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

Average Error: 0.1 → 0.1

Time: 6.8s

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	27.4
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-58}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+102}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	10.6
Cost	976

\[\begin{array}{l} t_1 := t + y \cdot z\\ t_2 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-12}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 86000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	10.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+68} \lor \neg \left(y \leq 52000000000\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 4
Error	6.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+129} \lor \neg \left(z \leq 2850\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 5
Error	12.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+155} \lor \neg \left(y \leq 1.65 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6
Error	0.1
Cost	576

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

Alternative 7
Error	25.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 8
Error	30.1
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))