Average Error: 0.3 → 0.2
Time: 10.5s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[x \cdot \left(6 - x \cdot 9\right)\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
x \cdot \left(6 - x \cdot 9\right)
double f(double x) {
        double r471236 = 3.0;
        double r471237 = 2.0;
        double r471238 = x;
        double r471239 = r471238 * r471236;
        double r471240 = r471237 - r471239;
        double r471241 = r471236 * r471240;
        double r471242 = r471241 * r471238;
        return r471242;
}
↓
double f(double x) {
        double r471243 = x;
        double r471244 = 6.0;
        double r471245 = 9.0;
        double r471246 = r471243 * r471245;
        double r471247 = r471244 - r471246;
        double r471248 = r471243 * r471247;
        return r471248;
}

Error

Bits error versus x

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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 flip--0.3

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

  4. Applied associate-*r/0.3

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

  5. Taylor expanded around 0 0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019298 
(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))