Examples.Basics.BasicTests:f1 from sbv-4.4

Average Error: 0.0 → 0.0

Time: 2.0s

Precision: binary64

Cost: 448

Math

\[\left(x + y\right) \cdot \left(x - y\right) \]

↓

\[\left(x + y\right) \cdot \left(x - y\right) \]

FPCore

(FPCore (x y) :precision binary64 (* (+ x y) (- x y)))

↓

(FPCore (x y) :precision binary64 (* (+ x y) (- x y)))

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

def code(x, y):
	return (x + y) * (x - y)

↓

def code(x, y):
	return (x + y) * (x - y)

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(x + y), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\left(x + y\right) \cdot \left(x - y\right) \]

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	13.3
Cost	1050

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-95} \lor \neg \left(x \leq -2.8 \cdot 10^{-116}\right) \land \left(x \leq 2 \cdot 10^{-144} \lor \neg \left(x \leq 8.5 \cdot 10^{-132}\right) \land x \leq 3.75 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	27.9
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022364 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f1 from sbv-4.4"
  :precision binary64
  (* (+ x y) (- x y)))