Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(0.5 \cdot e^{im} + \sqrt{0.5} \cdot \frac{\sqrt{0.5}}{e^{im}}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(0.5 \cdot e^{im} + \sqrt{0.5} \cdot \frac{\sqrt{0.5}}{e^{im}}\right)
double f(double re, double im) {
        double r284049 = 0.5;
        double r284050 = re;
        double r284051 = sin(r284050);
        double r284052 = r284049 * r284051;
        double r284053 = 0.0;
        double r284054 = im;
        double r284055 = r284053 - r284054;
        double r284056 = exp(r284055);
        double r284057 = exp(r284054);
        double r284058 = r284056 + r284057;
        double r284059 = r284052 * r284058;
        return r284059;
}
↓
double f(double re, double im) {
        double r284060 = re;
        double r284061 = sin(r284060);
        double r284062 = 0.5;
        double r284063 = im;
        double r284064 = exp(r284063);
        double r284065 = r284062 * r284064;
        double r284066 = sqrt(r284062);
        double r284067 = r284066 / r284064;
        double r284068 = r284066 * r284067;
        double r284069 = r284065 + r284068;
        double r284070 = r284061 * r284069;
        return r284070;
}

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. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto \left(e^{im} \cdot 0.5 + \frac{0.5}{\color{blue}{1 \cdot e^{im}}}\right) \cdot \sin re\]

  5. Applied add-sqr-sqrt0.1

    \[\leadsto \left(e^{im} \cdot 0.5 + \frac{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}}{1 \cdot e^{im}}\right) \cdot \sin re\]

  6. Applied times-frac0.0

    \[\leadsto \left(e^{im} \cdot 0.5 + \color{blue}{\frac{\sqrt{0.5}}{1} \cdot \frac{\sqrt{0.5}}{e^{im}}}\right) \cdot \sin re\]

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))