Average Error: 14.7 → 0.4
Time: 21.1s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right) \cdot 8.0}{3.0}\right)\right)\]
\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{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right) \cdot 8.0}{3.0}\right)\right)
double f(double x) {
        double r22249104 = 8.0;
        double r22249105 = 3.0;
        double r22249106 = r22249104 / r22249105;
        double r22249107 = x;
        double r22249108 = 0.5;
        double r22249109 = r22249107 * r22249108;
        double r22249110 = sin(r22249109);
        double r22249111 = r22249106 * r22249110;
        double r22249112 = r22249111 * r22249110;
        double r22249113 = sin(r22249107);
        double r22249114 = r22249112 / r22249113;
        return r22249114;
}
↓
double f(double x) {
        double r22249115 = x;
        double r22249116 = 0.5;
        double r22249117 = r22249115 * r22249116;
        double r22249118 = sin(r22249117);
        double r22249119 = sin(r22249115);
        double r22249120 = r22249118 / r22249119;
        double r22249121 = 8.0;
        double r22249122 = r22249118 * r22249121;
        double r22249123 = 3.0;
        double r22249124 = r22249122 / r22249123;
        double r22249125 = expm1(r22249124);
        double r22249126 = log1p(r22249125);
        double r22249127 = r22249120 * r22249126;
        return r22249127;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
Target0.3
Herbie0.4
\[\frac{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.7

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

  3. Applied *-un-lft-identity14.7

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

  4. Applied times-frac0.5

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

  5. Simplified0.3

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

  7. Applied log1p-expm1-u0.4

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right) \cdot 8.0}{3.0}\right)\right)} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  8. Final simplification0.4

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right) \cdot 8.0}{3.0}\right)\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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)))