Average Error: 0.0 → 0.0
Time: 18.7s
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 r382941 = 0.5;
        double r382942 = re;
        double r382943 = sin(r382942);
        double r382944 = r382941 * r382943;
        double r382945 = 0.0;
        double r382946 = im;
        double r382947 = r382945 - r382946;
        double r382948 = exp(r382947);
        double r382949 = exp(r382946);
        double r382950 = r382948 + r382949;
        double r382951 = r382944 * r382950;
        return r382951;
}
↓
double f(double re, double im) {
        double r382952 = im;
        double r382953 = exp(r382952);
        double r382954 = re;
        double r382955 = sin(r382954);
        double r382956 = r382953 * r382955;
        double r382957 = r382955 / r382953;
        double r382958 = r382956 + r382957;
        double r382959 = 0.5;
        double r382960 = r382958 * r382959;
        return r382960;
}

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 2019133 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))