Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Average Error: 0.1 → 0.1

Time: 10.2s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))

↓

(FPCore (x y z t) :precision binary64 (+ (+ (* y (* x y)) (* y z)) t))

C

double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

↓

double code(double x, double y, double z, double t) {
	return ((y * (x * y)) + (y * z)) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * y) + z) * y) + t
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((y * (x * y)) + (y * z)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

↓

public static double code(double x, double y, double z, double t) {
	return ((y * (x * y)) + (y * z)) + t;
}

Python

def code(x, y, z, t):
	return (((x * y) + z) * y) + t

↓

def code(x, y, z, t):
	return ((y * (x * y)) + (y * z)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * y) + z) * y) + t)
end

↓

function code(x, y, z, t)
	return Float64(Float64(Float64(y * Float64(x * y)) + Float64(y * z)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * y) + z) * y) + t;
end

↓

function tmp = code(x, y, z, t)
	tmp = ((y * (x * y)) + (y * z)) + t;
end

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\left(\left(x \cdot y\right) \cdot y + z \cdot y\right)} + t \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	12.5
Cost	1108

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot y + z\right)\\ t_2 := t + y \cdot z\\ \mathbf{if}\;t \leq -4.959385800530276 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.6069934447118557 \cdot 10^{-65}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;t \leq -8.35570235170745 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8044151725848973 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3358121268724357 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	25.2
Cost	720

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6142807226805107 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.6546399022149054 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.980149922310444 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.0177127986932875 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3
Error	7.9
Cost	712

\[\begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;z \leq -262.3362583228705:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.736178620154878 \cdot 10^{-55}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	5.2
Cost	712

\[\begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;z \leq -262.3362583228705:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3635984051604335 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \left(x \cdot y\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	13.5
Cost	584

\[\begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	0.1
Cost	576

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

Alternative 7
Error	30.1
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))