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

Average Error: 0.1 → 0.1

Time: 21.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 * y) * x)
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 * y) * x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

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

3. Applied egg-rr 0.1

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

Alternatives

Alternative 1
Error	17.8
Cost	648

\[\begin{array}{l} t_0 := \left(-x \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.0
Cost	648

\[\begin{array}{l} t_0 := \left(y \cdot x\right) \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.1
Cost	448

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

Alternative 4
Error	21.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))