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

Average Error: 0.1 → 0.1

Time: 2.8s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 5.1

   \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{1 + x \cdot y}{1 - {\left(x \cdot y\right)}^{2}}}} \]

3. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\frac{x}{\frac{1}{1 - x \cdot y}}} \]

4. Applied egg-rr 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2022210 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))