Average Error: 15.2 → 0.3
Time: 16.0s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}\]
\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(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}
double f(double x) {
        double r337092 = 8.0;
        double r337093 = 3.0;
        double r337094 = r337092 / r337093;
        double r337095 = x;
        double r337096 = 0.5;
        double r337097 = r337095 * r337096;
        double r337098 = sin(r337097);
        double r337099 = r337094 * r337098;
        double r337100 = r337099 * r337098;
        double r337101 = sin(r337095);
        double r337102 = r337100 / r337101;
        return r337102;
}
↓
double f(double x) {
        double r337103 = 8.0;
        double r337104 = x;
        double r337105 = 0.5;
        double r337106 = r337104 * r337105;
        double r337107 = sin(r337106);
        double r337108 = r337103 * r337107;
        double r337109 = sin(r337104);
        double r337110 = r337105 * r337104;
        double r337111 = sin(r337110);
        double r337112 = r337109 / r337111;
        double r337113 = 3.0;
        double r337114 = r337112 * r337113;
        double r337115 = r337108 / r337114;
        return r337115;
}

Error

Bits error versus x

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Results

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Target

Original15.2
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 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 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. Applied associate-/l/0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 +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)))