Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \frac{0.5}{e^{im}} + \left(e^{im} \cdot 0.5\right) \cdot \sin re\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \frac{0.5}{e^{im}} + \left(e^{im} \cdot 0.5\right) \cdot \sin re
double f(double re, double im) {
        double r816170 = 0.5;
        double r816171 = re;
        double r816172 = sin(r816171);
        double r816173 = r816170 * r816172;
        double r816174 = 0.0;
        double r816175 = im;
        double r816176 = r816174 - r816175;
        double r816177 = exp(r816176);
        double r816178 = exp(r816175);
        double r816179 = r816177 + r816178;
        double r816180 = r816173 * r816179;
        return r816180;
}
↓
double f(double re, double im) {
        double r816181 = re;
        double r816182 = sin(r816181);
        double r816183 = 0.5;
        double r816184 = im;
        double r816185 = exp(r816184);
        double r816186 = r816183 / r816185;
        double r816187 = r816182 * r816186;
        double r816188 = r816185 * r816183;
        double r816189 = r816188 * r816182;
        double r816190 = r816187 + r816189;
        return r816190;
}

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

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))