Average Error: 14.6 → 0.3
Time: 25.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\left(8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r419140 = 8.0;
        double r419141 = 3.0;
        double r419142 = r419140 / r419141;
        double r419143 = x;
        double r419144 = 0.5;
        double r419145 = r419143 * r419144;
        double r419146 = sin(r419145);
        double r419147 = r419142 * r419146;
        double r419148 = r419147 * r419146;
        double r419149 = sin(r419143);
        double r419150 = r419148 / r419149;
        return r419150;
}
↓
double f(double x) {
        double r419151 = 8.0;
        double r419152 = 0.5;
        double r419153 = x;
        double r419154 = r419152 * r419153;
        double r419155 = sin(r419154);
        double r419156 = 3.0;
        double r419157 = r419155 / r419156;
        double r419158 = r419151 * r419157;
        double r419159 = r419153 * r419152;
        double r419160 = sin(r419159);
        double r419161 = sin(r419153);
        double r419162 = r419160 / r419161;
        double r419163 = r419158 * r419162;
        return r419163;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.6
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 14.6

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

  3. Applied *-un-lft-identity14.6

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

  4. Applied times-frac0.5

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

  5. Simplified0.5

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

  7. Applied div-inv0.5

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

  8. Applied associate-*l*0.5

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 +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)))