Average Error: 0.0 → 0.0
Time: 17.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5 \cdot \sin re}{e^{im}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5 \cdot \sin re}{e^{im}}
double f(double re, double im) {
        double r855146 = 0.5;
        double r855147 = re;
        double r855148 = sin(r855147);
        double r855149 = r855146 * r855148;
        double r855150 = 0.0;
        double r855151 = im;
        double r855152 = r855150 - r855151;
        double r855153 = exp(r855152);
        double r855154 = exp(r855151);
        double r855155 = r855153 + r855154;
        double r855156 = r855149 * r855155;
        return r855156;
}
↓
double f(double re, double im) {
        double r855157 = 0.5;
        double r855158 = re;
        double r855159 = sin(r855158);
        double r855160 = r855157 * r855159;
        double r855161 = im;
        double r855162 = exp(r855161);
        double r855163 = r855160 * r855162;
        double r855164 = r855160 / r855162;
        double r855165 = r855163 + r855164;
        return r855165;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))