Average Error: 15.3 → 0.5
Time: 10.4s
Precision: binary64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(\sin \left(x \cdot 0.5\right) \cdot 2.6666666666666665\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\left(\sin \left(x \cdot 0.5\right) \cdot 2.6666666666666665\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
(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)) 2.6666666666666665) (/ (sin (* x 0.5)) (sin x))))
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) * 2.6666666666666665) * (sin(x * 0.5) / sin(x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.3
Target0.3
Herbie0.5
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 15.3

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

  2. Simplified15.3

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

  4. Applied *-un-lft-identity_binary64_1712815.3

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

  5. Applied times-frac_binary64_171340.5

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

  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. Using strategy rm

  8. Applied *-un-lft-identity_binary64_171280.5

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

  9. Applied times-frac_binary64_171340.5

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

  10. Applied associate-*r*_binary64_170680.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2021093 
(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)))