Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)
double f(double re, double im) {
        double r79967 = 0.5;
        double r79968 = re;
        double r79969 = sin(r79968);
        double r79970 = r79967 * r79969;
        double r79971 = 0.0;
        double r79972 = im;
        double r79973 = r79971 - r79972;
        double r79974 = exp(r79973);
        double r79975 = exp(r79972);
        double r79976 = r79974 + r79975;
        double r79977 = r79970 * r79976;
        return r79977;
}
↓
double f(double re, double im) {
        double r79978 = 0.5;
        double r79979 = -1.0;
        double r79980 = im;
        double r79981 = r79979 * r79980;
        double r79982 = exp(r79981);
        double r79983 = exp(r79980);
        double r79984 = r79982 + r79983;
        double r79985 = re;
        double r79986 = sin(r79985);
        double r79987 = r79984 * r79986;
        double r79988 = r79978 * r79987;
        return r79988;
}

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. Taylor expanded around inf 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(\left(e^{-1 \cdot im} + e^{im}\right) \cdot \sin re\right)\]

Reproduce

herbie shell --seed 2019318 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))