(FPCore (a b c) :precision binary64 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))
(FPCore (a b c)
:precision binary64
(let* ((t_0 (* c (* a -3.0))) (t_1 (sqrt t_0)))
(if (<= b -1100000000000.0)
(/ b (* a -1.5))
(if (<= b 1e-200)
(/ 1.0 (* a (/ 3.0 (- (hypot t_1 b) b))))
(if (<= b 0.4)
(* (/ t_0 (+ b (hypot b t_1))) (/ 0.3333333333333333 a))
(/ (* c -0.5) 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 t_0 = c * (a * -3.0);
double t_1 = sqrt(t_0);
double tmp;
if (b <= -1100000000000.0) {
tmp = b / (a * -1.5);
} else if (b <= 1e-200) {
tmp = 1.0 / (a * (3.0 / (hypot(t_1, b) - b)));
} else if (b <= 0.4) {
tmp = (t_0 / (b + hypot(b, t_1))) * (0.3333333333333333 / a);
} else {
tmp = (c * -0.5) / b;
}
return tmp;
}
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 t_0 = c * (a * -3.0);
double t_1 = Math.sqrt(t_0);
double tmp;
if (b <= -1100000000000.0) {
tmp = b / (a * -1.5);
} else if (b <= 1e-200) {
tmp = 1.0 / (a * (3.0 / (Math.hypot(t_1, b) - b)));
} else if (b <= 0.4) {
tmp = (t_0 / (b + Math.hypot(b, t_1))) * (0.3333333333333333 / a);
} else {
tmp = (c * -0.5) / 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): t_0 = c * (a * -3.0) t_1 = math.sqrt(t_0) tmp = 0 if b <= -1100000000000.0: tmp = b / (a * -1.5) elif b <= 1e-200: tmp = 1.0 / (a * (3.0 / (math.hypot(t_1, b) - b))) elif b <= 0.4: tmp = (t_0 / (b + math.hypot(b, t_1))) * (0.3333333333333333 / a) else: tmp = (c * -0.5) / 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) t_0 = Float64(c * Float64(a * -3.0)) t_1 = sqrt(t_0) tmp = 0.0 if (b <= -1100000000000.0) tmp = Float64(b / Float64(a * -1.5)); elseif (b <= 1e-200) tmp = Float64(1.0 / Float64(a * Float64(3.0 / Float64(hypot(t_1, b) - b)))); elseif (b <= 0.4) tmp = Float64(Float64(t_0 / Float64(b + hypot(b, t_1))) * Float64(0.3333333333333333 / a)); else tmp = Float64(Float64(c * -0.5) / 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) t_0 = c * (a * -3.0); t_1 = sqrt(t_0); tmp = 0.0; if (b <= -1100000000000.0) tmp = b / (a * -1.5); elseif (b <= 1e-200) tmp = 1.0 / (a * (3.0 / (hypot(t_1, b) - b))); elseif (b <= 0.4) tmp = (t_0 / (b + hypot(b, t_1))) * (0.3333333333333333 / a); else tmp = (c * -0.5) / 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_] := Block[{t$95$0 = N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[t$95$0], $MachinePrecision]}, If[LessEqual[b, -1100000000000.0], N[(b / N[(a * -1.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-200], N[(1.0 / N[(a * N[(3.0 / N[(N[Sqrt[t$95$1 ^ 2 + b ^ 2], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.4], N[(N[(t$95$0 / N[(b + N[Sqrt[b ^ 2 + t$95$1 ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.3333333333333333 / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
\begin{array}{l}
t_0 := c \cdot \left(a \cdot -3\right)\\
t_1 := \sqrt{t_0}\\
\mathbf{if}\;b \leq -1100000000000:\\
\;\;\;\;\frac{b}{a \cdot -1.5}\\
\mathbf{elif}\;b \leq 10^{-200}:\\
\;\;\;\;\frac{1}{a \cdot \frac{3}{\mathsf{hypot}\left(t_1, b\right) - b}}\\
\mathbf{elif}\;b \leq 0.4:\\
\;\;\;\;\frac{t_0}{b + \mathsf{hypot}\left(b, t_1\right)} \cdot \frac{0.3333333333333333}{a}\\
\mathbf{else}:\\
\;\;\;\;\frac{c \cdot -0.5}{b}\\
\end{array}
Results
if b < -1.1e12Initial program 33.7
Simplified33.7
Taylor expanded in b around -inf 7.1
Simplified7.1
Applied egg-rr47.8
Applied egg-rr7.0
if -1.1e12 < b < 9.9999999999999998e-201Initial program 12.2
Simplified12.4
Applied egg-rr14.8
Applied egg-rr14.8
Applied egg-rr14.7
if 9.9999999999999998e-201 < b < 0.40000000000000002Initial program 30.2
Simplified30.3
Applied egg-rr30.9
Taylor expanded in c around 0 25.5
Simplified25.4
if 0.40000000000000002 < b Initial program 55.0
Simplified55.0
Applied egg-rr48.4
Applied egg-rr48.4
Taylor expanded in b around inf 64.0
Simplified6.0
Final simplification11.6
| Alternative 1 | |
|---|---|
| Error | 11.5 |
| Cost | 7624 |
| Alternative 2 | |
|---|---|
| Error | 14.9 |
| Cost | 7368 |
| Alternative 3 | |
|---|---|
| Error | 39.5 |
| Cost | 452 |
| Alternative 4 | |
|---|---|
| Error | 22.9 |
| Cost | 452 |
| Alternative 5 | |
|---|---|
| Error | 56.7 |
| Cost | 320 |
herbie shell --seed 2022311
(FPCore (a b c)
:name "Cubic critical"
:precision binary64
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))