subtraction fraction

Average Error: 0.0 → 0.0

Time: 2.8s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (f + n) / (n - f)
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 (f + n) / (n - f);
}

Python

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

↓

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

Julia

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

MATLAB

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

↓

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

Wolfram

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]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.0
Cost	976

\[\begin{array}{l} t_0 := -2 \cdot \frac{n}{f} + -1\\ \mathbf{if}\;n \leq -2.6476397496637592 \cdot 10^{+63}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq -1.0465172999074706 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -7.709548087072705 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 388951867627.8923:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	16.7
Cost	976

\[\begin{array}{l} t_0 := 2 \cdot \frac{f}{n} + 1\\ t_1 := -2 \cdot \frac{n}{f} + -1\\ \mathbf{if}\;n \leq -2.6476397496637592 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -1.0465172999074706 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq -7.709548087072705 \cdot 10^{-51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 388951867627.8923:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	17.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;n \leq -1.1288238676881295 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq -1.0465172999074706 \cdot 10^{-13}:\\ \;\;\;\;-1\\ \mathbf{elif}\;n \leq -7.709548087072705 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 388951867627.8923:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	32.2
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022217 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))