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

↓

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

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 r622436 = 3.0;
        double r622437 = x;
        double r622438 = r622437 * r622436;
        double r622439 = r622438 * r622437;
        double r622440 = 4.0;
        double r622441 = r622437 * r622440;
        double r622442 = r622439 - r622441;
        double r622443 = 1.0;
        double r622444 = r622442 + r622443;
        double r622445 = r622436 * r622444;
        return r622445;
}

↓

double f(double x) {
        double r622446 = x;
        double r622447 = 2.0;
        double r622448 = pow(r622446, r622447);
        double r622449 = 9.0;
        double r622450 = 3.0;
        double r622451 = 12.0;
        double r622452 = r622451 * r622446;
        double r622453 = r622450 - r622452;
        double r622454 = fma(r622448, r622449, r622453);
        return r622454;
}

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 2020039 +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