Average Error: 0.0 → 0.0
Time: 16.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(0.5 \cdot e^{im} + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(0.5 \cdot e^{im} + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r311950 = 0.5;
        double r311951 = re;
        double r311952 = sin(r311951);
        double r311953 = r311950 * r311952;
        double r311954 = 0.0;
        double r311955 = im;
        double r311956 = r311954 - r311955;
        double r311957 = exp(r311956);
        double r311958 = exp(r311955);
        double r311959 = r311957 + r311958;
        double r311960 = r311953 * r311959;
        return r311960;
}
↓
double f(double re, double im) {
        double r311961 = re;
        double r311962 = sin(r311961);
        double r311963 = 0.5;
        double r311964 = im;
        double r311965 = exp(r311964);
        double r311966 = r311963 * r311965;
        double r311967 = r311963 / r311965;
        double r311968 = r311966 + r311967;
        double r311969 = r311962 * r311968;
        return r311969;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))