Average Error: 0.0 → 0.0
Time: 26.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r14062 = 0.5;
        double r14063 = re;
        double r14064 = sin(r14063);
        double r14065 = r14062 * r14064;
        double r14066 = 0.0;
        double r14067 = im;
        double r14068 = r14066 - r14067;
        double r14069 = exp(r14068);
        double r14070 = exp(r14067);
        double r14071 = r14069 + r14070;
        double r14072 = r14065 * r14071;
        return r14072;
}
↓
double f(double re, double im) {
        double r14073 = re;
        double r14074 = sin(r14073);
        double r14075 = im;
        double r14076 = exp(r14075);
        double r14077 = r14074 / r14076;
        double r14078 = 0.5;
        double r14079 = r14077 * r14078;
        double r14080 = r14078 * r14074;
        double r14081 = r14080 * r14076;
        double r14082 = r14079 + r14081;
        return r14082;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]

  4. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))