Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B

Average Accuracy: 100.0% → 100.0%

Time: 1.1s

Precision: binary64

Cost: 448

Math

\[x \cdot \left(1 - x \cdot 0.5\right) \]

↓

\[x - x \cdot \left(x \cdot 0.5\right) \]

FPCore

(FPCore (x) :precision binary64 (* x (- 1.0 (* x 0.5))))

↓

(FPCore (x) :precision binary64 (- x (* x (* x 0.5))))

C

double code(double x) {
	return x * (1.0 - (x * 0.5));
}

↓

double code(double x) {
	return x - (x * (x * 0.5));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (1.0d0 - (x * 0.5d0))
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - (x * (x * 0.5d0))
end function

Java

public static double code(double x) {
	return x * (1.0 - (x * 0.5));
}

↓

public static double code(double x) {
	return x - (x * (x * 0.5));
}

Python

def code(x):
	return x * (1.0 - (x * 0.5))

↓

def code(x):
	return x - (x * (x * 0.5))

Julia

function code(x)
	return Float64(x * Float64(1.0 - Float64(x * 0.5)))
end

↓

function code(x)
	return Float64(x - Float64(x * Float64(x * 0.5)))
end

MATLAB

function tmp = code(x)
	tmp = x * (1.0 - (x * 0.5));
end

↓

function tmp = code(x)
	tmp = x - (x * (x * 0.5));
end

Wolfram

code[x_] := N[(x * N[(1.0 - N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(x - N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(1 - x \cdot 0.5\right) \]

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{x + \left(x \cdot -0.5\right) \cdot x} \]
   Proof

   [Start] 100.0	\[ x \cdot \left(1 - x \cdot 0.5\right) \]
   cancel-sign-sub-inv [=>] 100.0	\[ x \cdot \color{blue}{\left(1 + \left(-x\right) \cdot 0.5\right)} \]
   distribute-rgt-in [=>] 100.0	\[ \color{blue}{1 \cdot x + \left(\left(-x\right) \cdot 0.5\right) \cdot x} \]
   *-un-lft-identity [<=] 100.0	\[ \color{blue}{x} + \left(\left(-x\right) \cdot 0.5\right) \cdot x \]
   distribute-lft-neg-in [<=] 100.0	\[ x + \color{blue}{\left(-x \cdot 0.5\right)} \cdot x \]
   distribute-rgt-neg-in [=>] 100.0	\[ x + \color{blue}{\left(x \cdot \left(-0.5\right)\right)} \cdot x \]
   metadata-eval [=>] 100.0	\[ x + \left(x \cdot \color{blue}{-0.5}\right) \cdot x \]

3. Final simplification 100.0%

   \[\leadsto x - x \cdot \left(x \cdot 0.5\right) \]

Alternatives

Alternative 1
Accuracy	97.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	448

\[x \cdot \left(1 - x \cdot 0.5\right) \]

Alternative 3
Accuracy	66.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))