Average Error: 14.8 → 0.3
Time: 6.9s
Precision: binary64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]
↓
\[\begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{-t_0}{\sin x} \cdot \frac{t_0}{-0.375} \end{array} \]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\begin{array}{l}
t_0 := \sin \left(x \cdot 0.5\right)\\
\frac{-t_0}{\sin x} \cdot \frac{t_0}{-0.375}
\end{array}

(FPCore (x)
 :precision binary64
 (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))
↓
(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (* (/ (- t_0) (sin x)) (/ t_0 -0.375))))
double code(double x) {
	return (((8.0 / 3.0) * sin(x * 0.5)) * sin(x * 0.5)) / sin(x);
}
↓
double code(double x) {
	double t_0 = sin(x * 0.5);
	return (-t_0 / sin(x)) * (t_0 / -0.375);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
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 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. Simplified14.8

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

  3. Applied associate-/l*_binary640.5

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

  4. Applied clear-num_binary640.4

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

  5. Applied frac-2neg_binary640.4

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

  6. Simplified0.3

    \[\leadsto \frac{-\sin \left(x \cdot 0.5\right)}{\color{blue}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot -0.375}} \]

  7. Applied neg-mul-1_binary640.3

    \[\leadsto \frac{\color{blue}{-1 \cdot \sin \left(x \cdot 0.5\right)}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot -0.375} \]

  8. Applied times-frac_binary640.3

    \[\leadsto \color{blue}{\frac{-1}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}} \cdot \frac{\sin \left(x \cdot 0.5\right)}{-0.375}} \]

  9. Simplified0.3

    \[\leadsto \color{blue}{\frac{-\sin \left(x \cdot 0.5\right)}{\sin x}} \cdot \frac{\sin \left(x \cdot 0.5\right)}{-0.375} \]

  10. Final simplification0.3

    \[\leadsto \frac{-\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \frac{\sin \left(x \cdot 0.5\right)}{-0.375} \]

Reproduce

herbie shell --seed 2021220 
(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)))