Average Error: 15.0 → 0.3
Time: 22.0s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}}{\frac{3.0}{8.0}}\]
\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) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}}{\frac{3.0}{8.0}}
double f(double x) {
        double r26158233 = 8.0;
        double r26158234 = 3.0;
        double r26158235 = r26158233 / r26158234;
        double r26158236 = x;
        double r26158237 = 0.5;
        double r26158238 = r26158236 * r26158237;
        double r26158239 = sin(r26158238);
        double r26158240 = r26158235 * r26158239;
        double r26158241 = r26158240 * r26158239;
        double r26158242 = sin(r26158236);
        double r26158243 = r26158241 / r26158242;
        return r26158243;
}
↓
double f(double x) {
        double r26158244 = x;
        double r26158245 = 0.5;
        double r26158246 = r26158244 * r26158245;
        double r26158247 = sin(r26158246);
        double r26158248 = sin(r26158244);
        double r26158249 = r26158247 / r26158248;
        double r26158250 = r26158247 * r26158249;
        double r26158251 = 3.0;
        double r26158252 = 8.0;
        double r26158253 = r26158251 / r26158252;
        double r26158254 = r26158250 / r26158253;
        return r26158254;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
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 15.0

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

  3. Applied *-un-lft-identity15.0

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

  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 associate-*l/0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 +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)))