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

↓

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

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 r577552 = 3.0;
        double r577553 = x;
        double r577554 = r577553 * r577552;
        double r577555 = r577554 * r577553;
        double r577556 = 4.0;
        double r577557 = r577553 * r577556;
        double r577558 = r577555 - r577557;
        double r577559 = 1.0;
        double r577560 = r577558 + r577559;
        double r577561 = r577552 * r577560;
        return r577561;
}

↓

double f(double x) {
        double r577562 = x;
        double r577563 = 2.0;
        double r577564 = pow(r577562, r577563);
        double r577565 = 9.0;
        double r577566 = 3.0;
        double r577567 = 12.0;
        double r577568 = r577567 * r577562;
        double r577569 = r577566 - r577568;
        double r577570 = fma(r577564, r577565, r577569);
        return r577570;
}

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 2020001 +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