Average Error: 14.8 → 0.3
Time: 15.5s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r416166 = 8.0;
        double r416167 = 3.0;
        double r416168 = r416166 / r416167;
        double r416169 = x;
        double r416170 = 0.5;
        double r416171 = r416169 * r416170;
        double r416172 = sin(r416171);
        double r416173 = r416168 * r416172;
        double r416174 = r416173 * r416172;
        double r416175 = sin(r416169);
        double r416176 = r416174 / r416175;
        return r416176;
}
↓
double f(double x) {
        double r416177 = 0.5;
        double r416178 = x;
        double r416179 = r416177 * r416178;
        double r416180 = sin(r416179);
        double r416181 = 8.0;
        double r416182 = r416180 * r416181;
        double r416183 = 3.0;
        double r416184 = r416182 / r416183;
        double r416185 = sin(r416178);
        double r416186 = r416185 / r416180;
        double r416187 = r416184 / r416186;
        return r416187;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +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)))