\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5.0\]

↓

\[\mathsf{fma}\left(\mathsf{fma}\left(z + y, 2, t\right), x, 5.0 \cdot y\right)\]

x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5.0

↓

\mathsf{fma}\left(\mathsf{fma}\left(z + y, 2, t\right), x, 5.0 \cdot y\right)

double f(double x, double y, double z, double t) {
        double r8277109 = x;
        double r8277110 = y;
        double r8277111 = z;
        double r8277112 = r8277110 + r8277111;
        double r8277113 = r8277112 + r8277111;
        double r8277114 = r8277113 + r8277110;
        double r8277115 = t;
        double r8277116 = r8277114 + r8277115;
        double r8277117 = r8277109 * r8277116;
        double r8277118 = 5.0;
        double r8277119 = r8277110 * r8277118;
        double r8277120 = r8277117 + r8277119;
        return r8277120;
}

↓

double f(double x, double y, double z, double t) {
        double r8277121 = z;
        double r8277122 = y;
        double r8277123 = r8277121 + r8277122;
        double r8277124 = 2.0;
        double r8277125 = t;
        double r8277126 = fma(r8277123, r8277124, r8277125);
        double r8277127 = x;
        double r8277128 = 5.0;
        double r8277129 = r8277128 * r8277122;
        double r8277130 = fma(r8277126, r8277127, r8277129);
        return r8277130;
}

Derivation

Initial program 0.1
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5.0\]
Simplified0.1
\[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y + z, 2, t\right), x, y \cdot 5.0\right)}\]
Final simplification0.1
\[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + y, 2, t\right), x, 5.0 \cdot y\right)\]

Reproduce

herbie shell --seed 2019163 +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