Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r29009 = 0.5;
        double r29010 = re;
        double r29011 = sin(r29010);
        double r29012 = r29009 * r29011;
        double r29013 = 0.0;
        double r29014 = im;
        double r29015 = r29013 - r29014;
        double r29016 = exp(r29015);
        double r29017 = exp(r29014);
        double r29018 = r29016 + r29017;
        double r29019 = r29012 * r29018;
        return r29019;
}
↓
double f(double re, double im) {
        double r29020 = 0.5;
        double r29021 = re;
        double r29022 = sin(r29021);
        double r29023 = r29020 * r29022;
        double r29024 = 0.0;
        double r29025 = exp(r29024);
        double r29026 = r29023 * r29025;
        double r29027 = im;
        double r29028 = exp(r29027);
        double r29029 = r29026 / r29028;
        double r29030 = r29023 * r29028;
        double r29031 = r29029 + r29030;
        return r29031;
}

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. Using strategy rm

  5. Applied exp-diff0.0

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))