Average Error: 14.5 → 0.3
Time: 4.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}\right) \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\left(8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}\right) \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}
double f(double x) {
        double r711708 = 8.0;
        double r711709 = 3.0;
        double r711710 = r711708 / r711709;
        double r711711 = x;
        double r711712 = 0.5;
        double r711713 = r711711 * r711712;
        double r711714 = sin(r711713);
        double r711715 = r711710 * r711714;
        double r711716 = r711715 * r711714;
        double r711717 = sin(r711711);
        double r711718 = r711716 / r711717;
        return r711718;
}
↓
double f(double x) {
        double r711719 = 8.0;
        double r711720 = 0.5;
        double r711721 = x;
        double r711722 = r711720 * r711721;
        double r711723 = sin(r711722);
        double r711724 = 3.0;
        double r711725 = r711723 / r711724;
        double r711726 = r711719 * r711725;
        double r711727 = sin(r711721);
        double r711728 = r711723 / r711727;
        double r711729 = r711726 * r711728;
        return r711729;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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Target

Original14.5
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 14.5

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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. Simplified0.5

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

  6. Applied div-inv0.5

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

  7. Applied associate-*l*0.5

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

  8. Simplified0.3

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

  10. Applied associate-/r/0.4

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

  12. Applied div-inv0.5

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

  13. Applied associate-*l*0.4

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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)))