Average Error: 14.2 → 0.4
Time: 15.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right) \cdot 8}{\frac{3 \cdot \sin x}{\sin \left(x \cdot 0.5\right)}}\]
\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{\sin \left(x \cdot 0.5\right) \cdot 8}{\frac{3 \cdot \sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r591387 = 8.0;
        double r591388 = 3.0;
        double r591389 = r591387 / r591388;
        double r591390 = x;
        double r591391 = 0.5;
        double r591392 = r591390 * r591391;
        double r591393 = sin(r591392);
        double r591394 = r591389 * r591393;
        double r591395 = r591394 * r591393;
        double r591396 = sin(r591390);
        double r591397 = r591395 / r591396;
        return r591397;
}
↓
double f(double x) {
        double r591398 = x;
        double r591399 = 0.5;
        double r591400 = r591398 * r591399;
        double r591401 = sin(r591400);
        double r591402 = 8.0;
        double r591403 = r591401 * r591402;
        double r591404 = 3.0;
        double r591405 = sin(r591398);
        double r591406 = r591404 * r591405;
        double r591407 = r591406 / r591401;
        double r591408 = r591403 / r591407;
        return r591408;
}

Error

Bits error versus x

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Results

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Target

Original14.2
Target0.3
Herbie0.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.2

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

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

  8. Applied div-inv0.5

    \[\leadsto \frac{\color{blue}{\left(8 \cdot \sin \left(0.5 \cdot x\right)\right) \cdot \frac{1}{3}}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

  9. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{8 \cdot \sin \left(0.5 \cdot x\right)}{\frac{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}{\frac{1}{3}}}}\]

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019194 
(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)))