quadp (p42, positive)

Percentage Accurate: 52.2% → 85.2%

Time: 6.9s

Alternatives: 7

Speedup: 2.5×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Fortran

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) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Fortran

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) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+156}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{b}{a}, 2 \cdot a, -2 \cdot \sqrt{\mathsf{fma}\left(c \cdot -4, a, b \cdot b\right)}\right)}{-2 \cdot \left(2 \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(\frac{a}{b} \cdot c, \frac{c}{b}, c\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e+156)
   (/ (- b) a)
   (if (<= b 5e-46)
     (/
      (fma (/ b a) (* 2.0 a) (* -2.0 (sqrt (fma (* c -4.0) a (* b b)))))
      (* -2.0 (* 2.0 a)))
     (/ (- (fma (* (/ a b) c) (/ c b) c)) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+156) {
		tmp = -b / a;
	} else if (b <= 5e-46) {
		tmp = fma((b / a), (2.0 * a), (-2.0 * sqrt(fma((c * -4.0), a, (b * b))))) / (-2.0 * (2.0 * a));
	} else {
		tmp = -fma(((a / b) * c), (c / b), c) / b;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e+156)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 5e-46)
		tmp = Float64(fma(Float64(b / a), Float64(2.0 * a), Float64(-2.0 * sqrt(fma(Float64(c * -4.0), a, Float64(b * b))))) / Float64(-2.0 * Float64(2.0 * a)));
	else
		tmp = Float64(Float64(-fma(Float64(Float64(a / b) * c), Float64(c / b), c)) / b);
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e+156], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 5e-46], N[(N[(N[(b / a), $MachinePrecision] * N[(2.0 * a), $MachinePrecision] + N[(-2.0 * N[Sqrt[N[(N[(c * -4.0), $MachinePrecision] * a + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-2.0 * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[(N[(N[(a / b), $MachinePrecision] * c), $MachinePrecision] * N[(c / b), $MachinePrecision] + c), $MachinePrecision]) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000024e156

   1. Initial program 44.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

      4. lower-neg.f64 100.0

         \[\leadsto \frac{\color{blue}{-b}}{a} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{-b}{a}} \]

   if -3.80000000000000024e156 < b < 4.99999999999999992e-46

   1. Initial program 80.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]

   6. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{b}{a}, 2 \cdot a, -2 \cdot \sqrt{\mathsf{fma}\left(c \cdot -4, a, b \cdot b\right)}\right)}{-2 \cdot \left(2 \cdot a\right)}} \]

   if 4.99999999999999992e-46 < b

   1. Initial program 11.6%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 11.6%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(c\right)\right)} + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}} + \left(\mathsf{neg}\left(c\right)\right)}}{b} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{a \cdot {c}^{2}}{{b}^{2}}\right)\right)} + \left(\mathsf{neg}\left(c\right)\right)}{b} \]

      5. distribute-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(\left(\frac{a \cdot {c}^{2}}{{b}^{2}} + c\right)\right)}}{b} \]

      6. lower-neg.f64 N/A

         \[\leadsto \frac{\color{blue}{-\left(\frac{a \cdot {c}^{2}}{{b}^{2}} + c\right)}}{b} \]

      7. *-commutative N/A

         \[\leadsto \frac{-\left(\frac{\color{blue}{{c}^{2} \cdot a}}{{b}^{2}} + c\right)}{b} \]

      8. unpow2 N/A

         \[\leadsto \frac{-\left(\frac{{c}^{2} \cdot a}{\color{blue}{b \cdot b}} + c\right)}{b} \]

      9. times-frac N/A

         \[\leadsto \frac{-\left(\color{blue}{\frac{{c}^{2}}{b} \cdot \frac{a}{b}} + c\right)}{b} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(\frac{{c}^{2}}{b}, \frac{a}{b}, c\right)}}{b} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{-\mathsf{fma}\left(\color{blue}{\frac{{c}^{2}}{b}}, \frac{a}{b}, c\right)}{b} \]

      12. unpow2 N/A

          \[\leadsto \frac{-\mathsf{fma}\left(\frac{\color{blue}{c \cdot c}}{b}, \frac{a}{b}, c\right)}{b} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{-\mathsf{fma}\left(\frac{\color{blue}{c \cdot c}}{b}, \frac{a}{b}, c\right)}{b} \]

