Average Error: 0.1 → 0.1
Time: 16.2s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + \left(9 \cdot x - 12\right) \cdot x\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + \left(9 \cdot x - 12\right) \cdot x
double f(double x) {
        double r35158366 = 3.0;
        double r35158367 = x;
        double r35158368 = r35158367 * r35158366;
        double r35158369 = r35158368 * r35158367;
        double r35158370 = 4.0;
        double r35158371 = r35158367 * r35158370;
        double r35158372 = r35158369 - r35158371;
        double r35158373 = 1.0;
        double r35158374 = r35158372 + r35158373;
        double r35158375 = r35158366 * r35158374;
        return r35158375;
}
↓
double f(double x) {
        double r35158376 = 3.0;
        double r35158377 = 9.0;
        double r35158378 = x;
        double r35158379 = r35158377 * r35158378;
        double r35158380 = 12.0;
        double r35158381 = r35158379 - r35158380;
        double r35158382 = r35158381 * r35158378;
        double r35158383 = r35158376 + r35158382;
        return r35158383;
}

Error

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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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))