Average Error: 0.0 → 0.0
Time: 34.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r83246 = 0.5;
        double r83247 = re;
        double r83248 = sin(r83247);
        double r83249 = r83246 * r83248;
        double r83250 = 0.0;
        double r83251 = im;
        double r83252 = r83250 - r83251;
        double r83253 = exp(r83252);
        double r83254 = exp(r83251);
        double r83255 = r83253 + r83254;
        double r83256 = r83249 * r83255;
        return r83256;
}
↓
double f(double re, double im) {
        double r83257 = 0.0;
        double r83258 = exp(r83257);
        double r83259 = 0.5;
        double r83260 = re;
        double r83261 = sin(r83260);
        double r83262 = r83259 * r83261;
        double r83263 = r83258 * r83262;
        double r83264 = im;
        double r83265 = exp(r83264);
        double r83266 = r83263 / r83265;
        double r83267 = r83265 * r83262;
        double r83268 = r83266 + r83267;
        return r83268;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied exp-diff0.0

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

  8. Applied associate-*l/0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))