\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]

↓

\[\mathsf{fma}\left(\mathsf{fma}\left(z + y, 2, t\right), x, 5 \cdot y\right)\]

x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5

↓

\mathsf{fma}\left(\mathsf{fma}\left(z + y, 2, t\right), x, 5 \cdot y\right)

double f(double x, double y, double z, double t) {
        double r7775666 = x;
        double r7775667 = y;
        double r7775668 = z;
        double r7775669 = r7775667 + r7775668;
        double r7775670 = r7775669 + r7775668;
        double r7775671 = r7775670 + r7775667;
        double r7775672 = t;
        double r7775673 = r7775671 + r7775672;
        double r7775674 = r7775666 * r7775673;
        double r7775675 = 5.0;
        double r7775676 = r7775667 * r7775675;
        double r7775677 = r7775674 + r7775676;
        return r7775677;
}

↓

double f(double x, double y, double z, double t) {
        double r7775678 = z;
        double r7775679 = y;
        double r7775680 = r7775678 + r7775679;
        double r7775681 = 2.0;
        double r7775682 = t;
        double r7775683 = fma(r7775680, r7775681, r7775682);
        double r7775684 = x;
        double r7775685 = 5.0;
        double r7775686 = r7775685 * r7775679;
        double r7775687 = fma(r7775683, r7775684, r7775686);
        return r7775687;
}

Derivation

Initial program 0.1
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
Simplified0.1
\[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y + z, 2, t\right), x, y \cdot 5\right)}\]
Final simplification0.1
\[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + y, 2, t\right), x, 5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

Error

Derivation

Reproduce