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 r708090 = 8.0;
        double r708091 = 3.0;
        double r708092 = r708090 / r708091;
        double r708093 = x;
        double r708094 = 0.5;
        double r708095 = r708093 * r708094;
        double r708096 = sin(r708095);
        double r708097 = r708092 * r708096;
        double r708098 = r708097 * r708096;
        double r708099 = sin(r708093);
        double r708100 = r708098 / r708099;
        return r708100;
}
↓
double f(double x) {
        double r708101 = 8.0;
        double r708102 = 3.0;
        double r708103 = r708101 / r708102;
        double r708104 = x;
        double r708105 = 0.5;
        double r708106 = r708104 * r708105;
        double r708107 = sin(r708106);
        double r708108 = r708103 * r708107;
        double r708109 = sin(r708104);
        double r708110 = cbrt(r708109);
        double r708111 = r708110 * r708110;
        double r708112 = r708108 / r708111;
        double r708113 = r708105 * r708104;
        double r708114 = sin(r708113);
        double r708115 = r708114 / r708110;
        double r708116 = r708112 * r708115;
        return r708116;
}

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)))