Average Error: 0.2 → 0.2
Time: 3.0s
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 r720077 = 3.0;
        double r720078 = 2.0;
        double r720079 = x;
        double r720080 = r720079 * r720077;
        double r720081 = r720078 - r720080;
        double r720082 = r720077 * r720081;
        double r720083 = r720082 * r720079;
        return r720083;
}
↓
double f(double x) {
        double r720084 = 6.0;
        double r720085 = 9.0;
        double r720086 = x;
        double r720087 = r720085 * r720086;
        double r720088 = r720084 - r720087;
        double r720089 = r720088 * r720086;
        return r720089;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.2

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

  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 2019353 +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))