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

Average Error: 0.0 → 0.0

Time: 5.1s

Precision: binary64

Cost: 704

Math

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

↓

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

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 (+ (* z t) (+ (* a b) (* 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 (z * t) + ((a * b) + (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 = (z * t) + ((a * b) + (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 (z * t) + ((a * b) + (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 (z * t) + ((a * b) + (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(z * t) + Float64(Float64(a * b) + 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 = (z * t) + ((a * b) + (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[(z * t), $MachinePrecision] + N[(N[(a * b), $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. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)} \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	35.6
Cost	1248

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5406307982697116 \cdot 10^{-67}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 1.5167315307053757 \cdot 10^{-203}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 1.344171999137543 \cdot 10^{-87}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 6.354518738739417 \cdot 10^{-7}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 145532068872.60223:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 2.5899427923798394 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+117}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 2
Error	15.0
Cost	976

\[\begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;t \leq -3.4806615369311467 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.453347472753344 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.0219529260341908 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	10.5
Cost	968

\[\begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -6.3930259599442986 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 3.5865632118185803 \cdot 10^{-138}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	35.6
Cost	720

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5406307982697116 \cdot 10^{-67}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 6.354518738739417 \cdot 10^{-7}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 145532068872.60223:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+117}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 5
Error	20.4
Cost	580

\[\begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6
Error	41.7
Cost	192

\[a \cdot b \]

Reproduce

herbie shell --seed 2022284 
(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)))