Average Error: 14.6 → 0.5
Time: 15.5s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(\frac{8}{3} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}\right) \cdot \sin \left(0.5 \cdot x\right)\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\left(\frac{8}{3} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}\right) \cdot \sin \left(0.5 \cdot x\right)
double f(double x) {
        double r413717 = 8.0;
        double r413718 = 3.0;
        double r413719 = r413717 / r413718;
        double r413720 = x;
        double r413721 = 0.5;
        double r413722 = r413720 * r413721;
        double r413723 = sin(r413722);
        double r413724 = r413719 * r413723;
        double r413725 = r413724 * r413723;
        double r413726 = sin(r413720);
        double r413727 = r413725 / r413726;
        return r413727;
}
↓
double f(double x) {
        double r413728 = 8.0;
        double r413729 = 3.0;
        double r413730 = r413728 / r413729;
        double r413731 = 0.5;
        double r413732 = x;
        double r413733 = r413731 * r413732;
        double r413734 = sin(r413733);
        double r413735 = sin(r413732);
        double r413736 = r413734 / r413735;
        double r413737 = r413730 * r413736;
        double r413738 = r413737 * r413734;
        return r413738;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target0.3
Herbie0.5
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.6

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

  3. Applied *-un-lft-identity14.6

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

  4. Applied times-frac0.5

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

  5. Simplified0.5

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

  6. Simplified0.5

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

  8. Applied add-sqr-sqrt0.5

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

  9. Applied associate-*l*0.4

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

  11. Applied associate-*l*0.4

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019291 
(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)))