Average Error: 14.8 → 0.4
Time: 14.9s
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 r466283 = 8.0;
        double r466284 = 3.0;
        double r466285 = r466283 / r466284;
        double r466286 = x;
        double r466287 = 0.5;
        double r466288 = r466286 * r466287;
        double r466289 = sin(r466288);
        double r466290 = r466285 * r466289;
        double r466291 = r466290 * r466289;
        double r466292 = sin(r466286);
        double r466293 = r466291 / r466292;
        return r466293;
}
↓
double f(double x) {
        double r466294 = 8.0;
        double r466295 = 0.5;
        double r466296 = x;
        double r466297 = r466295 * r466296;
        double r466298 = sin(r466297);
        double r466299 = r466294 * r466298;
        double r466300 = 3.0;
        double r466301 = r466299 / r466300;
        double r466302 = 1.0;
        double r466303 = sin(r466296);
        double r466304 = r466296 * r466295;
        double r466305 = sin(r466304);
        double r466306 = r466303 / r466305;
        double r466307 = exp(r466306);
        double r466308 = log(r466307);
        double r466309 = r466302 / r466308;
        double r466310 = r466301 * r466309;
        return r466310;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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)))