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 r747500 = 3.0;
        double r747501 = x;
        double r747502 = r747501 * r747500;
        double r747503 = r747502 * r747501;
        double r747504 = 4.0;
        double r747505 = r747501 * r747504;
        double r747506 = r747503 - r747505;
        double r747507 = 1.0;
        double r747508 = r747506 + r747507;
        double r747509 = r747500 * r747508;
        return r747509;
}
↓
double f(double x) {
        double r747510 = 9.0;
        double r747511 = x;
        double r747512 = 2.0;
        double r747513 = pow(r747511, r747512);
        double r747514 = r747510 * r747513;
        double r747515 = 3.0;
        double r747516 = r747514 + r747515;
        double r747517 = 12.0;
        double r747518 = r747517 * r747511;
        double r747519 = r747516 - r747518;
        return r747519;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2020001 
(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)))