Average Error: 0.1 → 0.1
Time: 18.9s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[\left(3 + 9 \cdot \left(x \cdot x\right)\right) - 12 \cdot x\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
\left(3 + 9 \cdot \left(x \cdot x\right)\right) - 12 \cdot x
double f(double x) {
        double r193553087 = 3.0;
        double r193553088 = x;
        double r193553089 = r193553088 * r193553087;
        double r193553090 = r193553089 * r193553088;
        double r193553091 = 4.0;
        double r193553092 = r193553088 * r193553091;
        double r193553093 = r193553090 - r193553092;
        double r193553094 = 1.0;
        double r193553095 = r193553093 + r193553094;
        double r193553096 = r193553087 * r193553095;
        return r193553096;
}
↓
double f(double x) {
        double r193553097 = 3.0;
        double r193553098 = 9.0;
        double r193553099 = x;
        double r193553100 = r193553099 * r193553099;
        double r193553101 = r193553098 * r193553100;
        double r193553102 = r193553097 + r193553101;
        double r193553103 = 12.0;
        double r193553104 = r193553103 * r193553099;
        double r193553105 = r193553102 - r193553104;
        return r193553105;
}

Error

Bits error versus x

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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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(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)))