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

Average Error: 0.0 → 0.0

Time: 1.4s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x) {
	return x * (1.0 + (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 * (1.0d0 + (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 * (1.0 + (x * -0.5));
}

Python

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

↓

def code(x):
	return x * (1.0 + (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(1.0 + Float64(x * -0.5)))
end

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	1.8
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(x \cdot -0.5\right)\\ \mathbf{if}\;x \leq -11598.679629717424:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.9194664671186019:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	21.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))