subtraction fraction

Average Error: 0.0 → 0.0

Time: 2.3s

Precision: binary64

Cost: 512

Math

\[\frac{-\left(f + n\right)}{f - n} \]

↓

\[\frac{\left(-n\right) - f}{f - n} \]

FPCore

(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))

↓

(FPCore (f n) :precision binary64 (/ (- (- n) f) (- f n)))

C

double code(double f, double n) {
	return -(f + n) / (f - n);
}

↓

double code(double f, double n) {
	return (-n - f) / (f - n);
}

Fortran

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = -(f + n) / (f - n)
end function

↓

real(8) function code(f, n)
    real(8), intent (in) :: f
    real(8), intent (in) :: n
    code = (-n - f) / (f - n)
end function

Java

public static double code(double f, double n) {
	return -(f + n) / (f - n);
}

↓

public static double code(double f, double n) {
	return (-n - f) / (f - n);
}

Python

def code(f, n):
	return -(f + n) / (f - n)

↓

def code(f, n):
	return (-n - f) / (f - n)

Julia

function code(f, n)
	return Float64(Float64(-Float64(f + n)) / Float64(f - n))
end

↓

function code(f, n)
	return Float64(Float64(Float64(-n) - f) / Float64(f - n))
end

MATLAB

function tmp = code(f, n)
	tmp = -(f + n) / (f - n);
end

↓

function tmp = code(f, n)
	tmp = (-n - f) / (f - n);
end

Wolfram

code[f_, n_] := N[((-N[(f + n), $MachinePrecision]) / N[(f - n), $MachinePrecision]), $MachinePrecision]

↓

code[f_, n_] := N[(N[((-n) - f), $MachinePrecision] / N[(f - n), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{-\left(f + n\right)}{f - n} \]

2. Final simplification 0.0

   \[\leadsto \frac{\left(-n\right) - f}{f - n} \]

Alternatives

Alternative 1
Error	0.0
Cost	448

\[\frac{f + n}{n - f} \]

Alternative 2
Error	18.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;f \leq -4.928140033601948 \cdot 10^{-129}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq 4.2399434910090636 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Reproduce

herbie shell --seed 2022289 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))