Average Error: 14.5 → 0.3
Time: 5.0s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}
double f(double x) {
        double r710003 = 8.0;
        double r710004 = 3.0;
        double r710005 = r710003 / r710004;
        double r710006 = x;
        double r710007 = 0.5;
        double r710008 = r710006 * r710007;
        double r710009 = sin(r710008);
        double r710010 = r710005 * r710009;
        double r710011 = r710010 * r710009;
        double r710012 = sin(r710006);
        double r710013 = r710011 / r710012;
        return r710013;
}
↓
double f(double x) {
        double r710014 = 8.0;
        double r710015 = x;
        double r710016 = 0.5;
        double r710017 = r710015 * r710016;
        double r710018 = sin(r710017);
        double r710019 = r710014 * r710018;
        double r710020 = sin(r710015);
        double r710021 = r710016 * r710015;
        double r710022 = sin(r710021);
        double r710023 = r710020 / r710022;
        double r710024 = 3.0;
        double r710025 = r710023 * r710024;
        double r710026 = r710019 / r710025;
        return r710026;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
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 14.5

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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. Simplified0.5

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

  6. Applied associate-*l/0.3

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

  7. Applied associate-/l/0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 +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)))