?

Average Error: 0.18% → 0.12%
Time: 10.4s
Precision: binary64
Cost: 7104

?

\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
↓
\[\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \]
(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))
↓
(FPCore (x y z t) :precision binary64 (fma y 5.0 (* x (+ t (* (+ y z) 2.0)))))
double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}
↓
double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (x * (t + ((y + z) * 2.0))));
}

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end
↓
function code(x, y, z, t)
	return fma(y, 5.0, Float64(x * Float64(t + Float64(Float64(y + z) * 2.0))))
end

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error?

Derivation?

  1. Initial program 0.18

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

  2. Applied egg-rr0.12

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

  3. Final simplification0.12

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

Alternatives

Alternative 1
Error0.17%
Cost7104
\[\mathsf{fma}\left(x, t + \left(y + z\right) \cdot 2, y \cdot 5\right) \]
Alternative 2
Error17.7%
Cost1369
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-137} \lor \neg \left(x \leq 1.3 \cdot 10^{-114}\right) \land x \leq 2.7 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error50.02%
Cost1248
\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+28}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-115}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-307}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-102}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 4
Error42.4%
Cost1240
\[\begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -1.38 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-138}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-137}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-114}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error39.67%
Cost1108
\[\begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-307}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-252}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-101}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error39.67%
Cost1108
\[\begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-252}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-101}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error14.45%
Cost1100
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.85 \cdot 10^{+114}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error14.54%
Cost969
\[\begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-34} \lor \neg \left(y \leq 5.6 \cdot 10^{-102}\right):\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
Alternative 9
Error0.18%
Cost960
\[y \cdot 5 + x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) \]
Alternative 10
Error20.05%
Cost841
\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+54} \lor \neg \left(y \leq 2.7 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
Alternative 11
Error22.66%
Cost713
\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-33} \lor \neg \left(y \leq 2.5 \cdot 10^{-50}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
Alternative 12
Error49.6%
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-101}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 13
Error73.47%
Cost192
\[x \cdot t \]

Error

Reproduce?

herbie shell --seed 2023121 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))