Average Error: 0.0 → 0.0
Time: 22.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)
double f(double re, double im) {
        double r597927 = 0.5;
        double r597928 = re;
        double r597929 = sin(r597928);
        double r597930 = r597927 * r597929;
        double r597931 = 0.0;
        double r597932 = im;
        double r597933 = r597931 - r597932;
        double r597934 = exp(r597933);
        double r597935 = exp(r597932);
        double r597936 = r597934 + r597935;
        double r597937 = r597930 * r597936;
        return r597937;
}
↓
double f(double re, double im) {
        double r597938 = re;
        double r597939 = sin(r597938);
        double r597940 = 0.5;
        double r597941 = im;
        double r597942 = exp(r597941);
        double r597943 = r597940 / r597942;
        double r597944 = r597942 * r597940;
        double r597945 = r597943 + r597944;
        double r597946 = r597939 * r597945;
        return r597946;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))