Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A

Average Error: 15.0 → 0.3

Time: 17.4s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r1349402 = 8.0;
        double r1349403 = 3.0;
        double r1349404 = r1349402 / r1349403;
        double r1349405 = x;
        double r1349406 = 0.5;
        double r1349407 = r1349405 * r1349406;
        double r1349408 = sin(r1349407);
        double r1349409 = r1349404 * r1349408;
        double r1349410 = r1349409 * r1349408;
        double r1349411 = sin(r1349405);
        double r1349412 = r1349410 / r1349411;
        return r1349412;
}

↓

double f(double x) {
        double r1349413 = 0.5;
        double r1349414 = x;
        double r1349415 = r1349413 * r1349414;
        double r1349416 = sin(r1349415);
        double r1349417 = 8.0;
        double r1349418 = r1349416 * r1349417;
        double r1349419 = sin(r1349414);
        double r1349420 = r1349416 / r1349419;
        double r1349421 = r1349418 * r1349420;
        double r1349422 = 3.0;
        double r1349423 = r1349421 / r1349422;
        return r1349423;
}

Error

Bits error versus x

Target

Original	15.0
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 15.0

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

3. Applied *-un-lft-identity 15.0

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

4. Applied times-frac 0.5

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

5. Simplified 0.5

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

7. Applied *-un-lft-identity 0.5

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

8. Applied *-un-lft-identity 0.5

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

9. Applied times-frac 0.5

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

10. Applied associate-*l* 0.5

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

11. Simplified 0.3

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

13. Applied frac-times 0.3

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

14. Applied associate-*l/ 0.3

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

15. Simplified 0.3

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

16. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019198 
(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)))