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

↓

\[\mathsf{fma}\left({x}^{2}, 9, 3 - 12 \cdot x\right)\]

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

↓

\mathsf{fma}\left({x}^{2}, 9, 3 - 12 \cdot x\right)

double f(double x) {
        double r708110 = 3.0;
        double r708111 = x;
        double r708112 = r708111 * r708110;
        double r708113 = r708112 * r708111;
        double r708114 = 4.0;
        double r708115 = r708111 * r708114;
        double r708116 = r708113 - r708115;
        double r708117 = 1.0;
        double r708118 = r708116 + r708117;
        double r708119 = r708110 * r708118;
        return r708119;
}

↓

double f(double x) {
        double r708120 = x;
        double r708121 = 2.0;
        double r708122 = pow(r708120, r708121);
        double r708123 = 9.0;
        double r708124 = 3.0;
        double r708125 = 12.0;
        double r708126 = r708125 * r708120;
        double r708127 = r708124 - r708126;
        double r708128 = fma(r708122, r708123, r708127);
        return r708128;
}

Original	0.1
Target	0.1
Herbie	0.1

Derivation

Initial program 0.1
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
Simplified0.1
\[\leadsto \color{blue}{\mathsf{fma}\left(x, x \cdot 3 - 4, 1\right) \cdot 3}\]
Taylor expanded around 0 0.1
\[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]
Simplified0.1
\[\leadsto \color{blue}{\mathsf{fma}\left({x}^{2}, 9, 3 - 12 \cdot x\right)}\]
Final simplification0.1
\[\leadsto \mathsf{fma}\left({x}^{2}, 9, 3 - 12 \cdot x\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(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)))

Error

Target

Derivation

Reproduce