Average Error: 14.7 → 0.5
Time: 17.6s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}}\]
\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{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}}
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) sin(((double) (x * 0.5)))) / ((double) (((double) sin(x)) / ((double) (((double) (8.0 / 3.0)) * ((double) sin(((double) (x * 0.5))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
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 14.7

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  2. Using strategy rm

  3. Applied *-commutative14.7

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

  4. Applied associate-*l*14.7

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

  5. Applied associate-/l*0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2020114 +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)))