Average Error: 0.2 → 0.2
Time: 2.4s
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 r689225 = 3.0;
        double r689226 = 2.0;
        double r689227 = x;
        double r689228 = r689227 * r689225;
        double r689229 = r689226 - r689228;
        double r689230 = r689225 * r689229;
        double r689231 = r689230 * r689227;
        return r689231;
}
↓
double f(double x) {
        double r689232 = 6.0;
        double r689233 = 9.0;
        double r689234 = x;
        double r689235 = r689233 * r689234;
        double r689236 = r689232 - r689235;
        double r689237 = r689236 * r689234;
        return r689237;
}

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 2020083 
(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))