Average Error: 14.8 → 1.4
Time: 5.6s
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 code(double x) {
	return ((double) (((double) (((double) (((double) (8.0 / 3.0)) * ((double) sin(((double) (x * 0.5)))))) * ((double) sin(((double) (x * 0.5)))))) / ((double) sin(x))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (8.0 / 3.0)) * ((double) sin(((double) (x * 0.5)))))) / ((double) (((double) cbrt(((double) sin(x)))) * ((double) cbrt(((double) sin(x)))))))) * ((double) (((double) sin(((double) (0.5 * x)))) / ((double) cbrt(((double) sin(x))))))));
}

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 2020120 
(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)))