Average Error: 14.6 → 0.3
Time: 24.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
\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 \frac{\sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r433942 = 8.0;
        double r433943 = 3.0;
        double r433944 = r433942 / r433943;
        double r433945 = x;
        double r433946 = 0.5;
        double r433947 = r433945 * r433946;
        double r433948 = sin(r433947);
        double r433949 = r433944 * r433948;
        double r433950 = r433949 * r433948;
        double r433951 = sin(r433945);
        double r433952 = r433950 / r433951;
        return r433952;
}
↓
double f(double x) {
        double r433953 = 8.0;
        double r433954 = x;
        double r433955 = 0.5;
        double r433956 = r433954 * r433955;
        double r433957 = sin(r433956);
        double r433958 = 3.0;
        double r433959 = r433957 / r433958;
        double r433960 = r433953 * r433959;
        double r433961 = sin(r433954);
        double r433962 = r433961 / r433957;
        double r433963 = r433960 / r433962;
        return r433963;
}

Error

Bits error versus x

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Results

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Target

Original14.6
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 14.6

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

  3. Applied div-inv14.6

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

  4. Applied associate-*l*14.6

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

  5. Simplified14.5

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

  7. Applied associate-/l*0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 
(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)))