Main:bigenough1 from B

Average Accuracy: 100.0% → 100.0%

Time: 1.1s

Precision: binary64

Cost: 320

Math

\[x + x \cdot x \]

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

   \[x + x \cdot x \]

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(x + 1\right) \cdot x} \]
   Proof

   [Start] 100.0	\[ x + x \cdot x \]
   distribute-rgt1-in [=>] 100.0	\[ \color{blue}{\left(x + 1\right) \cdot x} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	97.3%
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
Accuracy	66.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023130 
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))