Average Error: 0.1 → 0.1
Time: 11.1s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + x \cdot \left(9 \cdot x - 12\right)\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + x \cdot \left(9 \cdot x - 12\right)
double f(double x) {
        double r561451 = 3.0;
        double r561452 = x;
        double r561453 = r561452 * r561451;
        double r561454 = r561453 * r561452;
        double r561455 = 4.0;
        double r561456 = r561452 * r561455;
        double r561457 = r561454 - r561456;
        double r561458 = 1.0;
        double r561459 = r561457 + r561458;
        double r561460 = r561451 * r561459;
        return r561460;
}
↓
double f(double x) {
        double r561461 = 3.0;
        double r561462 = x;
        double r561463 = 9.0;
        double r561464 = r561463 * r561462;
        double r561465 = 12.0;
        double r561466 = r561464 - r561465;
        double r561467 = r561462 * r561466;
        double r561468 = r561461 + r561467;
        return r561468;
}

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. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 
(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)))