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

↓

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

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 r727345 = 3.0;
        double r727346 = x;
        double r727347 = r727346 * r727345;
        double r727348 = r727347 * r727346;
        double r727349 = 4.0;
        double r727350 = r727346 * r727349;
        double r727351 = r727348 - r727350;
        double r727352 = 1.0;
        double r727353 = r727351 + r727352;
        double r727354 = r727345 * r727353;
        return r727354;
}

↓

double f(double x) {
        double r727355 = x;
        double r727356 = 2.0;
        double r727357 = pow(r727355, r727356);
        double r727358 = 9.0;
        double r727359 = 3.0;
        double r727360 = 12.0;
        double r727361 = r727360 * r727355;
        double r727362 = r727359 - r727361;
        double r727363 = fma(r727357, r727358, r727362);
        return r727363;
}

Original	0.2
Target	0.1
Herbie	0.1

Derivation

Initial program 0.2
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
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 2019353 +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