Average Error: 15.2 → 0.3
Time: 14.2s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
\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{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r405285 = 8.0;
        double r405286 = 3.0;
        double r405287 = r405285 / r405286;
        double r405288 = x;
        double r405289 = 0.5;
        double r405290 = r405288 * r405289;
        double r405291 = sin(r405290);
        double r405292 = r405287 * r405291;
        double r405293 = r405292 * r405291;
        double r405294 = sin(r405288);
        double r405295 = r405293 / r405294;
        return r405295;
}
↓
double f(double x) {
        double r405296 = 0.5;
        double r405297 = x;
        double r405298 = r405296 * r405297;
        double r405299 = sin(r405298);
        double r405300 = 8.0;
        double r405301 = r405299 * r405300;
        double r405302 = 3.0;
        double r405303 = r405301 / r405302;
        double r405304 = sin(r405297);
        double r405305 = r405297 * r405296;
        double r405306 = sin(r405305);
        double r405307 = r405304 / r405306;
        double r405308 = r405303 / r405307;
        return r405308;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.2
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 15.2

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

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 
(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)))