Average Error: 14.8 → 1.4
Time: 5.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sqrt[3]{\sin x}}\]
\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 r541833 = 8.0;
        double r541834 = 3.0;
        double r541835 = r541833 / r541834;
        double r541836 = x;
        double r541837 = 0.5;
        double r541838 = r541836 * r541837;
        double r541839 = sin(r541838);
        double r541840 = r541835 * r541839;
        double r541841 = r541840 * r541839;
        double r541842 = sin(r541836);
        double r541843 = r541841 / r541842;
        return r541843;
}
↓
double f(double x) {
        double r541844 = 8.0;
        double r541845 = 3.0;
        double r541846 = r541844 / r541845;
        double r541847 = x;
        double r541848 = 0.5;
        double r541849 = r541847 * r541848;
        double r541850 = sin(r541849);
        double r541851 = r541846 * r541850;
        double r541852 = sin(r541847);
        double r541853 = cbrt(r541852);
        double r541854 = r541853 * r541853;
        double r541855 = r541851 / r541854;
        double r541856 = r541848 * r541847;
        double r541857 = sin(r541856);
        double r541858 = r541857 / r541853;
        double r541859 = r541855 * r541858;
        return r541859;
}

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 +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)))