(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 -1e+150)
(/ (- (hypot (* (/ c b) (* a 1.5)) b) b) (* a 3.0))
(if (<= b 3.5e-75)
(* (- (sqrt (fma b b (* c (* a -3.0)))) b) (/ (/ 1.0 a) 3.0))
(* (/ c b) -0.5))))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 <= -1e+150) {
tmp = (hypot(((c / b) * (a * 1.5)), b) - b) / (a * 3.0);
} else if (b <= 3.5e-75) {
tmp = (sqrt(fma(b, b, (c * (a * -3.0)))) - b) * ((1.0 / a) / 3.0);
} else {
tmp = (c / b) * -0.5;
}
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 <= -1e+150) tmp = Float64(Float64(hypot(Float64(Float64(c / b) * Float64(a * 1.5)), b) - b) / Float64(a * 3.0)); elseif (b <= 3.5e-75) tmp = Float64(Float64(sqrt(fma(b, b, Float64(c * Float64(a * -3.0)))) - b) * Float64(Float64(1.0 / a) / 3.0)); else tmp = Float64(Float64(c / b) * -0.5); end return 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, -1e+150], N[(N[(N[Sqrt[N[(N[(c / b), $MachinePrecision] * N[(a * 1.5), $MachinePrecision]), $MachinePrecision] ^ 2 + b ^ 2], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-75], N[(N[(N[Sqrt[N[(b * b + N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] * N[(N[(1.0 / a), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] * -0.5), $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 \cdot 10^{+150}:\\
\;\;\;\;\frac{\mathsf{hypot}\left(\frac{c}{b} \cdot \left(a \cdot 1.5\right), b\right) - b}{a \cdot 3}\\
\mathbf{elif}\;b \leq 3.5 \cdot 10^{-75}:\\
\;\;\;\;\left(\sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -3\right)\right)} - b\right) \cdot \frac{\frac{1}{a}}{3}\\
\mathbf{else}:\\
\;\;\;\;\frac{c}{b} \cdot -0.5\\
\end{array}
if b < -9.99999999999999981e149Initial program 61.9
Taylor expanded in b around -inf 10.9
Simplified2.8
Applied egg-rr2.9
if -9.99999999999999981e149 < b < 3.49999999999999985e-75Initial program 12.8
Simplified13.0
Applied egg-rr12.9
Applied egg-rr12.9
if 3.49999999999999985e-75 < b Initial program 52.1
Taylor expanded in b around inf 20.3
Simplified17.5
Applied egg-rr9.7
Final simplification10.5
| Alternative 1 | |
|---|---|
| Error | 10.5 |
| Cost | 7624 |
| Alternative 2 | |
|---|---|
| Error | 10.5 |
| Cost | 7624 |
| Alternative 3 | |
|---|---|
| Error | 13.9 |
| Cost | 7496 |
| Alternative 4 | |
|---|---|
| Error | 13.9 |
| Cost | 7368 |
| Alternative 5 | |
|---|---|
| Error | 13.8 |
| Cost | 7368 |
| Alternative 6 | |
|---|---|
| Error | 22.7 |
| Cost | 580 |
| Alternative 7 | |
|---|---|
| Error | 36.8 |
| Cost | 452 |
| Alternative 8 | |
|---|---|
| Error | 22.8 |
| Cost | 452 |
| Alternative 9 | |
|---|---|
| Error | 22.7 |
| Cost | 452 |
| Alternative 10 | |
|---|---|
| Error | 40.0 |
| Cost | 320 |
herbie shell --seed 2022291
(FPCore (a b c)
:name "Cubic critical"
:precision binary64
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))