Average Error: 14.9 → 0.3
Time: 5.6s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{1}{\sqrt[3]{1}} \cdot \frac{\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(8 \cdot \sin \left(x \cdot 0.5\right)\right)}{3}\]
\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{1}{\sqrt[3]{1}} \cdot \frac{\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(8 \cdot \sin \left(x \cdot 0.5\right)\right)}{3}
double f(double x) {
        double r508186 = 8.0;
        double r508187 = 3.0;
        double r508188 = r508186 / r508187;
        double r508189 = x;
        double r508190 = 0.5;
        double r508191 = r508189 * r508190;
        double r508192 = sin(r508191);
        double r508193 = r508188 * r508192;
        double r508194 = r508193 * r508192;
        double r508195 = sin(r508189);
        double r508196 = r508194 / r508195;
        return r508196;
}
↓
double f(double x) {
        double r508197 = 1.0;
        double r508198 = cbrt(r508197);
        double r508199 = r508197 / r508198;
        double r508200 = 0.5;
        double r508201 = x;
        double r508202 = r508200 * r508201;
        double r508203 = sin(r508202);
        double r508204 = sin(r508201);
        double r508205 = r508203 / r508204;
        double r508206 = 8.0;
        double r508207 = r508201 * r508200;
        double r508208 = sin(r508207);
        double r508209 = r508206 * r508208;
        double r508210 = r508205 * r508209;
        double r508211 = 3.0;
        double r508212 = r508210 / r508211;
        double r508213 = r508199 * r508212;
        return r508213;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
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 14.9

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

  3. Applied *-un-lft-identity14.9

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

  4. Applied times-frac0.5

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

  5. Simplified0.5

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

  6. Simplified0.5

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

  8. Applied associate-*l/0.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Applied associate-/r*0.6

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

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

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

  14. Applied cbrt-prod0.6

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

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

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

  16. Applied times-frac0.6

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

  17. Applied associate-*l*0.6

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

  18. Simplified0.3

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

  19. Final simplification0.3

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

Reproduce

herbie shell --seed 2020035 
(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)))