 + r19392;
        double r19394 = 3.0;
        double r19395 = pow(r19393, r19394);
        double r19396 = cbrt(r19395);
        double r19397 = r19387 * r19396;
        return r19397;
}

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 add-cbrt-cube0.2

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\sqrt[3]{\left(\left(e^{0.0 - im} + e^{im}\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\right) \cdot \left(e^{0.0 - im} + e^{im}\right)}}\]

  4. Simplified0.2

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{im} + e^{0.0 - im}\right)}^{3}}}\]

  5. Final simplification0.2

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{im} + e^{0.0 - im}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019347 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))