Average Error: 14.9 → 0.3
Time: 1.8m
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\frac{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}{2.666666666666666518636930049979127943516}}\]
\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(x \cdot 0.5\right)}{\frac{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}{2.666666666666666518636930049979127943516}}
double f(double x) {
        double r22865226 = 8.0;
        double r22865227 = 3.0;
        double r22865228 = r22865226 / r22865227;
        double r22865229 = x;
        double r22865230 = 0.5;
        double r22865231 = r22865229 * r22865230;
        double r22865232 = sin(r22865231);
        double r22865233 = r22865228 * r22865232;
        double r22865234 = r22865233 * r22865232;
        double r22865235 = sin(r22865229);
        double r22865236 = r22865234 / r22865235;
        return r22865236;
}
↓
double f(double x) {
        double r22865237 = x;
        double r22865238 = 0.5;
        double r22865239 = r22865237 * r22865238;
        double r22865240 = sin(r22865239);
        double r22865241 = sin(r22865237);
        double r22865242 = r22865241 / r22865240;
        double r22865243 = 2.6666666666666665;
        double r22865244 = r22865242 / r22865243;
        double r22865245 = r22865240 / r22865244;
        return r22865245;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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. Taylor expanded around inf 14.9

    \[\leadsto \color{blue}{2.666666666666666518636930049979127943516 \cdot \frac{{\left(\sin \left(0.5 \cdot x\right)\right)}^{2}}{\sin x}}\]

  3. Simplified0.5

    \[\leadsto \color{blue}{\frac{\sin \left(0.5 \cdot x\right) \cdot 2.666666666666666518636930049979127943516}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}}\]
  4. Using strategy rm

  5. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{\sin \left(0.5 \cdot x\right)}{\frac{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}{2.666666666666666518636930049979127943516}}}\]

  6. Final simplification0.3

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\frac{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}{2.666666666666666518636930049979127943516}}\]

Reproduce

herbie shell --seed 2019200 +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)))