      14. lower-/.f64 72.5

          \[\leadsto \frac{-\mathsf{fma}\left(\frac{c \cdot c}{b}, \color{blue}{\frac{a}{b}}, c\right)}{b} \]

   7. Applied rewrites 72.5%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(\frac{c \cdot c}{b}, \frac{a}{b}, c\right)}{b}} \]
   8. Step-by-step derivation

   9. Applied rewrites 88.4%

      \[\leadsto \frac{-\mathsf{fma}\left(\frac{a}{b} \cdot c, \frac{c}{b}, c\right)}{b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+156}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-46}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(c \cdot -4, a, b \cdot b\right)}}{-2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(\frac{a}{b} \cdot c, \frac{c}{b}, c\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e+156)
   (/ (- b) a)
   (if (<= b 5e-46)
     (/ (- b (sqrt (fma (* c -4.0) a (* b b)))) (* -2.0 a))
     (/ (- (fma (* (/ a b) c) (/ c b) c)) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+156) {
		tmp = -b / a;
	} else if (b <= 5e-46) {
		tmp = (b - sqrt(fma((c * -4.0), a, (b * b)))) / (-2.0 * a);
	} else {
		tmp = -fma(((a / b) * c), (c / b), c) / b;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e+156)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 5e-46)
		tmp = Float64(Float64(b - sqrt(fma(Float64(c * -4.0), a, Float64(b * b)))) / Float64(-2.0 * a));
	else
		tmp = Float64(Float64(-fma(Float64(Float64(a / b) * c), Float64(c / b), c)) / b);
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e+156], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 5e-46], N[(N[(b - N[Sqrt[N[(N[(c * -4.0), $MachinePrecision] * a + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(-2.0 * a), $MachinePrecision]), $MachinePrecision], N[((-N[(N[(N[(a / b), $MachinePrecision] * c), $MachinePrecision] * N[(c / b), $MachinePrecision] + c), $MachinePrecision]) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000024e156

   1. Initial program 44.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

      4. lower-neg.f64 100.0

         \[\leadsto \frac{\color{blue}{-b}}{a} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{-b}{a}} \]

   if -3.80000000000000024e156 < b < 4.99999999999999992e-46

   1. Initial program 80.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(c \cdot a\right) + b \cdot b}}}{-2 \cdot a} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{-4 \cdot \left(c \cdot a\right) + \color{blue}{b \cdot b}}}{-2 \cdot a} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(c \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}}{-2 \cdot a} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{-4 \cdot \color{blue}{\left(c \cdot a\right)} - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}{-2 \cdot a} \]

      5. associate-*r* N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{\left(-4 \cdot c\right) \cdot a} - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}{-2 \cdot a} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{\left(-4 \cdot c\right)} \cdot a - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}{-2 \cdot a} \]

      7. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{\left(-4 \cdot c\right) \cdot a + b \cdot b}}}{-2 \cdot a} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{\left(-4 \cdot c\right) \cdot a + \color{blue}{b \cdot b}}}{-2 \cdot a} \]

      9. lift-fma.f64 80.7

         \[\leadsto \frac{b - \sqrt{\color{blue}{\mathsf{fma}\left(-4 \cdot c, a, b \cdot b\right)}}}{-2 \cdot a} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{b - \sqrt{\mathsf{fma}\left(\color{blue}{-4 \cdot c}, a, b \cdot b\right)}}{-2 \cdot a} \]

      11. *-commutative N/A

          \[\leadsto \frac{b - \sqrt{\mathsf{fma}\left(\color{blue}{c \cdot -4}, a, b \cdot b\right)}}{-2 \cdot a} \]

      12. lower-*.f64 80.7

          \[\leadsto \frac{b - \sqrt{\mathsf{fma}\left(\color{blue}{c \cdot -4}, a, b \cdot b\right)}}{-2 \cdot a} \]

   6. Applied rewrites 80.7%

      \[\leadsto \frac{\color{blue}{b - \sqrt{\mathsf{fma}\left(c \cdot -4, a, b \cdot b\right)}}}{-2 \cdot a} \]

   if 4.99999999999999992e-46 < b

   1. Initial program 11.6%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 11.6%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(c\right)\right)} + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}} + \left(\mathsf{neg}\left(c\right)\right)}}{b} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{a \cdot {c}^{2}}{{b}^{2}}\right)\right)} + \left(\mathsf{neg}\left(c\right)\right)}{b} \]

