Average Error: 15.3 → 0.3
Time: 18.2s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\frac{\frac{\sin x}{8}}{\sin \left(x \cdot 0.5\right)} \cdot 3}\]
\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{\sin \left(x \cdot 0.5\right)}{\frac{\frac{\sin x}{8}}{\sin \left(x \cdot 0.5\right)} \cdot 3}
double f(double x) {
        double r519214 = 8.0;
        double r519215 = 3.0;
        double r519216 = r519214 / r519215;
        double r519217 = x;
        double r519218 = 0.5;
        double r519219 = r519217 * r519218;
        double r519220 = sin(r519219);
        double r519221 = r519216 * r519220;
        double r519222 = r519221 * r519220;
        double r519223 = sin(r519217);
        double r519224 = r519222 / r519223;
        return r519224;
}
↓
double f(double x) {
        double r519225 = x;
        double r519226 = 0.5;
        double r519227 = r519225 * r519226;
        double r519228 = sin(r519227);
        double r519229 = sin(r519225);
        double r519230 = 8.0;
        double r519231 = r519229 / r519230;
        double r519232 = r519231 / r519228;
        double r519233 = 3.0;
        double r519234 = r519232 * r519233;
        double r519235 = r519228 / r519234;
        return r519235;
}

Error

Bits error versus x

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Results

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Target

Original15.3
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 15.3

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

  2. Simplified15.3

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

  4. Applied associate-/l*0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"

  :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)))