Average Error: 0.0 → 0.0
Time: 50.8s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot (\left(\sin re\right) \cdot \left(e^{im}\right) + \left(\frac{\sin re}{e^{im}}\right))_*\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
0.5 \cdot (\left(\sin re\right) \cdot \left(e^{im}\right) + \left(\frac{\sin re}{e^{im}}\right))_*
double f(double re, double im) {
        double r1153164 = 0.5;
        double r1153165 = re;
        double r1153166 = sin(r1153165);
        double r1153167 = r1153164 * r1153166;
        double r1153168 = 0.0;
        double r1153169 = im;
        double r1153170 = r1153168 - r1153169;
        double r1153171 = exp(r1153170);
        double r1153172 = exp(r1153169);
        double r1153173 = r1153171 + r1153172;
        double r1153174 = r1153167 * r1153173;
        return r1153174;
}
↓
double f(double re, double im) {
        double r1153175 = 0.5;
        double r1153176 = re;
        double r1153177 = sin(r1153176);
        double r1153178 = im;
        double r1153179 = exp(r1153178);
        double r1153180 = r1153177 / r1153179;
        double r1153181 = fma(r1153177, r1153179, r1153180);
        double r1153182 = r1153175 * r1153181;
        return r1153182;
}

Error

Bits error versus re

Bits error versus im

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))