Average Error: 14.8 → 0.4
Time: 4.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sqrt{\frac{8}{3}} \cdot \left(\sqrt{\frac{8}{3}} \cdot \sin \left(x \cdot 0.5\right)\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{\sqrt{\frac{8}{3}} \cdot \left(\sqrt{\frac{8}{3}} \cdot \sin \left(x \cdot 0.5\right)\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r821526 = 8.0;
        double r821527 = 3.0;
        double r821528 = r821526 / r821527;
        double r821529 = x;
        double r821530 = 0.5;
        double r821531 = r821529 * r821530;
        double r821532 = sin(r821531);
        double r821533 = r821528 * r821532;
        double r821534 = r821533 * r821532;
        double r821535 = sin(r821529);
        double r821536 = r821534 / r821535;
        return r821536;
}
↓
double f(double x) {
        double r821537 = 8.0;
        double r821538 = 3.0;
        double r821539 = r821537 / r821538;
        double r821540 = sqrt(r821539);
        double r821541 = x;
        double r821542 = 0.5;
        double r821543 = r821541 * r821542;
        double r821544 = sin(r821543);
        double r821545 = r821540 * r821544;
        double r821546 = r821540 * r821545;
        double r821547 = sin(r821541);
        double r821548 = r821542 * r821541;
        double r821549 = sin(r821548);
        double r821550 = r821547 / r821549;
        double r821551 = r821546 / r821550;
        return r821551;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
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 14.8

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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 add-sqr-sqrt0.5

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

  7. Applied associate-*l*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020057 
(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)))