Average Error: 14.8 → 0.3
Time: 4.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r637616 = 8.0;
        double r637617 = 3.0;
        double r637618 = r637616 / r637617;
        double r637619 = x;
        double r637620 = 0.5;
        double r637621 = r637619 * r637620;
        double r637622 = sin(r637621);
        double r637623 = r637618 * r637622;
        double r637624 = r637623 * r637622;
        double r637625 = sin(r637619);
        double r637626 = r637624 / r637625;
        return r637626;
}
↓
double f(double x) {
        double r637627 = 8.0;
        double r637628 = 0.5;
        double r637629 = x;
        double r637630 = r637628 * r637629;
        double r637631 = sin(r637630);
        double r637632 = 3.0;
        double r637633 = r637631 / r637632;
        double r637634 = r637627 * r637633;
        double r637635 = sin(r637629);
        double r637636 = r637635 / r637631;
        double r637637 = r637634 / r637636;
        return r637637;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.3
Herbie0.3
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.8

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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 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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020021 +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)))