Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2

Average Error: 0.0 → 0.0

Time: 1.3s

Precision: binary64

Cost: 320

Math

\[x \cdot \left(x - 1\right) \]

↓

\[x \cdot x - x \]

FPCore

(FPCore (x) :precision binary64 (* x (- x 1.0)))

↓

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

C

double code(double x) {
	return x * (x - 1.0);
}

↓

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

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (x - 1.0d0)
end function

↓

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

Java

public static double code(double x) {
	return x * (x - 1.0);
}

↓

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

Python

def code(x):
	return x * (x - 1.0)

↓

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

Julia

function code(x)
	return Float64(x * Float64(x - 1.0))
end

↓

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

MATLAB

function tmp = code(x)
	tmp = x * (x - 1.0);
end

↓

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

Wolfram

code[x_] := N[(x * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[x \cdot x - x \]

Derivation

1. Initial program 0.0

   \[x \cdot \left(x - 1\right) \]

2. Simplified 0.0

   \[\leadsto \color{blue}{x \cdot x - x} \]
   Proof

   [Start] 0.0	\[ x \cdot \left(x - 1\right) \]
   sub-neg [=>] 0.0	\[ x \cdot \color{blue}{\left(x + \left(-1\right)\right)} \]
   distribute-rgt-in [=>] 0.0	\[ \color{blue}{x \cdot x + \left(-1\right) \cdot x} \]
   metadata-eval [=>] 0.0	\[ x \cdot x + \color{blue}{-1} \cdot x \]
   mul-1-neg [=>] 0.0	\[ x \cdot x + \color{blue}{\left(-x\right)} \]
   unsub-neg [=>] 0.0	\[ \color{blue}{x \cdot x - x} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	1.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

\[x \cdot \left(x + -1\right) \]

Alternative 3
Error	20.7
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2022354 
(FPCore (x)
  :name "Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (* x x) x)

  (* x (- x 1.0)))