Average Error: 0.1 → 0.1
Time: 14.4s
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 r28546389 = 3.0;
        double r28546390 = x;
        double r28546391 = r28546390 * r28546389;
        double r28546392 = r28546391 * r28546390;
        double r28546393 = 4.0;
        double r28546394 = r28546390 * r28546393;
        double r28546395 = r28546392 - r28546394;
        double r28546396 = 1.0;
        double r28546397 = r28546395 + r28546396;
        double r28546398 = r28546389 * r28546397;
        return r28546398;
}
↓
double f(double x) {
        double r28546399 = 3.0;
        double r28546400 = 9.0;
        double r28546401 = x;
        double r28546402 = r28546400 * r28546401;
        double r28546403 = 12.0;
        double r28546404 = r28546402 - r28546403;
        double r28546405 = r28546404 * r28546401;
        double r28546406 = r28546399 + r28546405;
        return r28546406;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(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)))