Average Error: 0.3 → 0.2
Time: 7.5s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[\left(6 - 9 \cdot x\right) \cdot x\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
\left(6 - 9 \cdot x\right) \cdot x
double f(double x) {
        double r713326 = 3.0;
        double r713327 = 2.0;
        double r713328 = x;
        double r713329 = r713328 * r713326;
        double r713330 = r713327 - r713329;
        double r713331 = r713326 * r713330;
        double r713332 = r713331 * r713328;
        return r713332;
}
↓
double f(double x) {
        double r713333 = 6.0;
        double r713334 = 9.0;
        double r713335 = x;
        double r713336 = r713334 * r713335;
        double r713337 = r713333 - r713336;
        double r713338 = r713337 * r713335;
        return r713338;
}

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. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(6 - 9 \cdot x\right)} \cdot x\]

  3. Final simplification0.2

    \[\leadsto \left(6 - 9 \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2020046 +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))