Average Error: 15.2 → 0.3
Time: 15.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{1}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}} \cdot \left(\frac{\sin \left(0.5 \cdot x\right)}{3} \cdot 8\right)\]
\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{1}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}} \cdot \left(\frac{\sin \left(0.5 \cdot x\right)}{3} \cdot 8\right)
double f(double x) {
        double r540513 = 8.0;
        double r540514 = 3.0;
        double r540515 = r540513 / r540514;
        double r540516 = x;
        double r540517 = 0.5;
        double r540518 = r540516 * r540517;
        double r540519 = sin(r540518);
        double r540520 = r540515 * r540519;
        double r540521 = r540520 * r540519;
        double r540522 = sin(r540516);
        double r540523 = r540521 / r540522;
        return r540523;
}
↓
double f(double x) {
        double r540524 = 1.0;
        double r540525 = x;
        double r540526 = sin(r540525);
        double r540527 = 0.5;
        double r540528 = r540527 * r540525;
        double r540529 = sin(r540528);
        double r540530 = r540526 / r540529;
        double r540531 = r540524 / r540530;
        double r540532 = 3.0;
        double r540533 = r540529 / r540532;
        double r540534 = 8.0;
        double r540535 = r540533 * r540534;
        double r540536 = r540531 * r540535;
        return r540536;
}

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. Simplified15.1

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

  4. Applied div-inv15.1

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

  5. Applied times-frac0.3

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

  6. Simplified0.3

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

  8. Applied clear-num0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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)))