Average Error: 0.2 → 0.3
Time: 21.2s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(\left(\frac{3 \cdot 3}{\frac{\left(x \cdot 2\right) \cdot \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) + 3 \cdot \left(3 \cdot 3\right)}{x}} - \frac{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}{\frac{\left(x \cdot 2\right) \cdot \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) + 3 \cdot \left(3 \cdot 3\right)}{x}}\right) \cdot x\right) \cdot \left(\left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - \left(x \cdot 2\right) \cdot 3\right) + 3 \cdot 3\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(\left(\frac{3 \cdot 3}{\frac{\left(x \cdot 2\right) \cdot \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) + 3 \cdot \left(3 \cdot 3\right)}{x}} - \frac{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}{\frac{\left(x \cdot 2\right) \cdot \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) + 3 \cdot \left(3 \cdot 3\right)}{x}}\right) \cdot x\right) \cdot \left(\left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - \left(x \cdot 2\right) \cdot 3\right) + 3 \cdot 3\right)
double f(double x) {
        double r37620173 = x;
        double r37620174 = r37620173 * r37620173;
        double r37620175 = 3.0;
        double r37620176 = 2.0;
        double r37620177 = r37620173 * r37620176;
        double r37620178 = r37620175 - r37620177;
        double r37620179 = r37620174 * r37620178;
        return r37620179;
}
↓
double f(double x) {
        double r37620180 = 3.0;
        double r37620181 = r37620180 * r37620180;
        double r37620182 = x;
        double r37620183 = 2.0;
        double r37620184 = r37620182 * r37620183;
        double r37620185 = r37620184 * r37620184;
        double r37620186 = r37620184 * r37620185;
        double r37620187 = r37620180 * r37620181;
        double r37620188 = r37620186 + r37620187;
        double r37620189 = r37620188 / r37620182;
        double r37620190 = r37620181 / r37620189;
        double r37620191 = r37620185 / r37620189;
        double r37620192 = r37620190 - r37620191;
        double r37620193 = r37620192 * r37620182;
        double r37620194 = r37620184 * r37620180;
        double r37620195 = r37620185 - r37620194;
        double r37620196 = r37620195 + r37620181;
        double r37620197 = r37620193 * r37620196;
        return r37620197;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)}\]
  4. Using strategy rm

  5. Applied flip--0.2

    \[\leadsto x \cdot \left(x \cdot \color{blue}{\frac{3 \cdot 3 - \left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}{3 + x \cdot 2}}\right)\]

  6. Applied associate-*r/0.2

    \[\leadsto x \cdot \color{blue}{\frac{x \cdot \left(3 \cdot 3 - \left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right)}{3 + x \cdot 2}}\]

  7. Simplified0.2

    \[\leadsto x \cdot \frac{\color{blue}{\left(\left(3 - x \cdot 2\right) \cdot \left(3 + x \cdot 2\right)\right) \cdot x}}{3 + x \cdot 2}\]
  8. Using strategy rm

  9. Applied flip3-+0.3

    \[\leadsto x \cdot \frac{\left(\left(3 - x \cdot 2\right) \cdot \left(3 + x \cdot 2\right)\right) \cdot x}{\color{blue}{\frac{{3}^{3} + {\left(x \cdot 2\right)}^{3}}{3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - 3 \cdot \left(x \cdot 2\right)\right)}}}\]

  10. Applied associate-/r/0.3

    \[\leadsto x \cdot \color{blue}{\left(\frac{\left(\left(3 - x \cdot 2\right) \cdot \left(3 + x \cdot 2\right)\right) \cdot x}{{3}^{3} + {\left(x \cdot 2\right)}^{3}} \cdot \left(3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - 3 \cdot \left(x \cdot 2\right)\right)\right)\right)}\]

  11. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(x \cdot \frac{\left(\left(3 - x \cdot 2\right) \cdot \left(3 + x \cdot 2\right)\right) \cdot x}{{3}^{3} + {\left(x \cdot 2\right)}^{3}}\right) \cdot \left(3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - 3 \cdot \left(x \cdot 2\right)\right)\right)}\]

  12. Simplified0.3

    \[\leadsto \color{blue}{\left(\left(\frac{3 \cdot 3}{\frac{3 \cdot \left(3 \cdot 3\right) + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) \cdot \left(x \cdot 2\right)}{x}} - \frac{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}{\frac{3 \cdot \left(3 \cdot 3\right) + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) \cdot \left(x \cdot 2\right)}{x}}\right) \cdot x\right)} \cdot \left(3 \cdot 3 + \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - 3 \cdot \left(x \cdot 2\right)\right)\right)\]

  13. Final simplification0.3

    \[\leadsto \left(\left(\frac{3 \cdot 3}{\frac{\left(x \cdot 2\right) \cdot \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) + 3 \cdot \left(3 \cdot 3\right)}{x}} - \frac{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)}{\frac{\left(x \cdot 2\right) \cdot \left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)\right) + 3 \cdot \left(3 \cdot 3\right)}{x}}\right) \cdot x\right) \cdot \left(\left(\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - \left(x \cdot 2\right) \cdot 3\right) + 3 \cdot 3\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

  (* (* x x) (- 3.0 (* x 2.0))))