quadp (p42, positive)

Percentage Accurate: 52.3% → 83.9%

Time: 10.9s

Alternatives: 7

Speedup: 19.1×

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: 52.3% 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: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e+166)
   (/ (- b) a)
   (if (<= b 4.1e-129)
     (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+166) {
		tmp = -b / a;
	} else if (b <= 4.1e-129) {
		tmp = (sqrt(((b * b) - (4.0 * (a * c)))) - b) / (a * 2.0);
	} 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 <= (-3.8d+166)) then
        tmp = -b / a
    else if (b <= 4.1d-129) then
        tmp = (sqrt(((b * b) - (4.0d0 * (a * c)))) - b) / (a * 2.0d0)
    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 <= -3.8e+166) {
		tmp = -b / a;
	} else if (b <= 4.1e-129) {
		tmp = (Math.sqrt(((b * b) - (4.0 * (a * c)))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.8e+166:
		tmp = -b / a
	elif b <= 4.1e-129:
		tmp = (math.sqrt(((b * b) - (4.0 * (a * c)))) - b) / (a * 2.0)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e+166)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 4.1e-129)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c)))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.8e+166)
		tmp = -b / a;
	elseif (b <= 4.1e-129)
		tmp = (sqrt(((b * b) - (4.0 * (a * c)))) - b) / (a * 2.0);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e+166], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 4.1e-129], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000007e166

   1. Initial program 37.6%

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

   2. Taylor expanded in b around -inf 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   4. Simplified 95.7%

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

   if -3.80000000000000007e166 < b < 4.1e-129

   1. Initial program 90.8%

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

   if 4.1e-129 < b

   1. Initial program 16.2%

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

   2. Taylor expanded in b around inf 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

   4. Simplified 84.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 2: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-129}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6.6e-46)
   (- (/ c b) (/ b a))
   (if (<= b 2.05e-129)
     (/ (- (sqrt (* c (* a -4.0))) b) (* a 2.0))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.6e-46) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.05e-129) {
		tmp = (sqrt((c * (a * -4.0))) - b) / (a * 2.0);
	} 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 <= (-6.6d-46)) then
        tmp = (c / b) - (b / a)
    else if (b <= 2.05d-129) then
        tmp = (sqrt((c * (a * (-4.0d0)))) - b) / (a * 2.0d0)
    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 <= -6.6e-46) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.05e-129) {
		tmp = (Math.sqrt((c * (a * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6.6e-46:
		tmp = (c / b) - (b / a)
	elif b <= 2.05e-129:
		tmp = (math.sqrt((c * (a * -4.0))) - b) / (a * 2.0)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6.6e-46)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 2.05e-129)
		tmp = Float64(Float64(sqrt(Float64(c * Float64(a * -4.0))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6.6e-46)
		tmp = (c / b) - (b / a);
	elseif (b <= 2.05e-129)
		tmp = (sqrt((c * (a * -4.0))) - b) / (a * 2.0);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6.6e-46], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e-129], N[(N[(N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.60000000000000027e-46

   1. Initial program 69.0%

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

   2. Taylor expanded in b around -inf 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

   4. Simplified 90.0%

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

   if -6.60000000000000027e-46 < b < 2.05e-129

   1. Initial program 86.8%

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

   2. Taylor expanded in b around 0 74.4%

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

      1. associate-*r* 74.4%

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

   4. Simplified 74.4%

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

   if 2.05e-129 < b

   1. Initial program 16.2%

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

   2. Taylor expanded in b around inf 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

   4. Simplified 84.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-129}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 3: 67.3% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-310) (- (/ c b) (/ b a)) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = (c / b) - (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 <= (-2d-310)) then
        tmp = (c / b) - (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 <= -2e-310) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-310:
		tmp = (c / b) - (b / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-310)
		tmp = Float64(Float64(c / b) - 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 <= -2e-310)
		tmp = (c / b) - (b / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-310], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.999999999999994e-310

   1. Initial program 77.3%

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

   2. Taylor expanded in b around -inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   4. Simplified 67.8%

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

   if -1.999999999999994e-310 < b

   1. Initial program 25.6%

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

   2. Taylor expanded in b around inf 72.6%

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

      1. associate-*r/ 72.6%

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

      2. neg-mul-1 72.6%

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

   4. Simplified 72.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 4: 42.6% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 6.6e+57) (/ (- b) a) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 6.6e+57) {
		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 <= 6.6d+57) 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 <= 6.6e+57) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 6.6e+57:
		tmp = -b / a
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 6.6e+57)
		tmp = Float64(Float64(-b) / a);
	else
		tmp = Float64(c / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 6.6e+57)
		tmp = -b / a;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 6.6e+57], N[((-b) / a), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.6000000000000002e57

   1. Initial program 65.7%

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

   2. Taylor expanded in b around -inf 48.4%

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

      1. associate-*r/ 48.4%

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

      2. mul-1-neg 48.4%

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

   4. Simplified 48.4%

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

   if 6.6000000000000002e57 < 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. Step-by-step derivation

