Average Error: 0.0 → 0.0
Time: 4.8s
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 r26220 = 0.5;
        double r26221 = re;
        double r26222 = sin(r26221);
        double r26223 = r26220 * r26222;
        double r26224 = 0.0;
        double r26225 = im;
        double r26226 = r26224 - r26225;
        double r26227 = exp(r26226);
        double r26228 = exp(r26225);
        double r26229 = r26227 + r26228;
        double r26230 = r26223 * r26229;
        return r26230;
}
↓
double f(double re, double im) {
        double r26231 = 0.5;
        double r26232 = re;
        double r26233 = sin(r26232);
        double r26234 = r26231 * r26233;
        double r26235 = 0.0;
        double r26236 = exp(r26235);
        double r26237 = r26234 * r26236;
        double r26238 = im;
        double r26239 = exp(r26238);
        double r26240 = r26237 / r26239;
        double r26241 = r26234 * r26239;
        double r26242 = r26240 + r26241;
        return r26242;
}

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 2019344 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))