Average Error: 14.5 → 0.3
Time: 4.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}\]
\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{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}
double f(double x) {
        double r572422 = 8.0;
        double r572423 = 3.0;
        double r572424 = r572422 / r572423;
        double r572425 = x;
        double r572426 = 0.5;
        double r572427 = r572425 * r572426;
        double r572428 = sin(r572427);
        double r572429 = r572424 * r572428;
        double r572430 = r572429 * r572428;
        double r572431 = sin(r572425);
        double r572432 = r572430 / r572431;
        return r572432;
}
↓
double f(double x) {
        double r572433 = 8.0;
        double r572434 = x;
        double r572435 = 0.5;
        double r572436 = r572434 * r572435;
        double r572437 = sin(r572436);
        double r572438 = r572433 * r572437;
        double r572439 = sin(r572434);
        double r572440 = r572435 * r572434;
        double r572441 = sin(r572440);
        double r572442 = r572439 / r572441;
        double r572443 = 3.0;
        double r572444 = r572442 * r572443;
        double r572445 = r572438 / r572444;
        return r572445;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
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 14.5

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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. Applied associate-/l/0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(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)))