Linear.V3:$cdot from linear-1.19.1.3, B

Average Error: 0.0 → 0.0

Time: 4.1s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	30.0
Cost	1752

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.9761330102945274 \cdot 10^{+36}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5.313330851374238 \cdot 10^{-70}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -9.043797328819099 \cdot 10^{-163}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2.849338957755232 \cdot 10^{-211}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.7460505636471884 \cdot 10^{-126}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.0936144743594102 \cdot 10^{-16}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 2
Error	14.1
Cost	968

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.9761330102945274 \cdot 10^{+36}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.0936144743594102 \cdot 10^{-16}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 3
Error	9.2
Cost	968

\[\begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -3.7245213771211815 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.0936144743594102 \cdot 10^{-16}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	9.6
Cost	968

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.7245213771211815 \cdot 10^{+22}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.325764281842692 \cdot 10^{-20}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 5
Error	30.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.7245213771211815 \cdot 10^{+22}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.0936144743594102 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 6
Error	41.8
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  (+ (+ (* x y) (* z t)) (* a b)))