Average Error: 14.8 → 0.3
Time: 18.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}\]
\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{\sin \left(0.5 \cdot x\right) \cdot 8}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}
double f(double x) {
        double r28257567 = 8.0;
        double r28257568 = 3.0;
        double r28257569 = r28257567 / r28257568;
        double r28257570 = x;
        double r28257571 = 0.5;
        double r28257572 = r28257570 * r28257571;
        double r28257573 = sin(r28257572);
        double r28257574 = r28257569 * r28257573;
        double r28257575 = r28257574 * r28257573;
        double r28257576 = sin(r28257570);
        double r28257577 = r28257575 / r28257576;
        return r28257577;
}
↓
double f(double x) {
        double r28257578 = 0.5;
        double r28257579 = x;
        double r28257580 = r28257578 * r28257579;
        double r28257581 = sin(r28257580);
        double r28257582 = 8.0;
        double r28257583 = r28257581 * r28257582;
        double r28257584 = sin(r28257579);
        double r28257585 = r28257584 / r28257581;
        double r28257586 = 3.0;
        double r28257587 = r28257585 * r28257586;
        double r28257588 = r28257583 / r28257587;
        return r28257588;
}

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. Using strategy rm

  5. Applied associate-*l/0.3

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

  6. Applied associate-/l/0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019169 
(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)))