Average Error: 0.0 → 0.0
Time: 18.3s
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 r194950 = 0.5;
        double r194951 = re;
        double r194952 = sin(r194951);
        double r194953 = r194950 * r194952;
        double r194954 = 0.0;
        double r194955 = im;
        double r194956 = r194954 - r194955;
        double r194957 = exp(r194956);
        double r194958 = exp(r194955);
        double r194959 = r194957 + r194958;
        double r194960 = r194953 * r194959;
        return r194960;
}
↓
double f(double re, double im) {
        double r194961 = im;
        double r194962 = exp(r194961);
        double r194963 = re;
        double r194964 = sin(r194963);
        double r194965 = r194962 * r194964;
        double r194966 = r194964 / r194962;
        double r194967 = r194965 + r194966;
        double r194968 = 0.5;
        double r194969 = r194967 * r194968;
        return r194969;
}

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 2019146 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))