Average Error: 0.1 → 0.0
Time: 12.2s
Precision: binary64
Cost: 7104
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
↓
\[\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right) \]
(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 (+ (* (+ y z) 2.0) t))))
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 * (((y + z) * 2.0) + t)));
}

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(Float64(Float64(y + z) * 2.0) + t)))
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[(N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision] + t), $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(\left(y + z\right) \cdot 2 + t\right)\right)

Error

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.1
Cost7104
\[\mathsf{fma}\left(\left(y + z\right) \cdot 2 + t, x, y \cdot 5\right) \]
Alternative 2
Error33.4
Cost1380
\[\begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -6.857707392897386 \cdot 10^{+59}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4466052778300237000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8693927057562255 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -2.208063290084773 \cdot 10^{-82}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -2.3287888846806855 \cdot 10^{-96}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 1.6872565259915895 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.573200644390177 \cdot 10^{-15}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 3
Error20.0
Cost1240
\[\begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -6.857707392897386 \cdot 10^{+59}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4466052778300237000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.326893248254141 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 4.971356079521299 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 4
Error20.1
Cost1240
\[\begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -6.857707392897386 \cdot 10^{+59}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4466052778300237000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.326893248254141 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 4.971356079521299 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 5
Error15.5
Cost1240
\[\begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;y \leq -6.857707392897386 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4466052778300237000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6432139544644515 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.6872565259915895 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3735017161368545 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.971356079521299 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error9.8
Cost1236
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;x \leq -7.967679231863752 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.340763113667047 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1366297399494267 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.7370733649823096 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.380053297819964 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error32.7
Cost1116
\[\begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;y \leq -6.857707392897386 \cdot 10^{+59}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4466052778300237000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8693927057562255 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -2.208063290084773 \cdot 10^{-82}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -2.3287888846806855 \cdot 10^{-96}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 1.6872565259915895 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.573200644390177 \cdot 10^{-15}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 8
Error14.8
Cost976
\[\begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -6.857707392897386 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4466052778300237000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8693927057562255 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.971356079521299 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error8.4
Cost968
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.415341302626598 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.646869915931763 \cdot 10^{+89}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error0.1
Cost960
\[y \cdot 5 + x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) \]
Alternative 11
Error9.7
Cost840
\[\begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\\ \mathbf{if}\;x \leq -5.336571372234044 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.380053297819964 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error35.1
Cost456
\[\begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+165}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.240265539428813 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
Alternative 13
Error38.6
Cost192
\[y \cdot 5 \]

Error

Reproduce

herbie shell --seed 2022308 
(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)))