Average Error: 0.3 → 0.2
Time: 17.9s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[3 \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
3 \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)
double f(double x) {
        double r450006 = 3.0;
        double r450007 = 2.0;
        double r450008 = x;
        double r450009 = r450008 * r450006;
        double r450010 = r450007 - r450009;
        double r450011 = r450006 * r450010;
        double r450012 = r450011 * r450008;
        return r450012;
}
↓
double f(double x) {
        double r450013 = 3.0;
        double r450014 = 2.0;
        double r450015 = x;
        double r450016 = r450015 * r450013;
        double r450017 = r450014 - r450016;
        double r450018 = r450017 * r450015;
        double r450019 = r450013 * r450018;
        return r450019;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.3

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

  3. Applied associate-*l*0.2

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

  4. Final simplification0.2

    \[\leadsto 3 \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

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