(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 -1.25e+91)
(/ (* b -0.6666666666666666) a)
(if (<= b 2.9e-167)
(/ (- (sqrt (+ (* b b) (* c (* a -3.0)))) 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 <= -1.25e+91) {
tmp = (b * -0.6666666666666666) / a;
} else if (b <= 2.9e-167) {
tmp = (sqrt(((b * b) + (c * (a * -3.0)))) - 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 <= (-1.25d+91)) then
tmp = (b * (-0.6666666666666666d0)) / a
else if (b <= 2.9d-167) then
tmp = (sqrt(((b * b) + (c * (a * (-3.0d0))))) - 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 <= -1.25e+91) {
tmp = (b * -0.6666666666666666) / a;
} else if (b <= 2.9e-167) {
tmp = (Math.sqrt(((b * b) + (c * (a * -3.0)))) - 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 <= -1.25e+91: tmp = (b * -0.6666666666666666) / a elif b <= 2.9e-167: tmp = (math.sqrt(((b * b) + (c * (a * -3.0)))) - 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 <= -1.25e+91) tmp = Float64(Float64(b * -0.6666666666666666) / a); elseif (b <= 2.9e-167) tmp = Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(c * Float64(a * -3.0)))) - 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 <= -1.25e+91) tmp = (b * -0.6666666666666666) / a; elseif (b <= 2.9e-167) tmp = (sqrt(((b * b) + (c * (a * -3.0)))) - 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, -1.25e+91], N[(N[(b * -0.6666666666666666), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 2.9e-167], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(c * N[(a * -3.0), $MachinePrecision]), $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 -1.25 \cdot 10^{+91}:\\
\;\;\;\;\frac{b \cdot -0.6666666666666666}{a}\\
\mathbf{elif}\;b \leq 2.9 \cdot 10^{-167}:\\
\;\;\;\;\frac{\sqrt{b \cdot b + c \cdot \left(a \cdot -3\right)} - b}{a \cdot 3}\\
\mathbf{else}:\\
\;\;\;\;-0.5 \cdot \frac{c}{b}\\
\end{array}
Results
if b < -1.2500000000000001e91Initial program 44.8
Simplified44.9
Applied egg-rr44.9
Applied egg-rr44.9
Applied egg-rr36.5
Taylor expanded in b around -inf 4.0
Simplified4.0
if -1.2500000000000001e91 < b < 2.90000000000000003e-167Initial program 11.9
if 2.90000000000000003e-167 < b Initial program 49.2
Taylor expanded in b around inf 14.2
Final simplification11.6
| Alternative 1 | |
|---|---|
| Error | 11.6 |
| Cost | 7624 |
| Alternative 2 | |
|---|---|
| Error | 14.6 |
| Cost | 7368 |
| Alternative 3 | |
|---|---|
| Error | 14.6 |
| Cost | 7368 |
| Alternative 4 | |
|---|---|
| Error | 14.6 |
| Cost | 7368 |
| Alternative 5 | |
|---|---|
| Error | 23.0 |
| Cost | 580 |
| Alternative 6 | |
|---|---|
| Error | 39.9 |
| Cost | 452 |
| Alternative 7 | |
|---|---|
| Error | 23.3 |
| Cost | 452 |
| Alternative 8 | |
|---|---|
| Error | 23.0 |
| Cost | 452 |
| Alternative 9 | |
|---|---|
| Error | 45.5 |
| Cost | 320 |
herbie shell --seed 2022289
(FPCore (a b c)
:name "Cubic critical"
:precision binary64
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))