Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Average Accuracy: 99.9% → 99.9%

Time: 12.6s

Precision: binary64

Cost: 7104

Math

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

↓

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

FPCore

(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)))))

C

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))));
}

Julia

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

Wolfram

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]

Derivation

1. Initial program 99.9%

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

2. Applied egg-rr 99.9%

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

   [Start] 99.9	\[ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   +-commutative [=>] 99.9	\[ \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]
   fma-def [=>] 99.9	\[ \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]
   associate-+l+ [=>] 99.9	\[ \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right)\right) \]
   *-un-lft-identity [=>] 99.9	\[ \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]
   +-commutative [<=] 99.9	\[ \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]
   *-un-lft-identity [=>] 99.9	\[ \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]
   distribute-rgt-out [=>] 99.9	\[ \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]
   metadata-eval [=>] 99.9	\[ \mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right)\right) \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	84.3%
Cost	1628

\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ t_2 := y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 2
Accuracy	53.6%
Cost	1372

\[\begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ t_2 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;y \leq -32000000:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.45 \cdot 10^{-308}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 3
Accuracy	61.0%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;y \leq -8.45 \cdot 10^{-308}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-257}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	51.5%
Cost	1116

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;y \leq -12000:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-173}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.45 \cdot 10^{-308}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-76}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 5
Accuracy	98.3%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+22} \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + \left(x \cdot \left(z \cdot 2\right) + x \cdot t\right)\\ \end{array} \]

Alternative 6
Accuracy	50.7%
Cost	984

\[\begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-173}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.45 \cdot 10^{-308}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 7
Accuracy	85.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -0.18 \lor \neg \left(y \leq 5 \cdot 10^{-76}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 8
Accuracy	98.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+22} \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 9
Accuracy	99.9%
Cost	960

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

Alternative 10
Accuracy	78.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+84} \lor \neg \left(y \leq 5 \cdot 10^{-76}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 11
Accuracy	78.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + y \cdot \left(x \cdot 2\right)\\ \end{array} \]

Alternative 12
Accuracy	76.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+19} \lor \neg \left(y \leq 5 \cdot 10^{-76}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 13
Accuracy	50.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 14
Accuracy	26.0%
Cost	192

\[x \cdot t \]

Reproduce

herbie shell --seed 2023138 
(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)))