Alternative 1 | |
---|---|
Error | 0.5 |
Cost | 832 |
\[\frac{1}{x \cdot -0.125 + \left(0.5 + 2 \cdot \frac{1}{x}\right)}
\]
(FPCore (x) :precision binary64 (- (sqrt (+ 1.0 x)) 1.0))
(FPCore (x) :precision binary64 (/ x (+ 1.0 (sqrt (+ x 1.0)))))
double code(double x) { return sqrt((1.0 + x)) - 1.0; }
double code(double x) { return x / (1.0 + sqrt((x + 1.0))); }
real(8) function code(x) real(8), intent (in) :: x code = sqrt((1.0d0 + x)) - 1.0d0 end function
real(8) function code(x) real(8), intent (in) :: x code = x / (1.0d0 + sqrt((x + 1.0d0))) end function
public static double code(double x) { return Math.sqrt((1.0 + x)) - 1.0; }
public static double code(double x) { return x / (1.0 + Math.sqrt((x + 1.0))); }
def code(x): return math.sqrt((1.0 + x)) - 1.0
def code(x): return x / (1.0 + math.sqrt((x + 1.0)))
function code(x) return Float64(sqrt(Float64(1.0 + x)) - 1.0) end
function code(x) return Float64(x / Float64(1.0 + sqrt(Float64(x + 1.0)))) end
function tmp = code(x) tmp = sqrt((1.0 + x)) - 1.0; end
function tmp = code(x) tmp = x / (1.0 + sqrt((x + 1.0))); end
code[x_] := N[(N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]
code[x_] := N[(x / N[(1.0 + N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt{1 + x} - 1
\frac{x}{1 + \sqrt{x + 1}}
Results
Initial program 58.6
Applied egg-rr0.0
Final simplification0.0
Alternative 1 | |
---|---|
Error | 0.5 |
Cost | 832 |
Alternative 2 | |
---|---|
Error | 0.6 |
Cost | 448 |
Alternative 3 | |
---|---|
Error | 0.6 |
Cost | 448 |
Alternative 4 | |
---|---|
Error | 1.3 |
Cost | 192 |
herbie shell --seed 1
(FPCore (x)
:name "sqrt(1+x)-1"
:precision binary64
:pre (and (<= -1.0 x) (<= x 1.0))
(- (sqrt (+ 1.0 x)) 1.0))