Average Error: 0.1 → 0.1
Time: 12.8s
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 r45029544 = 3.0;
        double r45029545 = x;
        double r45029546 = r45029545 * r45029544;
        double r45029547 = r45029546 * r45029545;
        double r45029548 = 4.0;
        double r45029549 = r45029545 * r45029548;
        double r45029550 = r45029547 - r45029549;
        double r45029551 = 1.0;
        double r45029552 = r45029550 + r45029551;
        double r45029553 = r45029544 * r45029552;
        return r45029553;
}
↓
double f(double x) {
        double r45029554 = 3.0;
        double r45029555 = 9.0;
        double r45029556 = x;
        double r45029557 = r45029555 * r45029556;
        double r45029558 = 12.0;
        double r45029559 = r45029557 - r45029558;
        double r45029560 = r45029559 * r45029556;
        double r45029561 = r45029554 + r45029560;
        return r45029561;
}

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

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. 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)))