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

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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) * (-0.5d0)) + x
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) * -0.5) + x;
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	448

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

Alternative 2
Error	21.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))