Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x
double f(double x) {
        double r836531 = 3.0;
        double r836532 = x;
        double r836533 = r836532 * r836531;
        double r836534 = r836533 * r836532;
        double r836535 = 4.0;
        double r836536 = r836532 * r836535;
        double r836537 = r836534 - r836536;
        double r836538 = 1.0;
        double r836539 = r836537 + r836538;
        double r836540 = r836531 * r836539;
        return r836540;
}
↓
double f(double x) {
        double r836541 = 9.0;
        double r836542 = x;
        double r836543 = 2.0;
        double r836544 = pow(r836542, r836543);
        double r836545 = r836541 * r836544;
        double r836546 = 3.0;
        double r836547 = r836545 + r836546;
        double r836548 = 12.0;
        double r836549 = r836548 * r836542;
        double r836550 = r836547 - r836549;
        return r836550;
}

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. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(1 + x \cdot \left(x \cdot 3 - 4\right)\right)}\]

  3. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(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)))