Average Error: 0.2 → 0.1
Time: 2.4s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r1018140 = x;
        double r1018141 = r1018140 * r1018140;
        double r1018142 = 3.0;
        double r1018143 = 2.0;
        double r1018144 = r1018140 * r1018143;
        double r1018145 = r1018142 - r1018144;
        double r1018146 = r1018141 * r1018145;
        return r1018146;
}
↓
double f(double x) {
        double r1018147 = x;
        double r1018148 = 3.0;
        double r1018149 = r1018147 * r1018148;
        double r1018150 = r1018147 * r1018149;
        double r1018151 = 2.0;
        double r1018152 = 3.0;
        double r1018153 = pow(r1018147, r1018152);
        double r1018154 = r1018151 * r1018153;
        double r1018155 = -r1018154;
        double r1018156 = r1018150 + r1018155;
        return r1018156;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

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

  3. Applied sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.1

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

  7. Applied associate-*l*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3 (* x 2))))

  (* (* x x) (- 3 (* x 2))))