Average Error: 14.8 → 0.4
Time: 15.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}\]
\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{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}
double f(double x) {
        double r416652 = 8.0;
        double r416653 = 3.0;
        double r416654 = r416652 / r416653;
        double r416655 = x;
        double r416656 = 0.5;
        double r416657 = r416655 * r416656;
        double r416658 = sin(r416657);
        double r416659 = r416654 * r416658;
        double r416660 = r416659 * r416658;
        double r416661 = sin(r416655);
        double r416662 = r416660 / r416661;
        return r416662;
}
↓
double f(double x) {
        double r416663 = 8.0;
        double r416664 = 0.5;
        double r416665 = x;
        double r416666 = r416664 * r416665;
        double r416667 = sin(r416666);
        double r416668 = r416663 * r416667;
        double r416669 = 3.0;
        double r416670 = r416668 / r416669;
        double r416671 = 1.0;
        double r416672 = sin(r416665);
        double r416673 = r416665 * r416664;
        double r416674 = sin(r416673);
        double r416675 = r416672 / r416674;
        double r416676 = exp(r416675);
        double r416677 = log(r416676);
        double r416678 = r416671 / r416677;
        double r416679 = r416670 * r416678;
        return r416679;
}

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. Using strategy rm

  5. Applied associate-*l/0.3

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

  6. Simplified0.3

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

  8. Applied div-inv0.3

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

  10. Applied add-log-exp0.4

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

  11. Final simplification0.4

    \[\leadsto \frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}\]

Reproduce

herbie shell --seed 2019323 
(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)))