Average Error: 0.0 → 0.0

Time: 10.2s

Precision: binary64

Cost: 448

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

↓

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

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

↓

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

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

↓

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

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 = (f + n) / (n - f)
end function

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[\frac{-\left(f + n\right)}{f - n} \]
Simplified0.0
\[\leadsto \color{blue}{\frac{f + n}{n - f}} \]
Proof

Alternatives

Alternative 1
Error	17.1
Cost	712

\[\begin{array}{l} t_0 := 2 \cdot \frac{f}{n} + 1\\ \mathbf{if}\;n \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 5.9 \cdot 10^{+103}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;n \leq -3.3 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 3.9 \cdot 10^{+77}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	31.9
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023010 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))