Average Error: 14.8 → 0.3
Time: 9.0s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
\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{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r693740 = 8.0;
        double r693741 = 3.0;
        double r693742 = r693740 / r693741;
        double r693743 = x;
        double r693744 = 0.5;
        double r693745 = r693743 * r693744;
        double r693746 = sin(r693745);
        double r693747 = r693742 * r693746;
        double r693748 = r693747 * r693746;
        double r693749 = sin(r693743);
        double r693750 = r693748 / r693749;
        return r693750;
}
↓
double f(double x) {
        double r693751 = 8.0;
        double r693752 = x;
        double r693753 = 0.5;
        double r693754 = r693752 * r693753;
        double r693755 = sin(r693754);
        double r693756 = r693751 * r693755;
        double r693757 = 3.0;
        double r693758 = r693756 / r693757;
        double r693759 = sin(r693752);
        double r693760 = r693759 / r693755;
        double r693761 = r693758 / r693760;
        return r693761;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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. Using strategy rm

  3. Applied associate-/l*0.5

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

  5. Applied associate-*l/0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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)))