Average Error: 14.8 → 0.4
Time: 15.6s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)}\right)\right)}\]
\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{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)}\right)\right)}
double f(double x) {
        double r335027 = 8.0;
        double r335028 = 3.0;
        double r335029 = r335027 / r335028;
        double r335030 = x;
        double r335031 = 0.5;
        double r335032 = r335030 * r335031;
        double r335033 = sin(r335032);
        double r335034 = r335029 * r335033;
        double r335035 = r335034 * r335033;
        double r335036 = sin(r335030);
        double r335037 = r335035 / r335036;
        return r335037;
}
↓
double f(double x) {
        double r335038 = 8.0;
        double r335039 = 0.5;
        double r335040 = x;
        double r335041 = r335039 * r335040;
        double r335042 = sin(r335041);
        double r335043 = 3.0;
        double r335044 = r335042 / r335043;
        double r335045 = r335038 * r335044;
        double r335046 = sin(r335040);
        double r335047 = r335046 / r335042;
        double r335048 = expm1(r335047);
        double r335049 = log1p(r335048);
        double r335050 = r335045 / r335049;
        return r335050;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.3
Herbie0.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

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 div-inv0.5

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

  7. Applied associate-*l*0.5

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

  8. Simplified0.3

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

  10. Applied log1p-expm1-u0.4

    \[\leadsto \frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)}\right)\right)}}\]

  11. Final simplification0.4

    \[\leadsto \frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2019322 +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)))