Average Error: 14.9 → 0.6
Time: 5.6s
Precision: binary64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(\sin \left(x \cdot 0.5\right) \cdot \sqrt[3]{18.962962962962962}\right) \cdot \sqrt[3]{{\left(\frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right)}^{3}}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\left(\sin \left(x \cdot 0.5\right) \cdot \sqrt[3]{18.962962962962962}\right) \cdot \sqrt[3]{{\left(\frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right)}^{3}}
(FPCore (x)
 :precision binary64
 (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))
↓
(FPCore (x)
 :precision binary64
 (*
  (* (sin (* x 0.5)) (cbrt 18.962962962962962))
  (cbrt (pow (/ (sin (* x 0.5)) (sin x)) 3.0))))
double code(double x) {
	return (((8.0 / 3.0) * sin(x * 0.5)) * sin(x * 0.5)) / sin(x);
}
↓
double code(double x) {
	return (sin(x * 0.5) * cbrt(18.962962962962962)) * cbrt(pow((sin(x * 0.5) / sin(x)), 3.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.3
Herbie0.6
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.9

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

  2. Simplified14.9

    \[\leadsto \color{blue}{\frac{\sin \left(x \cdot 0.5\right) \cdot \left(2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)\right)}{\sin x}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity_binary6414.9

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right) \cdot \left(2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)\right)}{\color{blue}{1 \cdot \sin x}}\]

  5. Applied times-frac_binary640.5

    \[\leadsto \color{blue}{\frac{\sin \left(x \cdot 0.5\right)}{1} \cdot \frac{2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)}{\sin x}}\]

  6. Simplified0.5

    \[\leadsto \color{blue}{\sin \left(x \cdot 0.5\right)} \cdot \frac{2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]

  7. Simplified0.5

    \[\leadsto \sin \left(x \cdot 0.5\right) \cdot \color{blue}{\frac{\sin \left(x \cdot 0.5\right) \cdot 2.6666666666666665}{\sin x}}\]
  8. Using strategy rm

  9. Applied add-cbrt-cube_binary640.8

    \[\leadsto \sin \left(x \cdot 0.5\right) \cdot \color{blue}{\sqrt[3]{\left(\frac{\sin \left(x \cdot 0.5\right) \cdot 2.6666666666666665}{\sin x} \cdot \frac{\sin \left(x \cdot 0.5\right) \cdot 2.6666666666666665}{\sin x}\right) \cdot \frac{\sin \left(x \cdot 0.5\right) \cdot 2.6666666666666665}{\sin x}}}\]

  10. Simplified0.7

    \[\leadsto \sin \left(x \cdot 0.5\right) \cdot \sqrt[3]{\color{blue}{18.962962962962962 \cdot {\left(\frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right)}^{3}}}\]
  11. Using strategy rm

  12. Applied cbrt-prod_binary640.6

    \[\leadsto \sin \left(x \cdot 0.5\right) \cdot \color{blue}{\left(\sqrt[3]{18.962962962962962} \cdot \sqrt[3]{{\left(\frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right)}^{3}}\right)}\]

  13. Applied associate-*r*_binary640.6

    \[\leadsto \color{blue}{\left(\sin \left(x \cdot 0.5\right) \cdot \sqrt[3]{18.962962962962962}\right) \cdot \sqrt[3]{{\left(\frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right)}^{3}}}\]

  14. Final simplification0.6

    \[\leadsto \left(\sin \left(x \cdot 0.5\right) \cdot \sqrt[3]{18.962962962962962}\right) \cdot \sqrt[3]{{\left(\frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020253 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :herbie-target
  (/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))