Average Error: 15.2 → 0.4
Time: 8.5s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \log \left(e^{\frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\right)\]
\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{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \log \left(e^{\frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\right)
double f(double x) {
        double r124281 = 8.0;
        double r124282 = 3.0;
        double r124283 = r124281 / r124282;
        double r124284 = x;
        double r124285 = 0.5;
        double r124286 = r124284 * r124285;
        double r124287 = sin(r124286);
        double r124288 = r124283 * r124287;
        double r124289 = r124288 * r124287;
        double r124290 = sin(r124284);
        double r124291 = r124289 / r124290;
        return r124291;
}
↓
double f(double x) {
        double r124292 = 0.5;
        double r124293 = x;
        double r124294 = r124292 * r124293;
        double r124295 = sin(r124294);
        double r124296 = 8.0;
        double r124297 = r124295 * r124296;
        double r124298 = 3.0;
        double r124299 = r124297 / r124298;
        double r124300 = r124293 * r124292;
        double r124301 = sin(r124300);
        double r124302 = sin(r124293);
        double r124303 = r124301 / r124302;
        double r124304 = exp(r124303);
        double r124305 = log(r124304);
        double r124306 = r124299 * r124305;
        return r124306;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.2
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 15.2

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

  3. Applied *-un-lft-identity15.2

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

  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

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

  7. Applied associate-*r/0.3

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

  9. Applied add-log-exp0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020045 +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)))