      5. distribute-neg-out N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(\left(\frac{a \cdot {c}^{2}}{{b}^{2}} + c\right)\right)}}{b} \]

      6. lower-neg.f64 N/A

         \[\leadsto \frac{\color{blue}{-\left(\frac{a \cdot {c}^{2}}{{b}^{2}} + c\right)}}{b} \]

      7. *-commutative N/A

         \[\leadsto \frac{-\left(\frac{\color{blue}{{c}^{2} \cdot a}}{{b}^{2}} + c\right)}{b} \]

      8. unpow2 N/A

         \[\leadsto \frac{-\left(\frac{{c}^{2} \cdot a}{\color{blue}{b \cdot b}} + c\right)}{b} \]

      9. times-frac N/A

         \[\leadsto \frac{-\left(\color{blue}{\frac{{c}^{2}}{b} \cdot \frac{a}{b}} + c\right)}{b} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{-\color{blue}{\mathsf{fma}\left(\frac{{c}^{2}}{b}, \frac{a}{b}, c\right)}}{b} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{-\mathsf{fma}\left(\color{blue}{\frac{{c}^{2}}{b}}, \frac{a}{b}, c\right)}{b} \]

      12. unpow2 N/A

          \[\leadsto \frac{-\mathsf{fma}\left(\frac{\color{blue}{c \cdot c}}{b}, \frac{a}{b}, c\right)}{b} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{-\mathsf{fma}\left(\frac{\color{blue}{c \cdot c}}{b}, \frac{a}{b}, c\right)}{b} \]

      14. lower-/.f64 72.5

          \[\leadsto \frac{-\mathsf{fma}\left(\frac{c \cdot c}{b}, \color{blue}{\frac{a}{b}}, c\right)}{b} \]

   7. Applied rewrites 72.5%

      \[\leadsto \color{blue}{\frac{-\mathsf{fma}\left(\frac{c \cdot c}{b}, \frac{a}{b}, c\right)}{b}} \]
   8. Step-by-step derivation

   9. Applied rewrites 88.4%

      \[\leadsto \frac{-\mathsf{fma}\left(\frac{a}{b} \cdot c, \frac{c}{b}, c\right)}{b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+156}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(c \cdot -4, a, b \cdot b\right)}}{-2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e+156)
   (/ (- b) a)
   (if (<= b 4.5e-46)
     (/ (- b (sqrt (fma (* c -4.0) a (* b b)))) (* -2.0 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+156) {
		tmp = -b / a;
	} else if (b <= 4.5e-46) {
		tmp = (b - sqrt(fma((c * -4.0), a, (b * b)))) / (-2.0 * a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e+156)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 4.5e-46)
		tmp = Float64(Float64(b - sqrt(fma(Float64(c * -4.0), a, Float64(b * b)))) / Float64(-2.0 * a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e+156], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 4.5e-46], N[(N[(b - N[Sqrt[N[(N[(c * -4.0), $MachinePrecision] * a + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(-2.0 * a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000024e156

   1. Initial program 44.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

      4. lower-neg.f64 100.0

         \[\leadsto \frac{\color{blue}{-b}}{a} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{-b}{a}} \]

   if -3.80000000000000024e156 < b < 4.50000000000000001e-46

   1. Initial program 80.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(c \cdot a\right) + b \cdot b}}}{-2 \cdot a} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{-4 \cdot \left(c \cdot a\right) + \color{blue}{b \cdot b}}}{-2 \cdot a} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(c \cdot a\right) - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}}{-2 \cdot a} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{-4 \cdot \color{blue}{\left(c \cdot a\right)} - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}{-2 \cdot a} \]

      5. associate-*r* N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{\left(-4 \cdot c\right) \cdot a} - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}{-2 \cdot a} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{\left(-4 \cdot c\right)} \cdot a - \left(\mathsf{neg}\left(b\right)\right) \cdot b}}{-2 \cdot a} \]

      7. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{\left(-4 \cdot c\right) \cdot a + b \cdot b}}}{-2 \cdot a} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{\left(-4 \cdot c\right) \cdot a + \color{blue}{b \cdot b}}}{-2 \cdot a} \]

