Alternative 1 | |
---|---|
Error | 30.5 |
Cost | 13120 |
\[\sqrt{1 + x} - \sqrt{x}
\]
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))
(FPCore (x) :precision binary64 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
double code(double x) { return sqrt((x + 1.0)) - sqrt(x); }
double code(double x) { return 1.0 / (sqrt((1.0 + x)) + sqrt(x)); }
real(8) function code(x) real(8), intent (in) :: x code = sqrt((x + 1.0d0)) - sqrt(x) end function
real(8) function code(x) real(8), intent (in) :: x code = 1.0d0 / (sqrt((1.0d0 + x)) + sqrt(x)) end function
public static double code(double x) { return Math.sqrt((x + 1.0)) - Math.sqrt(x); }
public static double code(double x) { return 1.0 / (Math.sqrt((1.0 + x)) + Math.sqrt(x)); }
def code(x): return math.sqrt((x + 1.0)) - math.sqrt(x)
def code(x): return 1.0 / (math.sqrt((1.0 + x)) + math.sqrt(x))
function code(x) return Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) end
function code(x) return Float64(1.0 / Float64(sqrt(Float64(1.0 + x)) + sqrt(x))) end
function tmp = code(x) tmp = sqrt((x + 1.0)) - sqrt(x); end
function tmp = code(x) tmp = 1.0 / (sqrt((1.0 + x)) + sqrt(x)); end
code[x_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]
code[x_] := N[(1.0 / N[(N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt{x + 1} - \sqrt{x}
\frac{1}{\sqrt{1 + x} + \sqrt{x}}
Results
Initial program 30.5
Applied egg-rr0.4
Simplified0.4
[Start]0.4 | \[ \left(x + \left(1 - x\right)\right) \cdot \frac{1}{\sqrt{x + 1} + \sqrt{x}}
\] |
---|---|
*-commutative [=>]0.4 | \[ \color{blue}{\frac{1}{\sqrt{x + 1} + \sqrt{x}} \cdot \left(x + \left(1 - x\right)\right)}
\] |
associate-*l/ [=>]0.4 | \[ \color{blue}{\frac{1 \cdot \left(x + \left(1 - x\right)\right)}{\sqrt{x + 1} + \sqrt{x}}}
\] |
*-lft-identity [=>]0.4 | \[ \frac{\color{blue}{x + \left(1 - x\right)}}{\sqrt{x + 1} + \sqrt{x}}
\] |
+-commutative [=>]0.4 | \[ \frac{\color{blue}{\left(1 - x\right) + x}}{\sqrt{x + 1} + \sqrt{x}}
\] |
associate-+l- [=>]0.4 | \[ \frac{\color{blue}{1 - \left(x - x\right)}}{\sqrt{x + 1} + \sqrt{x}}
\] |
+-inverses [=>]0.4 | \[ \frac{1 - \color{blue}{0}}{\sqrt{x + 1} + \sqrt{x}}
\] |
metadata-eval [=>]0.4 | \[ \frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}
\] |
+-commutative [=>]0.4 | \[ \frac{1}{\sqrt{\color{blue}{1 + x}} + \sqrt{x}}
\] |
Final simplification0.4
Alternative 1 | |
---|---|
Error | 30.5 |
Cost | 13120 |
Alternative 2 | |
---|---|
Error | 56.1 |
Cost | 64 |
herbie shell --seed 1
(FPCore (x)
:name "sqrt(x+1)-sqrt(x)"
:precision binary64
:pre (and (<= 1000000000.0 x) (<= x 10000000000.0))
(- (sqrt (+ x 1.0)) (sqrt x)))