Average Error: 0.0 → 0.0
Time: 15.6s
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 r248155 = 0.5;
        double r248156 = re;
        double r248157 = sin(r248156);
        double r248158 = r248155 * r248157;
        double r248159 = 0.0;
        double r248160 = im;
        double r248161 = r248159 - r248160;
        double r248162 = exp(r248161);
        double r248163 = exp(r248160);
        double r248164 = r248162 + r248163;
        double r248165 = r248158 * r248164;
        return r248165;
}
↓
double f(double re, double im) {
        double r248166 = im;
        double r248167 = exp(r248166);
        double r248168 = re;
        double r248169 = sin(r248168);
        double r248170 = r248167 * r248169;
        double r248171 = r248169 / r248167;
        double r248172 = r248170 + r248171;
        double r248173 = 0.5;
        double r248174 = r248172 * r248173;
        return r248174;
}

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

    \[\leadsto \color{blue}{0.5 \cdot (\left(\sin re\right) \cdot \left(e^{im}\right) + \left(\frac{\sin re}{e^{im}}\right))_*}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))