(FPCore (a b c) :precision binary64 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))
(FPCore (a b c)
:precision binary64
(if (<= b -2.4e+95)
(/ b (* a -1.5))
(if (<= b 4.7e-67)
(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
(* -0.5 (/ c b)))))double code(double a, double b, double c) {
return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}
double code(double a, double b, double c) {
double tmp;
if (b <= -2.4e+95) {
tmp = b / (a * -1.5);
} else if (b <= 4.7e-67) {
tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
} else {
tmp = -0.5 * (c / b);
}
return tmp;
}
real(8) function code(a, b, c)
real(8), intent (in) :: a
real(8), intent (in) :: b
real(8), intent (in) :: c
code = (-b + sqrt(((b * b) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function
real(8) function code(a, b, c)
real(8), intent (in) :: a
real(8), intent (in) :: b
real(8), intent (in) :: c
real(8) :: tmp
if (b <= (-2.4d+95)) then
tmp = b / (a * (-1.5d0))
else if (b <= 4.7d-67) then
tmp = (sqrt(((b * b) - ((a * 3.0d0) * c))) - b) / (a * 3.0d0)
else
tmp = (-0.5d0) * (c / b)
end if
code = tmp
end function
public static double code(double a, double b, double c) {
return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}
public static double code(double a, double b, double c) {
double tmp;
if (b <= -2.4e+95) {
tmp = b / (a * -1.5);
} else if (b <= 4.7e-67) {
tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
} else {
tmp = -0.5 * (c / b);
}
return tmp;
}
def code(a, b, c): return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)
def code(a, b, c): tmp = 0 if b <= -2.4e+95: tmp = b / (a * -1.5) elif b <= 4.7e-67: tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0) else: tmp = -0.5 * (c / b) return tmp
function code(a, b, c) return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a)) end
function code(a, b, c) tmp = 0.0 if (b <= -2.4e+95) tmp = Float64(b / Float64(a * -1.5)); elseif (b <= 4.7e-67) tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0)); else tmp = Float64(-0.5 * Float64(c / b)); end return tmp end
function tmp = code(a, b, c) tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a); end
function tmp_2 = code(a, b, c) tmp = 0.0; if (b <= -2.4e+95) tmp = b / (a * -1.5); elseif (b <= 4.7e-67) tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0); else tmp = -0.5 * (c / b); end tmp_2 = tmp; end
code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]
code[a_, b_, c_] := If[LessEqual[b, -2.4e+95], N[(b / N[(a * -1.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e-67], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(a * 3.0), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]]]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
\begin{array}{l}
\mathbf{if}\;b \leq -2.4 \cdot 10^{+95}:\\
\;\;\;\;\frac{b}{a \cdot -1.5}\\
\mathbf{elif}\;b \leq 4.7 \cdot 10^{-67}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\
\mathbf{else}:\\
\;\;\;\;-0.5 \cdot \frac{c}{b}\\
\end{array}
Results
if b < -2.4e95Initial program 44.5
Simplified44.5
Taylor expanded in b around inf 45.4
Simplified45.4
Taylor expanded in b around -inf 4.3
Simplified4.2
Taylor expanded in b around 0 4.3
Simplified4.1
if -2.4e95 < b < 4.70000000000000004e-67Initial program 13.5
if 4.70000000000000004e-67 < b Initial program 53.7
Simplified53.7
Taylor expanded in b around inf 8.9
Final simplification10.2
| Alternative 1 | |
|---|---|
| Error | 10.3 |
| Cost | 7624 |
| Alternative 2 | |
|---|---|
| Error | 13.5 |
| Cost | 7368 |
| Alternative 3 | |
|---|---|
| Error | 13.5 |
| Cost | 7368 |
| Alternative 4 | |
|---|---|
| Error | 13.5 |
| Cost | 7368 |
| Alternative 5 | |
|---|---|
| Error | 23.2 |
| Cost | 452 |
| Alternative 6 | |
|---|---|
| Error | 23.2 |
| Cost | 452 |
| Alternative 7 | |
|---|---|
| Error | 23.2 |
| Cost | 452 |
| Alternative 8 | |
|---|---|
| Error | 40.2 |
| Cost | 320 |
| Alternative 9 | |
|---|---|
| Error | 56.1 |
| Cost | 64 |
herbie shell --seed 2022331
(FPCore (a b c)
:name "Cubic critical"
:precision binary64
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))