?

Average Error: 0.0 → 0.0
Time: 7.0s
Precision: binary64
Cost: 448

?

\[\left(-1000000000 \leq a \land a \leq 1000000000\right) \land \left(-1000000000 \leq b \land b \leq 1000000000\right)\]
\[a + \frac{1}{a - b} \]
↓
\[a + \frac{1}{a - b} \]
(FPCore (a b) :precision binary64 (+ a (/ 1.0 (- a b))))
↓
(FPCore (a b) :precision binary64 (+ a (/ 1.0 (- a b))))
double code(double a, double b) {
	return a + (1.0 / (a - b));
}
↓
double code(double a, double b) {
	return a + (1.0 / (a - b));
}

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a + (1.0d0 / (a - b))
end function
↓
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a + (1.0d0 / (a - b))
end function

public static double code(double a, double b) {
	return a + (1.0 / (a - b));
}
↓
public static double code(double a, double b) {
	return a + (1.0 / (a - b));
}

def code(a, b):
	return a + (1.0 / (a - b))
↓
def code(a, b):
	return a + (1.0 / (a - b))

function code(a, b)
	return Float64(a + Float64(1.0 / Float64(a - b)))
end
↓
function code(a, b)
	return Float64(a + Float64(1.0 / Float64(a - b)))
end

function tmp = code(a, b)
	tmp = a + (1.0 / (a - b));
end
↓
function tmp = code(a, b)
	tmp = a + (1.0 / (a - b));
end

code[a_, b_] := N[(a + N[(1.0 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[a_, b_] := N[(a + N[(1.0 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

a + \frac{1}{a - b}
↓
a + \frac{1}{a - b}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.0

    \[a + \frac{1}{a - b} \]

  2. Final simplification0.0

    \[\leadsto a + \frac{1}{a - b} \]

Alternatives

Alternative 1
Error16.7
Cost584
\[\begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-184}:\\ \;\;\;\;\frac{-1}{b}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-153}:\\ \;\;\;\;a - \frac{-1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{b}\\ \end{array} \]
Alternative 2
Error16.7
Cost584
\[\begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-185}:\\ \;\;\;\;a + \frac{-1}{b}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-153}:\\ \;\;\;\;a - \frac{-1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{b}\\ \end{array} \]
Alternative 3
Error17.6
Cost456
\[\begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{-1}{b}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-154}:\\ \;\;\;\;\frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{b}\\ \end{array} \]
Alternative 4
Error31.9
Cost324
\[\begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-33}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{b}\\ \end{array} \]
Alternative 5
Error60.5
Cost64
\[a \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (a b)
  :name "a + 1/(a - b)"
  :precision binary64
  :pre (and (and (<= -1000000000.0 a) (<= a 1000000000.0)) (and (<= -1000000000.0 b) (<= b 1000000000.0)))
  (+ a (/ 1.0 (- a b))))