Average Error: 0.1 → 0.0
Time: 11.9s
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 0.1

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

  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

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

Alternatives

Alternative 1
Error27.0
Cost1504
\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -30:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-85}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-110}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error10.2
Cost1368
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;x \leq -2 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error10.3
Cost1368
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-243}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error10.3
Cost1368
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := \left(y + z\right) \cdot 2\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-84}:\\ \;\;\;\;x \cdot t_2 + x \cdot t\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-244}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + t_2\right)\\ \end{array} \]
Alternative 5
Error10.2
Cost1368
\[\begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := \left(y + z\right) \cdot 2\\ \mathbf{if}\;x \leq -5 \cdot 10^{-85}:\\ \;\;\;\;x \cdot t_2 + x \cdot t\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y + t\right) + \left(y \cdot 5 + y \cdot x\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + t_2\right)\\ \end{array} \]
Alternative 6
Error0.1
Cost960
\[y \cdot 5 + x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) \]
Alternative 7
Error0.1
Cost960
\[y \cdot 5 + \left(x \cdot \left(\left(y + z\right) \cdot 2\right) + x \cdot t\right) \]
Alternative 8
Error33.0
Cost852
\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -800:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
Alternative 9
Error22.9
Cost845
\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-147} \lor \neg \left(x \leq 2.6 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 10
Error17.6
Cost845
\[\begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-139} \lor \neg \left(x \leq 4.5 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
Alternative 11
Error11.3
Cost841
\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-139} \lor \neg \left(x \leq 2.5 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
Alternative 12
Error27.1
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-139}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
Alternative 13
Error32.1
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-84}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
Alternative 14
Error33.2
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-145}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
Alternative 15
Error46.8
Cost192
\[x \cdot t \]

Error

Reproduce

herbie shell --seed 2022343 
(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)))