Average Error: 15.2 → 0.3
Time: 22.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
\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{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r16231613 = 8.0;
        double r16231614 = 3.0;
        double r16231615 = r16231613 / r16231614;
        double r16231616 = x;
        double r16231617 = 0.5;
        double r16231618 = r16231616 * r16231617;
        double r16231619 = sin(r16231618);
        double r16231620 = r16231615 * r16231619;
        double r16231621 = r16231620 * r16231619;
        double r16231622 = sin(r16231616);
        double r16231623 = r16231621 / r16231622;
        return r16231623;
}
↓
double f(double x) {
        double r16231624 = x;
        double r16231625 = 0.5;
        double r16231626 = r16231624 * r16231625;
        double r16231627 = sin(r16231626);
        double r16231628 = 3.0;
        double r16231629 = 8.0;
        double r16231630 = r16231628 / r16231629;
        double r16231631 = r16231627 / r16231630;
        double r16231632 = sin(r16231624);
        double r16231633 = r16231632 / r16231627;
        double r16231634 = r16231631 / r16231633;
        return r16231634;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
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 15.2

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

  5. Applied *-un-lft-identity0.5

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

  6. Applied *-un-lft-identity0.5

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

  7. Applied times-frac0.5

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

  8. Applied associate-/r*0.5

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(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)))