Average Error: 15.0 → 0.3
Time: 4.0s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}}
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)) / (sin(x) / (sin((x * 0.5)) / (3.0 / 8.0))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
Target0.3
Herbie0.3
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 15.0

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

  3. Applied *-commutative15.0

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

  4. Applied associate-*l*15.0

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

  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. Using strategy rm

  7. Applied clear-num0.5

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\color{blue}{\frac{1}{\frac{3}{8}}} \cdot \sin \left(x \cdot 0.5\right)}}\]

  8. Applied associate-*l/0.3

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\color{blue}{\frac{1 \cdot \sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}}}\]

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020078 +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)))