Average Error: 14.3 → 0.5
Time: 6.1s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(\frac{8}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sqrt[3]{3}}\right) \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}\]
\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(\frac{8}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sqrt[3]{3}}\right) \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sin x}
double f(double x) {
        double r723854 = 8.0;
        double r723855 = 3.0;
        double r723856 = r723854 / r723855;
        double r723857 = x;
        double r723858 = 0.5;
        double r723859 = r723857 * r723858;
        double r723860 = sin(r723859);
        double r723861 = r723856 * r723860;
        double r723862 = r723861 * r723860;
        double r723863 = sin(r723857);
        double r723864 = r723862 / r723863;
        return r723864;
}
↓
double f(double x) {
        double r723865 = 8.0;
        double r723866 = 3.0;
        double r723867 = cbrt(r723866);
        double r723868 = r723867 * r723867;
        double r723869 = r723865 / r723868;
        double r723870 = x;
        double r723871 = 0.5;
        double r723872 = r723870 * r723871;
        double r723873 = sin(r723872);
        double r723874 = r723873 / r723867;
        double r723875 = r723869 * r723874;
        double r723876 = r723871 * r723870;
        double r723877 = sin(r723876);
        double r723878 = sin(r723870);
        double r723879 = r723877 / r723878;
        double r723880 = r723875 * r723879;
        return r723880;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.3
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 14.3

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

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

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

  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 associate-*l/0.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Applied times-frac0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019353 +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)))