Average Error: 0.3 → 0.2
Time: 2.4s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[x \cdot \left(6 - 9 \cdot x\right)\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
x \cdot \left(6 - 9 \cdot x\right)
double f(double x) {
        double r754993 = 3.0;
        double r754994 = 2.0;
        double r754995 = x;
        double r754996 = r754995 * r754993;
        double r754997 = r754994 - r754996;
        double r754998 = r754993 * r754997;
        double r754999 = r754998 * r754995;
        return r754999;
}
↓
double f(double x) {
        double r755000 = x;
        double r755001 = 6.0;
        double r755002 = 9.0;
        double r755003 = r755002 * r755000;
        double r755004 = r755001 - r755003;
        double r755005 = r755000 * r755004;
        return r755005;
}

Error

Bits error versus x

Try it out

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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

    \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019356 
(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))