Average Error: 14.9 → 0.5
Time: 43.4s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(\left(\sin \left(0.5 \cdot x\right) \cdot 8\right) \cdot \frac{1}{3}\right)\]
\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{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(\left(\sin \left(0.5 \cdot x\right) \cdot 8\right) \cdot \frac{1}{3}\right)
double f(double x) {
        double r26819984 = 8.0;
        double r26819985 = 3.0;
        double r26819986 = r26819984 / r26819985;
        double r26819987 = x;
        double r26819988 = 0.5;
        double r26819989 = r26819987 * r26819988;
        double r26819990 = sin(r26819989);
        double r26819991 = r26819986 * r26819990;
        double r26819992 = r26819991 * r26819990;
        double r26819993 = sin(r26819987);
        double r26819994 = r26819992 / r26819993;
        return r26819994;
}
↓
double f(double x) {
        double r26819995 = 0.5;
        double r26819996 = x;
        double r26819997 = r26819995 * r26819996;
        double r26819998 = sin(r26819997);
        double r26819999 = sin(r26819996);
        double r26820000 = r26819998 / r26819999;
        double r26820001 = 8.0;
        double r26820002 = r26819998 * r26820001;
        double r26820003 = 1.0;
        double r26820004 = 3.0;
        double r26820005 = r26820003 / r26820004;
        double r26820006 = r26820002 * r26820005;
        double r26820007 = r26820000 * r26820006;
        return r26820007;
}

Error

Bits error versus x

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Results

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Target

Original14.9
Target0.3
Herbie0.5
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.9

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

  3. Applied *-un-lft-identity14.9

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

  4. Applied times-frac0.5

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

  5. Simplified0.3

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

  7. Applied div-inv0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019200 
(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)))