Average Error: 0.1 → 0.1
Time: 9.7s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[x \cdot \left(9 \cdot x - 12\right) + 3\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
x \cdot \left(9 \cdot x - 12\right) + 3
double f(double x) {
        double r387180 = 3.0;
        double r387181 = x;
        double r387182 = r387181 * r387180;
        double r387183 = r387182 * r387181;
        double r387184 = 4.0;
        double r387185 = r387181 * r387184;
        double r387186 = r387183 - r387185;
        double r387187 = 1.0;
        double r387188 = r387186 + r387187;
        double r387189 = r387180 * r387188;
        return r387189;
}
↓
double f(double x) {
        double r387190 = x;
        double r387191 = 9.0;
        double r387192 = r387191 * r387190;
        double r387193 = 12.0;
        double r387194 = r387192 - r387193;
        double r387195 = r387190 * r387194;
        double r387196 = 3.0;
        double r387197 = r387195 + r387196;
        return r387197;
}

Error

Bits error versus x

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Results

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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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))