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

Average Error: 0.1 → 0.1

Time: 11.7s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (+ (* y (+ (* x y) 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) + 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) + 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) + 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) + 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(y * Float64(Float64(x * 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) + 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[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	28.0
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+236}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+252}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	27.6
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{+65}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+236}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+252}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	5.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-23} \lor \neg \left(z \leq 4.7 \cdot 10^{-33}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4
Error	12.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5
Error	30.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023055 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))