Average Error: 0.0 → 0.0
Time: 19.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\frac{\sin re}{e^{im}} + \sin re \cdot e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\frac{\sin re}{e^{im}} + \sin re \cdot e^{im}\right)
double f(double re, double im) {
        double r1588964 = 0.5;
        double r1588965 = re;
        double r1588966 = sin(r1588965);
        double r1588967 = r1588964 * r1588966;
        double r1588968 = 0.0;
        double r1588969 = im;
        double r1588970 = r1588968 - r1588969;
        double r1588971 = exp(r1588970);
        double r1588972 = exp(r1588969);
        double r1588973 = r1588971 + r1588972;
        double r1588974 = r1588967 * r1588973;
        return r1588974;
}
↓
double f(double re, double im) {
        double r1588975 = 0.5;
        double r1588976 = re;
        double r1588977 = sin(r1588976);
        double r1588978 = im;
        double r1588979 = exp(r1588978);
        double r1588980 = r1588977 / r1588979;
        double r1588981 = r1588977 * r1588979;
        double r1588982 = r1588980 + r1588981;
        double r1588983 = r1588975 * r1588982;
        return r1588983;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))