Average Error: 14.8 → 1.4
Time: 5.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sqrt[3]{\sin x}}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sqrt[3]{\sin x}}
double f(double x) {
        double r683884 = 8.0;
        double r683885 = 3.0;
        double r683886 = r683884 / r683885;
        double r683887 = x;
        double r683888 = 0.5;
        double r683889 = r683887 * r683888;
        double r683890 = sin(r683889);
        double r683891 = r683886 * r683890;
        double r683892 = r683891 * r683890;
        double r683893 = sin(r683887);
        double r683894 = r683892 / r683893;
        return r683894;
}
↓
double f(double x) {
        double r683895 = 8.0;
        double r683896 = 3.0;
        double r683897 = r683895 / r683896;
        double r683898 = x;
        double r683899 = 0.5;
        double r683900 = r683898 * r683899;
        double r683901 = sin(r683900);
        double r683902 = r683897 * r683901;
        double r683903 = sin(r683898);
        double r683904 = cbrt(r683903);
        double r683905 = r683904 * r683904;
        double r683906 = r683902 / r683905;
        double r683907 = r683899 * r683898;
        double r683908 = sin(r683907);
        double r683909 = r683908 / r683904;
        double r683910 = r683906 * r683909;
        return r683910;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.3
Herbie1.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

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 add-cube-cbrt15.4

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

  4. Applied times-frac1.4

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

  5. Simplified1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2020062 
(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)))