Average Error: 0.2 → 0.2
Time: 13.2s
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 r32264239 = 3.0;
        double r32264240 = 2.0;
        double r32264241 = x;
        double r32264242 = r32264241 * r32264239;
        double r32264243 = r32264240 - r32264242;
        double r32264244 = r32264239 * r32264243;
        double r32264245 = r32264244 * r32264241;
        return r32264245;
}
↓
double f(double x) {
        double r32264246 = x;
        double r32264247 = 6.0;
        double r32264248 = 9.0;
        double r32264249 = r32264248 * r32264246;
        double r32264250 = r32264247 - r32264249;
        double r32264251 = r32264246 * r32264250;
        return r32264251;
}

Error

Bits error versus x

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Results

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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

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

  3. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(6 - x \cdot 9\right)}\]
  4. Using strategy rm

  5. Applied *-commutative0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

  (* (* 3.0 (- 2.0 (* x 3.0))) x))