Average Error: 14.8 → 0.3
Time: 13.3s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right)}{\frac{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}{\frac{8}{3}}}\]
\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{\sin \left(0.5 \cdot x\right)}{\frac{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}{\frac{8}{3}}}
double f(double x) {
        double r467270 = 8.0;
        double r467271 = 3.0;
        double r467272 = r467270 / r467271;
        double r467273 = x;
        double r467274 = 0.5;
        double r467275 = r467273 * r467274;
        double r467276 = sin(r467275);
        double r467277 = r467272 * r467276;
        double r467278 = r467277 * r467276;
        double r467279 = sin(r467273);
        double r467280 = r467278 / r467279;
        return r467280;
}
↓
double f(double x) {
        double r467281 = 0.5;
        double r467282 = x;
        double r467283 = r467281 * r467282;
        double r467284 = sin(r467283);
        double r467285 = sin(r467282);
        double r467286 = r467285 / r467284;
        double r467287 = 8.0;
        double r467288 = 3.0;
        double r467289 = r467287 / r467288;
        double r467290 = r467286 / r467289;
        double r467291 = r467284 / r467290;
        return r467291;
}

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 associate-*l/0.3

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

  7. Simplified0.3

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

  9. Applied *-un-lft-identity0.3

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

  10. Applied times-frac0.5

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

  11. Applied associate-/l*0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019347 +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)))