Average Error: 15.1 → 0.3
Time: 14.5s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r466234 = 8.0;
        double r466235 = 3.0;
        double r466236 = r466234 / r466235;
        double r466237 = x;
        double r466238 = 0.5;
        double r466239 = r466237 * r466238;
        double r466240 = sin(r466239);
        double r466241 = r466236 * r466240;
        double r466242 = r466241 * r466240;
        double r466243 = sin(r466237);
        double r466244 = r466242 / r466243;
        return r466244;
}
↓
double f(double x) {
        double r466245 = 8.0;
        double r466246 = 0.5;
        double r466247 = x;
        double r466248 = r466246 * r466247;
        double r466249 = sin(r466248);
        double r466250 = 3.0;
        double r466251 = r466249 / r466250;
        double r466252 = r466245 * r466251;
        double r466253 = sin(r466247);
        double r466254 = r466247 * r466246;
        double r466255 = sin(r466254);
        double r466256 = r466253 / r466255;
        double r466257 = r466252 / r466256;
        return r466257;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.3
Herbie0.3
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 15.1

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  2. Using strategy rm

  3. Applied associate-/l*0.5

    \[\leadsto \color{blue}{\frac{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}}\]
  4. Using strategy rm

  5. Applied div-inv0.5

    \[\leadsto \frac{\color{blue}{\left(8 \cdot \frac{1}{3}\right)} \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

  6. Applied associate-*l*0.5

    \[\leadsto \frac{\color{blue}{8 \cdot \left(\frac{1}{3} \cdot \sin \left(x \cdot 0.5\right)\right)}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

  7. Simplified0.3

    \[\leadsto \frac{8 \cdot \color{blue}{\frac{\sin \left(0.5 \cdot x\right)}{3}}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

  8. Final simplification0.3

    \[\leadsto \frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :herbie-target
  (/ (/ (* 8 (sin (* x 0.5))) 3) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8 3) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))