Average Error: 0.0 → 0.0
Time: 26.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r686054 = 0.5;
        double r686055 = re;
        double r686056 = sin(r686055);
        double r686057 = r686054 * r686056;
        double r686058 = 0.0;
        double r686059 = im;
        double r686060 = r686058 - r686059;
        double r686061 = exp(r686060);
        double r686062 = exp(r686059);
        double r686063 = r686061 + r686062;
        double r686064 = r686057 * r686063;
        return r686064;
}
↓
double f(double re, double im) {
        double r686065 = im;
        double r686066 = exp(r686065);
        double r686067 = re;
        double r686068 = sin(r686067);
        double r686069 = r686066 * r686068;
        double r686070 = r686068 / r686066;
        double r686071 = r686069 + r686070;
        double r686072 = 0.5;
        double r686073 = r686071 * r686072;
        return r686073;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))