Average Error: 0.1 → 0.1
Time: 16.4s
Precision: 64
\[3.0 \cdot \left(\left(\left(x \cdot 3.0\right) \cdot x - x \cdot 4.0\right) + 1.0\right)\]
↓
\[9.0 \cdot \left(x \cdot x\right) + \left(3.0 - 12.0 \cdot x\right)\]
3.0 \cdot \left(\left(\left(x \cdot 3.0\right) \cdot x - x \cdot 4.0\right) + 1.0\right)
↓
9.0 \cdot \left(x \cdot x\right) + \left(3.0 - 12.0 \cdot x\right)
double f(double x) {
        double r38459274 = 3.0;
        double r38459275 = x;
        double r38459276 = r38459275 * r38459274;
        double r38459277 = r38459276 * r38459275;
        double r38459278 = 4.0;
        double r38459279 = r38459275 * r38459278;
        double r38459280 = r38459277 - r38459279;
        double r38459281 = 1.0;
        double r38459282 = r38459280 + r38459281;
        double r38459283 = r38459274 * r38459282;
        return r38459283;
}
↓
double f(double x) {
        double r38459284 = 9.0;
        double r38459285 = x;
        double r38459286 = r38459285 * r38459285;
        double r38459287 = r38459284 * r38459286;
        double r38459288 = 3.0;
        double r38459289 = 12.0;
        double r38459290 = r38459289 * r38459285;
        double r38459291 = r38459288 - r38459290;
        double r38459292 = r38459287 + r38459291;
        return r38459292;
}

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
\[3.0 + \left(\left(9.0 \cdot x\right) \cdot x - 12.0 \cdot x\right)\]

Derivation

  1. Initial program 0.1

    \[3.0 \cdot \left(\left(\left(x \cdot 3.0\right) \cdot x - x \cdot 4.0\right) + 1.0\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{3.0 \cdot \left(1.0 - \left(4.0 - x \cdot 3.0\right) \cdot x\right)}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto 3.0 \cdot \left(1.0 - \color{blue}{\left(4.0 \cdot x - 3.0 \cdot {x}^{2}\right)}\right)\]

  4. Simplified0.1

    \[\leadsto 3.0 \cdot \left(1.0 - \color{blue}{x \cdot \left(4.0 - 3.0 \cdot x\right)}\right)\]

  5. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(9.0 \cdot {x}^{2} + 3.0\right) - 12.0 \cdot x}\]

  6. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot 9.0 + \left(3.0 - x \cdot 12.0\right)}\]

  7. Final simplification0.1

    \[\leadsto 9.0 \cdot \left(x \cdot x\right) + \left(3.0 - 12.0 \cdot x\right)\]

Reproduce

herbie shell --seed 2019164 
(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)))