Average Error: 0.0 → 0.0
Time: 6.5s
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 r33861 = 0.5;
        double r33862 = re;
        double r33863 = sin(r33862);
        double r33864 = r33861 * r33863;
        double r33865 = 0.0;
        double r33866 = im;
        double r33867 = r33865 - r33866;
        double r33868 = exp(r33867);
        double r33869 = exp(r33866);
        double r33870 = r33868 + r33869;
        double r33871 = r33864 * r33870;
        return r33871;
}
↓
double f(double re, double im) {
        double r33872 = 0.5;
        double r33873 = re;
        double r33874 = sin(r33873);
        double r33875 = r33872 * r33874;
        double r33876 = 0.0;
        double r33877 = im;
        double r33878 = r33876 - r33877;
        double r33879 = exp(r33878);
        double r33880 = exp(r33877);
        double r33881 = r33879 + r33880;
        double r33882 = r33875 * r33881;
        return r33882;
}

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 2020034 +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))))