The quadratic formula (r1)

Percentage Accurate: 52.4% → 85.2%

Time: 11.6s

Alternatives: 9

Speedup: 2.5×

Specification

Math

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

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(Float64(4.0 * 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[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 52.4% accurate, 1.0× speedup

Math

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

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(Float64(4.0 * 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[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+158}:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{b}, a \cdot \frac{c}{b}, c\right)}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.1e+158)
   (- (/ b a))
   (if (<= b 3.1e-86)
     (/ (- (sqrt (- (* b b) (* c (* 4.0 a)))) b) (* a 2.0))
     (/ (fma (/ c b) (* a (/ c b)) c) (- b)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.1e+158) {
		tmp = -(b / a);
	} else if (b <= 3.1e-86) {
		tmp = (sqrt(((b * b) - (c * (4.0 * a)))) - b) / (a * 2.0);
	} else {
		tmp = fma((c / b), (a * (c / b)), c) / -b;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.1e+158)
		tmp = Float64(-Float64(b / a));
	elseif (b <= 3.1e-86)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(c * Float64(4.0 * a)))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(fma(Float64(c / b), Float64(a * Float64(c / b)), c) / Float64(-b));
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.1e+158], (-N[(b / a), $MachinePrecision]), If[LessEqual[b, 3.1e-86], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c / b), $MachinePrecision] * N[(a * N[(c / b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision] / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1000000000000001e158

   1. Initial program 27.2%

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

   3. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 97.9

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

   5. Applied rewrites 97.9%

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

   if -1.1000000000000001e158 < b < 3.09999999999999989e-86

   1. Initial program 83.3%

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

   if 3.09999999999999989e-86 < b

   1. Initial program 16.6%

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

   3. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 2.8

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

   5. Applied rewrites 2.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]
   7. 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. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      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

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 75.2

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

   8. Applied rewrites 75.2%

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

   10. Applied rewrites 90.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+158}:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{b}, a \cdot \frac{c}{b}, c\right)}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+158}:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{b}, a \cdot \frac{c}{b}, c\right)}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.1e+158)
   (- (/ b a))
   (if (<= b 3.1e-86)
     (* (/ -0.5 a) (- b (sqrt (fma a (* c -4.0) (* b b)))))
     (/ (fma (/ c b) (* a (/ c b)) c) (- b)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.1e+158) {
		tmp = -(b / a);
	} else if (b <= 3.1e-86) {
		tmp = (-0.5 / a) * (b - sqrt(fma(a, (c * -4.0), (b * b))));
	} else {
		tmp = fma((c / b), (a * (c / b)), c) / -b;
	}
	return tmp;
}

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.1e+158)
		tmp = Float64(-Float64(b / a));
	elseif (b <= 3.1e-86)
		tmp = Float64(Float64(-0.5 / a) * Float64(b - sqrt(fma(a, Float64(c * -4.0), Float64(b * b)))));
	else
		tmp = Float64(fma(Float64(c / b), Float64(a * Float64(c / b)), c) / Float64(-b));
	end
	return tmp
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.1e+158], (-N[(b / a), $MachinePrecision]), If[LessEqual[b, 3.1e-86], N[(N[(-0.5 / a), $MachinePrecision] * N[(b - N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision] + N[(b * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c / b), $MachinePrecision] * N[(a * N[(c / b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision] / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1000000000000001e158

   1. Initial program 39.1%

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

   3. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -1.1000000000000001e158 < b < 3.09999999999999989e-86

   1. Initial program 81.5%

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

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\frac{-0.5}{a} \cdot \left(b - \sqrt{\mathsf{fma}\left(a, -4 \cdot c, b \cdot b\right)}\right)} \]

   if 3.09999999999999989e-86 < b

   1. Initial program 18.7%

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

   3. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 2.6

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

   5. Applied rewrites 2.6%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]
   7. 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. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      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

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 70.7

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

   8. Applied rewrites 70.7%

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

   10. Applied rewrites 84.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+158}:\\ \;\;\;\;-\frac{b}{a}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{b}, a \cdot \frac{c}{b}, c\right)}{-b}\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\\ \mathbf{if}\;b < 0:\\ \;\;\;\;\frac{\left(-b\right) + t\_0}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) - t\_0}{2 \cdot a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (if (< b 0.0)
     (/ (+ (- b) t_0) (* 2.0 a))
     (/ c (* a (/ (- (- b) t_0) (* 2.0 a)))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - ((4.0 * a) * c)));
	double tmp;
	if (b < 0.0) {
		tmp = (-b + t_0) / (2.0 * a);
	} else {
		tmp = c / (a * ((-b - t_0) / (2.0 * a)));
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((b * b) - ((4.0d0 * a) * c)))
    if (b < 0.0d0) then
        tmp = (-b + t_0) / (2.0d0 * a)
    else
        tmp = c / (a * ((-b - t_0) / (2.0d0 * a)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.sqrt(((b * b) - ((4.0 * a) * c)));
	double tmp;
	if (b < 0.0) {
		tmp = (-b + t_0) / (2.0 * a);
	} else {
		tmp = c / (a * ((-b - t_0) / (2.0 * a)));
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - ((4.0 * a) * c)))
	tmp = 0
	if b < 0.0:
		tmp = (-b + t_0) / (2.0 * a)
	else:
		tmp = c / (a * ((-b - t_0) / (2.0 * a)))
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))
	tmp = 0.0
	if (b < 0.0)
		tmp = Float64(Float64(Float64(-b) + t_0) / Float64(2.0 * a));
	else
		tmp = Float64(c / Float64(a * Float64(Float64(Float64(-b) - t_0) / Float64(2.0 * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = sqrt(((b * b) - ((4.0 * a) * c)));
	tmp = 0.0;
	if (b < 0.0)
		tmp = (-b + t_0) / (2.0 * a);
	else
		tmp = c / (a * ((-b - t_0) / (2.0 * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[Less[b, 0.0], N[(N[((-b) + t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(c / N[(a * N[(N[((-b) - t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024225 
(FPCore (a b c)
  :name "The quadratic formula (r1)"
  :precision binary64

  :alt
  (! :herbie-platform default (let ((d (- (* b b) (* (* 4 a) c)))) (let ((r1 (/ (+ (- b) (sqrt d)) (* 2 a)))) (let ((r2 (/ (- (- b) (sqrt d)) (* 2 a)))) (if (< b 0) r1 (/ c (* a r2)))))))

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