Average Error: 14.5 → 0.4
Time: 23.2s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}{\sqrt[3]{\left(\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot \frac{\sin x}{\sin \left(x \cdot 0.5\right)}\right) \cdot \left(\frac{1}{\sin \left(x \cdot 0.5\right)} \cdot \sin x\right)}}\]
\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{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}}{\sqrt[3]{\left(\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot \frac{\sin x}{\sin \left(x \cdot 0.5\right)}\right) \cdot \left(\frac{1}{\sin \left(x \cdot 0.5\right)} \cdot \sin x\right)}}
double f(double x) {
        double r32278631 = 8.0;
        double r32278632 = 3.0;
        double r32278633 = r32278631 / r32278632;
        double r32278634 = x;
        double r32278635 = 0.5;
        double r32278636 = r32278634 * r32278635;
        double r32278637 = sin(r32278636);
        double r32278638 = r32278633 * r32278637;
        double r32278639 = r32278638 * r32278637;
        double r32278640 = sin(r32278634);
        double r32278641 = r32278639 / r32278640;
        return r32278641;
}
↓
double f(double x) {
        double r32278642 = x;
        double r32278643 = 0.5;
        double r32278644 = r32278642 * r32278643;
        double r32278645 = sin(r32278644);
        double r32278646 = 3.0;
        double r32278647 = 8.0;
        double r32278648 = r32278646 / r32278647;
        double r32278649 = r32278645 / r32278648;
        double r32278650 = sin(r32278642);
        double r32278651 = r32278650 / r32278645;
        double r32278652 = r32278651 * r32278651;
        double r32278653 = 1.0;
        double r32278654 = r32278653 / r32278645;
        double r32278655 = r32278654 * r32278650;
        double r32278656 = r32278652 * r32278655;
        double r32278657 = cbrt(r32278656);
        double r32278658 = r32278649 / r32278657;
        return r32278658;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
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 14.5

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

  11. Applied add-cbrt-cube0.4

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

  13. Applied div-inv0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 
(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)))