Average Error: 14.8 → 0.3
Time: 18.2s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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(0.5 \cdot x\right)}}
double f(double x) {
        double r541362 = 8.0;
        double r541363 = 3.0;
        double r541364 = r541362 / r541363;
        double r541365 = x;
        double r541366 = 0.5;
        double r541367 = r541365 * r541366;
        double r541368 = sin(r541367);
        double r541369 = r541364 * r541368;
        double r541370 = r541369 * r541368;
        double r541371 = sin(r541365);
        double r541372 = r541370 / r541371;
        return r541372;
}
↓
double f(double x) {
        double r541373 = 0.5;
        double r541374 = x;
        double r541375 = r541373 * r541374;
        double r541376 = sin(r541375);
        double r541377 = 8.0;
        double r541378 = r541376 * r541377;
        double r541379 = 3.0;
        double r541380 = r541378 / r541379;
        double r541381 = sin(r541374);
        double r541382 = r541381 / r541376;
        double r541383 = r541380 / r541382;
        return r541383;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.8
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 14.8

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

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +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)))