      9. lift-fma.f64 80.7

         \[\leadsto \frac{b - \sqrt{\color{blue}{\mathsf{fma}\left(-4 \cdot c, a, b \cdot b\right)}}}{-2 \cdot a} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{b - \sqrt{\mathsf{fma}\left(\color{blue}{-4 \cdot c}, a, b \cdot b\right)}}{-2 \cdot a} \]

      11. *-commutative N/A

          \[\leadsto \frac{b - \sqrt{\mathsf{fma}\left(\color{blue}{c \cdot -4}, a, b \cdot b\right)}}{-2 \cdot a} \]

      12. lower-*.f64 80.7

          \[\leadsto \frac{b - \sqrt{\mathsf{fma}\left(\color{blue}{c \cdot -4}, a, b \cdot b\right)}}{-2 \cdot a} \]

   6. Applied rewrites 80.7%

      \[\leadsto \frac{\color{blue}{b - \sqrt{\mathsf{fma}\left(c \cdot -4, a, b \cdot b\right)}}}{-2 \cdot a} \]

   if 4.50000000000000001e-46 < b

   1. Initial program 11.6%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot c}{b}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(c\right)}}{b} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(c\right)}{b}} \]

      4. lower-neg.f64 88.4

         \[\leadsto \frac{\color{blue}{-c}}{b} \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\frac{-c}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+156}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e+156)
   (/ (- b) a)
   (if (<= b 4.5e-46)
     (/ (- b (sqrt (fma -4.0 (* c a) (* b b)))) (* -2.0 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+156) {
		tmp = -b / a;
	} else if (b <= 4.5e-46) {
		tmp = (b - sqrt(fma(-4.0, (c * a), (b * b)))) / (-2.0 * a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e+156)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 4.5e-46)
		tmp = Float64(Float64(b - sqrt(fma(-4.0, Float64(c * a), Float64(b * b)))) / Float64(-2.0 * a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e+156], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 4.5e-46], N[(N[(b - N[Sqrt[N[(-4.0 * N[(c * a), $MachinePrecision] + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(-2.0 * a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000024e156

   1. Initial program 44.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

      4. lower-neg.f64 100.0

         \[\leadsto \frac{\color{blue}{-b}}{a} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{-b}{a}} \]

   if -3.80000000000000024e156 < b < 4.50000000000000001e-46

   1. Initial program 80.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]

   if 4.50000000000000001e-46 < b

   1. Initial program 11.6%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot c}{b}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(c\right)}}{b} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(c\right)}{b}} \]

      4. lower-neg.f64 88.4

         \[\leadsto \frac{\color{blue}{-c}}{b} \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\frac{-c}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0077:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-46}:\\ \;\;\;\;\frac{b - \sqrt{-4 \cdot \left(a \cdot c\right)}}{-2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -0.0077)
   (/ (- b) a)
   (if (<= b 1.15e-46)
     (/ (- b (sqrt (* -4.0 (* a c)))) (* -2.0 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -0.0077) {
		tmp = -b / a;
	} else if (b <= 1.15e-46) {
		tmp = (b - sqrt((-4.0 * (a * c)))) / (-2.0 * a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

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 <= (-0.0077d0)) then
        tmp = -b / a
    else if (b <= 1.15d-46) then
        tmp = (b - sqrt(((-4.0d0) * (a * c)))) / ((-2.0d0) * a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -0.0077) {
		tmp = -b / a;
	} else if (b <= 1.15e-46) {
		tmp = (b - Math.sqrt((-4.0 * (a * c)))) / (-2.0 * a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -0.0077:
		tmp = -b / a
	elif b <= 1.15e-46:
		tmp = (b - math.sqrt((-4.0 * (a * c)))) / (-2.0 * a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -0.0077)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 1.15e-46)
		tmp = Float64(Float64(b - sqrt(Float64(-4.0 * Float64(a * c)))) / Float64(-2.0 * a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -0.0077)
		tmp = -b / a;
	elseif (b <= 1.15e-46)
		tmp = (b - sqrt((-4.0 * (a * c)))) / (-2.0 * a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -0.0077], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 1.15e-46], N[(N[(b - N[Sqrt[N[(-4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(-2.0 * a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0077000000000000002

