Average Error: 14.6 → 0.4
Time: 19.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}\right)\right)\]
\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(0.5 \cdot x\right)}{\sin x} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}\right)\right)
double f(double x) {
        double r24800472 = 8.0;
        double r24800473 = 3.0;
        double r24800474 = r24800472 / r24800473;
        double r24800475 = x;
        double r24800476 = 0.5;
        double r24800477 = r24800475 * r24800476;
        double r24800478 = sin(r24800477);
        double r24800479 = r24800474 * r24800478;
        double r24800480 = r24800479 * r24800478;
        double r24800481 = sin(r24800475);
        double r24800482 = r24800480 / r24800481;
        return r24800482;
}
↓
double f(double x) {
        double r24800483 = 0.5;
        double r24800484 = x;
        double r24800485 = r24800483 * r24800484;
        double r24800486 = sin(r24800485);
        double r24800487 = sin(r24800484);
        double r24800488 = r24800486 / r24800487;
        double r24800489 = 8.0;
        double r24800490 = r24800486 * r24800489;
        double r24800491 = 3.0;
        double r24800492 = r24800490 / r24800491;
        double r24800493 = expm1(r24800492);
        double r24800494 = log1p(r24800493);
        double r24800495 = r24800488 * r24800494;
        return r24800495;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
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 14.6

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

  3. Applied *-un-lft-identity14.6

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

  4. Applied times-frac0.5

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

  5. Simplified0.3

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

  7. Applied log1p-expm1-u0.4

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}\right)\right)} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  8. Final simplification0.4

    \[\leadsto \frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}\right)\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))