Examples.Basics.BasicTests:f2 from sbv-4.4

Average Error: 0.0 → 0.0

Time: 1.7s

Precision: binary64

Cost: 448

Math

\[x \cdot x - y \cdot y \]

↓

\[x \cdot x - y \cdot y \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[x \cdot x - y \cdot y \]

2. Final simplification 0.0

   \[\leadsto x \cdot x - y \cdot y \]

Alternatives

Alternative 1
Error	14.7
Cost	784

\[\begin{array}{l} t_0 := y \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -5.731263211366129 \cdot 10^{-29}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.850980348804523 \cdot 10^{-98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.5872514117791137 \cdot 10^{-76}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 9.656345218715828 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	28.4
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022310 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))