   1. Initial program 59.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

      4. lower-neg.f64 97.1

         \[\leadsto \frac{\color{blue}{-b}}{a} \]

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\frac{-b}{a}} \]

   if -0.0077000000000000002 < b < 1.15e-46

   1. Initial program 77.3%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   4. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\frac{b - \sqrt{\mathsf{fma}\left(-4, c \cdot a, b \cdot b\right)}}{-2 \cdot a}} \]

   5. Taylor expanded in a around inf

      \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(a \cdot c\right)}}}{-2 \cdot a} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(a \cdot c\right)}}}{-2 \cdot a} \]

      2. lower-*.f64 65.0

         \[\leadsto \frac{b - \sqrt{-4 \cdot \color{blue}{\left(a \cdot c\right)}}}{-2 \cdot a} \]

   7. Applied rewrites 65.0%

      \[\leadsto \frac{b - \sqrt{\color{blue}{-4 \cdot \left(a \cdot c\right)}}}{-2 \cdot a} \]

   if 1.15e-46 < b

   1. Initial program 11.6%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot c}{b}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(c\right)}}{b} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(c\right)}{b}} \]

      4. lower-neg.f64 88.4

         \[\leadsto \frac{\color{blue}{-c}}{b} \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\frac{-c}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 66.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-310) (/ (- b) a) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

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 <= (-5d-310)) then
        tmp = -b / a
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-310:
		tmp = -b / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-310)
		tmp = Float64(Float64(-b) / a);
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-310)
		tmp = -b / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-310], N[((-b) / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.999999999999985e-310

   1. Initial program 69.6%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

      4. lower-neg.f64 67.5

         \[\leadsto \frac{\color{blue}{-b}}{a} \]

   5. Applied rewrites 67.5%

      \[\leadsto \color{blue}{\frac{-b}{a}} \]

   if -4.999999999999985e-310 < b

   1. Initial program 33.4%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot c}{b}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(c\right)}}{b} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(c\right)}{b}} \]

      4. lower-neg.f64 61.5

         \[\leadsto \frac{\color{blue}{-c}}{b} \]

   5. Applied rewrites 61.5%

      \[\leadsto \color{blue}{\frac{-c}{b}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 35.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{-b}{a} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (/ (- b) a))

C

double code(double a, double b, double c) {
	return -b / a;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = -b / a
end function

Java

public static double code(double a, double b, double c) {
	return -b / a;
}

Python

def code(a, b, c):
	return -b / a

Julia

function code(a, b, c)
	return Float64(Float64(-b) / a)
end

MATLAB

function tmp = code(a, b, c)
	tmp = -b / a;
end

Wolfram

code[a_, b_, c_] := N[((-b) / a), $MachinePrecision]

Derivation

1. Initial program 50.1%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]
2. Add Preprocessing

3. Taylor expanded in b around -inf

   \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

      \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

   2. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{-1 \cdot b}{a}} \]

   3. mul-1-neg N/A

      \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(b\right)}}{a} \]

   4. lower-neg.f64 32.7

      \[\leadsto \frac{\color{blue}{-b}}{a} \]

5. Applied rewrites 32.7%

   \[\leadsto \color{blue}{\frac{-b}{a}} \]
6. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{b}{2}\right|\\ t_1 := \sqrt{\left|a\right|} \cdot \sqrt{\left|c\right|}\\ t_2 := \begin{array}{l} \mathbf{if}\;\mathsf{copysign}\left(a, c\right) = a:\\ \;\;\;\;\sqrt{t\_0 - t\_1} \cdot \sqrt{t\_0 + t\_1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{hypot}\left(\frac{b}{2}, t\_1\right)\\ \end{array}\\ \mathbf{if}\;b < 0:\\ \;\;\;\;\frac{t\_2 - \frac{b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{\frac{b}{2} + t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (fabs (/ b 2.0)))
        (t_1 (* (sqrt (fabs a)) (sqrt (fabs c))))
        (t_2
         (if (== (copysign a c) a)
           (* (sqrt (- t_0 t_1)) (sqrt (+ t_0 t_1)))
           (hypot (/ b 2.0) t_1))))
   (if (< b 0.0) (/ (- t_2 (/ b 2.0)) a) (/ (- c) (+ (/ b 2.0) t_2)))))

