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

Average Accuracy: 99.9% → 99.9%

Time: 13.1s

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	52.0%
Cost	2165

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ t_3 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+19} \lor \neg \left(z \leq 1.5 \cdot 10^{+130}\right) \land z \leq 3 \cdot 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	99.9%
Cost	1600

\[\left(\left(2 \cdot \left(y \cdot x\right) + \left(x \cdot t + 4 \cdot \left(x \cdot z\right)\right)\right) + \left(x \cdot z\right) \cdot -2\right) + y \cdot 5 \]

Alternative 3
Accuracy	84.0%
Cost	1364

\[\begin{array}{l} t_1 := x \cdot t + y \cdot 5\\ t_2 := y \cdot 5 + x \cdot \left(z + z\right)\\ t_3 := \left(y + z\right) \cdot 2\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(t + t_3\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-244}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.065:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + x \cdot t_3\\ \end{array} \]

Alternative 4
Accuracy	51.1%
Cost	1244

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+85}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 42000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 5
Accuracy	84.1%
Cost	1236

\[\begin{array}{l} t_1 := x \cdot t + y \cdot 5\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot \left(z + z\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.065:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	49.9%
Cost	980

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-255}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 44000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 7
Accuracy	77.8%
Cost	978

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+45} \lor \neg \left(y \leq -7.4 \cdot 10^{-5} \lor \neg \left(y \leq -3.35 \cdot 10^{-37}\right) \land y \leq 40000000000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 8
Accuracy	78.6%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-33}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;y \leq 54000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	99.9%
Cost	960

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

Alternative 10
Accuracy	84.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-31} \lor \neg \left(x \leq 1.2 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \end{array} \]

Alternative 11
Accuracy	50.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 4300000000000:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 12
Accuracy	26.8%
Cost	192

\[x \cdot t \]

Reproduce

herbie shell --seed 2023140 
(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)))