Average Error: 14.8 → 0.5
Time: 4.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(\sqrt{\frac{8}{3}} \cdot \left(\sqrt{\frac{8}{3}} \cdot \sin \left(x \cdot 0.5\right)\right)\right) \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}\]
\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(\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}
double f(double x) {
        double r683736 = 8.0;
        double r683737 = 3.0;
        double r683738 = r683736 / r683737;
        double r683739 = x;
        double r683740 = 0.5;
        double r683741 = r683739 * r683740;
        double r683742 = sin(r683741);
        double r683743 = r683738 * r683742;
        double r683744 = r683743 * r683742;
        double r683745 = sin(r683739);
        double r683746 = r683744 / r683745;
        return r683746;
}
↓
double f(double x) {
        double r683747 = 8.0;
        double r683748 = 3.0;
        double r683749 = r683747 / r683748;
        double r683750 = sqrt(r683749);
        double r683751 = x;
        double r683752 = 0.5;
        double r683753 = r683751 * r683752;
        double r683754 = sin(r683753);
        double r683755 = r683750 * r683754;
        double r683756 = r683750 * r683755;
        double r683757 = r683752 * r683751;
        double r683758 = sin(r683757);
        double r683759 = sin(r683751);
        double r683760 = r683758 / r683759;
        double r683761 = r683756 * r683760;
        return r683761;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
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 14.8

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

  3. Applied *-un-lft-identity14.8

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

  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*0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2020060 
(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)))