Average Error: 0.0 → 0.0

Time: 2.1s

Precision: binary64

Cost: 320

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

↓

\[x \cdot x - x \]

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

↓

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

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

↓

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

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

x \cdot x - x

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

\[x \cdot x - x \]

Derivation

Initial program 0.0
\[x \cdot \left(x - 1\right) \]
Simplified0.0
\[\leadsto \color{blue}{x \cdot x - x} \]
Proof
(-.f64 (*.f64 x x) x): 0 points increase in error, 0 points decrease in error
(Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 x x) (neg.f64 x))): 0 points increase in error, 0 points decrease in error
(+.f64 (*.f64 x x) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 x))): 0 points increase in error, 0 points decrease in error
(+.f64 (*.f64 x x) (*.f64 (Rewrite<= metadata-eval (neg.f64 1)) x)): 0 points increase in error, 0 points decrease in error
(Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 x x) (*.f64 1 x))): 0 points increase in error, 0 points decrease in error
(Rewrite=> distribute-rgt-out--_binary64 (*.f64 x (-.f64 x 1))): 5 points increase in error, 3 points decrease in error
Final simplification0.0
\[\leadsto x \cdot x - x \]

Alternatives

Alternative 1
Error	2.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -58528585.50392605:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 2.2078869502073876 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	21.6
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2022308 
(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)))