Average Error: 0.0 → 0.0
Time: 20.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right)
double f(double re, double im) {
        double r699982 = 0.5;
        double r699983 = re;
        double r699984 = sin(r699983);
        double r699985 = r699982 * r699984;
        double r699986 = 0.0;
        double r699987 = im;
        double r699988 = r699986 - r699987;
        double r699989 = exp(r699988);
        double r699990 = exp(r699987);
        double r699991 = r699989 + r699990;
        double r699992 = r699985 * r699991;
        return r699992;
}
↓
double f(double re, double im) {
        double r699993 = re;
        double r699994 = sin(r699993);
        double r699995 = 0.5;
        double r699996 = im;
        double r699997 = exp(r699996);
        double r699998 = r699995 / r699997;
        double r699999 = r699997 * r699995;
        double r700000 = r699998 + r699999;
        double r700001 = r699994 * r700000;
        return r700001;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))