C

double code(double a, double b, double c) {
	double t_0 = fabs((b / 2.0));
	double t_1 = sqrt(fabs(a)) * sqrt(fabs(c));
	double tmp;
	if (copysign(a, c) == a) {
		tmp = sqrt((t_0 - t_1)) * sqrt((t_0 + t_1));
	} else {
		tmp = hypot((b / 2.0), t_1);
	}
	double t_2 = tmp;
	double tmp_1;
	if (b < 0.0) {
		tmp_1 = (t_2 - (b / 2.0)) / a;
	} else {
		tmp_1 = -c / ((b / 2.0) + t_2);
	}
	return tmp_1;
}

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.abs((b / 2.0));
	double t_1 = Math.sqrt(Math.abs(a)) * Math.sqrt(Math.abs(c));
	double tmp;
	if (Math.copySign(a, c) == a) {
		tmp = Math.sqrt((t_0 - t_1)) * Math.sqrt((t_0 + t_1));
	} else {
		tmp = Math.hypot((b / 2.0), t_1);
	}
	double t_2 = tmp;
	double tmp_1;
	if (b < 0.0) {
		tmp_1 = (t_2 - (b / 2.0)) / a;
	} else {
		tmp_1 = -c / ((b / 2.0) + t_2);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = math.fabs((b / 2.0))
	t_1 = math.sqrt(math.fabs(a)) * math.sqrt(math.fabs(c))
	tmp = 0
	if math.copysign(a, c) == a:
		tmp = math.sqrt((t_0 - t_1)) * math.sqrt((t_0 + t_1))
	else:
		tmp = math.hypot((b / 2.0), t_1)
	t_2 = tmp
	tmp_1 = 0
	if b < 0.0:
		tmp_1 = (t_2 - (b / 2.0)) / a
	else:
		tmp_1 = -c / ((b / 2.0) + t_2)
	return tmp_1

Julia

function code(a, b, c)
	t_0 = abs(Float64(b / 2.0))
	t_1 = Float64(sqrt(abs(a)) * sqrt(abs(c)))
	tmp = 0.0
	if (copysign(a, c) == a)
		tmp = Float64(sqrt(Float64(t_0 - t_1)) * sqrt(Float64(t_0 + t_1)));
	else
		tmp = hypot(Float64(b / 2.0), t_1);
	end
	t_2 = tmp
	tmp_1 = 0.0
	if (b < 0.0)
		tmp_1 = Float64(Float64(t_2 - Float64(b / 2.0)) / a);
	else
		tmp_1 = Float64(Float64(-c) / Float64(Float64(b / 2.0) + t_2));
	end
	return tmp_1
end

MATLAB

function tmp_3 = code(a, b, c)
	t_0 = abs((b / 2.0));
	t_1 = sqrt(abs(a)) * sqrt(abs(c));
	tmp = 0.0;
	if ((sign(c) * abs(a)) == a)
		tmp = sqrt((t_0 - t_1)) * sqrt((t_0 + t_1));
	else
		tmp = hypot((b / 2.0), t_1);
	end
	t_2 = tmp;
	tmp_2 = 0.0;
	if (b < 0.0)
		tmp_2 = (t_2 - (b / 2.0)) / a;
	else
		tmp_2 = -c / ((b / 2.0) + t_2);
	end
	tmp_3 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Abs[N[(b / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[N[Abs[a], $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[Abs[c], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = If[Equal[N[With[{TMP1 = Abs[a], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], a], N[(N[Sqrt[N[(t$95$0 - t$95$1), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(t$95$0 + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(b / 2.0), $MachinePrecision] ^ 2 + t$95$1 ^ 2], $MachinePrecision]]}, If[Less[b, 0.0], N[(N[(t$95$2 - N[(b / 2.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-c) / N[(N[(b / 2.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2024343 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64
  :herbie-expected 10

  :alt
  (! :herbie-platform default (let ((sqtD (let ((x (* (sqrt (fabs a)) (sqrt (fabs c))))) (if (== (copysign a c) a) (* (sqrt (- (fabs (/ b 2)) x)) (sqrt (+ (fabs (/ b 2)) x))) (hypot (/ b 2) x))))) (if (< b 0) (/ (- sqtD (/ b 2)) a) (/ (- c) (+ (/ b 2) sqtD)))))

  (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))