Average Error: 0.2 → 0.1
Time: 2.0s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[x \cdot \left(x \cdot 9 - 12\right) + 3\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
x \cdot \left(x \cdot 9 - 12\right) + 3
double f(double x) {
        double r938252 = 3.0;
        double r938253 = x;
        double r938254 = r938253 * r938252;
        double r938255 = r938254 * r938253;
        double r938256 = 4.0;
        double r938257 = r938253 * r938256;
        double r938258 = r938255 - r938257;
        double r938259 = 1.0;
        double r938260 = r938258 + r938259;
        double r938261 = r938252 * r938260;
        return r938261;
}
↓
double f(double x) {
        double r938262 = x;
        double r938263 = 9.0;
        double r938264 = r938262 * r938263;
        double r938265 = 12.0;
        double r938266 = r938264 - r938265;
        double r938267 = r938262 * r938266;
        double r938268 = 3.0;
        double r938269 = r938267 + r938268;
        return r938269;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original0.2
Target0.1
Herbie0.1
\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

  1. Initial program 0.2

    \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

  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. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(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)))