Average Error: 14.9 → 0.3
Time: 9.4s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{1}{\frac{\sin \left(0.5 \cdot x\right)}{\sin x}}}\]
\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 \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{1}{\frac{\sin \left(0.5 \cdot x\right)}{\sin x}}}
double f(double x) {
        double r528368 = 8.0;
        double r528369 = 3.0;
        double r528370 = r528368 / r528369;
        double r528371 = x;
        double r528372 = 0.5;
        double r528373 = r528371 * r528372;
        double r528374 = sin(r528373);
        double r528375 = r528370 * r528374;
        double r528376 = r528375 * r528374;
        double r528377 = sin(r528371);
        double r528378 = r528376 / r528377;
        return r528378;
}
↓
double f(double x) {
        double r528379 = 8.0;
        double r528380 = 0.5;
        double r528381 = x;
        double r528382 = r528380 * r528381;
        double r528383 = sin(r528382);
        double r528384 = 3.0;
        double r528385 = r528383 / r528384;
        double r528386 = r528379 * r528385;
        double r528387 = 1.0;
        double r528388 = sin(r528381);
        double r528389 = r528383 / r528388;
        double r528390 = r528387 / r528389;
        double r528391 = r528386 / r528390;
        return r528391;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
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 14.9

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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 div-inv0.5

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

  7. Applied associate-*l*0.5

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

  8. Simplified0.3

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

  10. Applied clear-num0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019351 +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)))