Average Error: 14.9 → 0.3
Time: 13.1s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{1}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}\]
\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{1}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}
double f(double x) {
        double r12480243 = 8.0;
        double r12480244 = 3.0;
        double r12480245 = r12480243 / r12480244;
        double r12480246 = x;
        double r12480247 = 0.5;
        double r12480248 = r12480246 * r12480247;
        double r12480249 = sin(r12480248);
        double r12480250 = r12480245 * r12480249;
        double r12480251 = r12480250 * r12480249;
        double r12480252 = sin(r12480246);
        double r12480253 = r12480251 / r12480252;
        return r12480253;
}
↓
double f(double x) {
        double r12480254 = 1.0;
        double r12480255 = x;
        double r12480256 = sin(r12480255);
        double r12480257 = 0.5;
        double r12480258 = r12480257 * r12480255;
        double r12480259 = sin(r12480258);
        double r12480260 = r12480256 / r12480259;
        double r12480261 = r12480254 / r12480260;
        double r12480262 = 8.0;
        double r12480263 = r12480259 * r12480262;
        double r12480264 = 3.0;
        double r12480265 = r12480263 / r12480264;
        double r12480266 = r12480261 * r12480265;
        return r12480266;
}

Error

Bits error versus x

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Results

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Target

Original14.9
Target0.3
Herbie0.3
\[\frac{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.9

    \[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  2. Using strategy rm

  3. Applied associate-/l*0.5

    \[\leadsto \color{blue}{\frac{\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}}\]
  4. Using strategy rm

  5. Applied associate-*l/0.3

    \[\leadsto \frac{\color{blue}{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
  6. Using strategy rm

  7. Applied div-inv0.3

    \[\leadsto \color{blue}{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0} \cdot \frac{1}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}}\]

  8. Final simplification0.3

    \[\leadsto \frac{1}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}\]

Reproduce

herbie shell --seed 2019156 
(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)))