Average Error: 15.1 → 0.3
Time: 19.5s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\frac{\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot 3.0}{8.0}}\]
\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)}{\frac{\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot 3.0}{8.0}}
double f(double x) {
        double r24941194 = 8.0;
        double r24941195 = 3.0;
        double r24941196 = r24941194 / r24941195;
        double r24941197 = x;
        double r24941198 = 0.5;
        double r24941199 = r24941197 * r24941198;
        double r24941200 = sin(r24941199);
        double r24941201 = r24941196 * r24941200;
        double r24941202 = r24941201 * r24941200;
        double r24941203 = sin(r24941197);
        double r24941204 = r24941202 / r24941203;
        return r24941204;
}
↓
double f(double x) {
        double r24941205 = x;
        double r24941206 = 0.5;
        double r24941207 = r24941205 * r24941206;
        double r24941208 = sin(r24941207);
        double r24941209 = sin(r24941205);
        double r24941210 = r24941209 / r24941208;
        double r24941211 = 3.0;
        double r24941212 = r24941210 * r24941211;
        double r24941213 = 8.0;
        double r24941214 = r24941212 / r24941213;
        double r24941215 = r24941208 / r24941214;
        return r24941215;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.3
Herbie0.3
\[\frac{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 15.1

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

  3. Applied *-un-lft-identity15.1

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

  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

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

  7. Applied clear-num0.3

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

  9. Applied log1p-expm1-u0.4

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\frac{3.0}{8.0}} \cdot \frac{1}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin x}{\sin \left(x \cdot 0.5\right)}\right)\right)}}\]
  10. Using strategy rm

  11. Applied frac-times0.3

    \[\leadsto \color{blue}{\frac{\sin \left(x \cdot 0.5\right) \cdot 1}{\frac{3.0}{8.0} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin x}{\sin \left(x \cdot 0.5\right)}\right)\right)}}\]

  12. Simplified0.3

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 +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)))