Average Error: 0.1 → 0.1
Time: 9.7s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[x \cdot \left(9 \cdot x - 12\right) + 3\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
x \cdot \left(9 \cdot x - 12\right) + 3
double f(double x) {
        double r775545 = 3.0;
        double r775546 = x;
        double r775547 = r775546 * r775545;
        double r775548 = r775547 * r775546;
        double r775549 = 4.0;
        double r775550 = r775546 * r775549;
        double r775551 = r775548 - r775550;
        double r775552 = 1.0;
        double r775553 = r775551 + r775552;
        double r775554 = r775545 * r775553;
        return r775554;
}
↓
double f(double x) {
        double r775555 = x;
        double r775556 = 9.0;
        double r775557 = r775556 * r775555;
        double r775558 = 12.0;
        double r775559 = r775557 - r775558;
        double r775560 = r775555 * r775559;
        double r775561 = 3.0;
        double r775562 = r775560 + r775561;
        return r775562;
}

Error

Bits error versus x

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

  1. Initial program 0.1

    \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(9 \cdot x - 12\right) + 3}\]

  4. Final simplification0.1

    \[\leadsto x \cdot \left(9 \cdot x - 12\right) + 3\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3 (- (* (* 9 x) x) (* 12 x)))

  (* 3 (+ (- (* (* x 3) x) (* x 4)) 1)))