      1. add-sqr-sqrt 6.2%

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

      2. pow2 6.2%

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

      3. pow1/2 6.2%

         \[\leadsto \frac{\left(-b\right) + {\left(\sqrt{\color{blue}{{\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right)}^{0.5}}}\right)}^{2}}{2 \cdot a} \]

      4. sqrt-pow1 6.1%

         \[\leadsto \frac{\left(-b\right) + {\color{blue}{\left({\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2}}{2 \cdot a} \]

      5. fma-neg 6.2%

         \[\leadsto \frac{\left(-b\right) + {\left({\color{blue}{\left(\mathsf{fma}\left(b, b, -4 \cdot \left(a \cdot c\right)\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      6. distribute-lft-neg-in 6.2%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \color{blue}{\left(-4\right) \cdot \left(a \cdot c\right)}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      7. *-commutative 6.2%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \left(-4\right) \cdot \color{blue}{\left(c \cdot a\right)}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      8. associate-*r* 6.2%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \color{blue}{\left(\left(-4\right) \cdot c\right) \cdot a}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      9. metadata-eval 6.2%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \left(\color{blue}{-4} \cdot c\right) \cdot a\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      10. metadata-eval 6.2%

          \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)\right)}^{\color{blue}{0.25}}\right)}^{2}}{2 \cdot a} \]

   3. Applied egg-rr 6.2%

      \[\leadsto \frac{\left(-b\right) + \color{blue}{{\left({\left(\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)\right)}^{0.25}\right)}^{2}}}{2 \cdot a} \]

   4. Taylor expanded in b around -inf 1.9%

      \[\leadsto \frac{\color{blue}{2 \cdot \left(-1 \cdot b\right) + 2 \cdot \frac{a \cdot c}{b}}}{2 \cdot a} \]
   5. Step-by-step derivation

      1. mul-1-neg 1.9%

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

      2. distribute-lft-out 1.9%

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

      3. *-commutative 1.9%

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

      4. associate-*l/ 2.0%

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

      5. *-commutative 2.0%

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

   6. Simplified 2.0%

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

   7. Taylor expanded in b around 0 29.1%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 5: 67.1% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 9 \cdot 10^{-297}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 9e-297) (/ (- b) a) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 9e-297) {
		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 <= 9d-297) 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 <= 9e-297) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 9e-297:
		tmp = -b / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 9e-297)
		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 <= 9e-297)
		tmp = -b / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 9e-297], N[((-b) / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.99999999999999951e-297

   1. Initial program 77.4%

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

   2. Taylor expanded in b around -inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. mul-1-neg 67.3%

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

   4. Simplified 67.3%

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

   if 8.99999999999999951e-297 < b

   1. Initial program 25.0%

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

   2. Taylor expanded in b around inf 73.2%

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

      1. associate-*r/ 73.2%

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

      2. neg-mul-1 73.2%

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

   4. Simplified 73.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 9 \cdot 10^{-297}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 6: 12.4% accurate, 22.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 1.0) (* b c) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.0) {
		tmp = b * c;
	} 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 <= 1.0d0) then
        tmp = b * c
    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 <= 1.0) {
		tmp = b * c;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.0:
		tmp = b * c
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.0)
		tmp = Float64(b * c);
	else
		tmp = Float64(c / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.0)
		tmp = b * c;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.0], N[(b * c), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1

   1. Initial program 67.9%

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

   2. Taylor expanded in b around inf 8.2%

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

      1. associate-/l* 11.1%

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

   4. Simplified 11.1%

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

      1. add-cube-cbrt 11.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}} \cdot \sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}}\right) \cdot \sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}}} \]

      2. pow3 11.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}}\right)}^{3}} \]

      3. times-frac 11.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{-2}{2} \cdot \frac{\frac{a}{\frac{b}{c}}}{a}}}\right)}^{3} \]

      4. metadata-eval 11.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{-1} \cdot \frac{\frac{a}{\frac{b}{c}}}{a}}\right)}^{3} \]

      5. associate-/r/ 10.9%

         \[\leadsto {\left(\sqrt[3]{-1 \cdot \frac{\color{blue}{\frac{a}{b} \cdot c}}{a}}\right)}^{3} \]

   6. Applied egg-rr 10.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{-1 \cdot \frac{\frac{a}{b} \cdot c}{a}}\right)}^{3}} \]

   7. Taylor expanded in a around 0 6.5%

      \[\leadsto {\color{blue}{\left({\left(\frac{1 \cdot c}{b}\right)}^{0.3333333333333333} \cdot \sqrt[3]{-1}\right)}}^{3} \]

   9. Applied egg-rr 5.7%

      \[\leadsto \color{blue}{b \cdot c} \]

   if 1 < b

   1. Initial program 13.6%

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

      1. add-sqr-sqrt 9.0%

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

      2. pow2 9.0%

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

      3. pow1/2 9.0%

         \[\leadsto \frac{\left(-b\right) + {\left(\sqrt{\color{blue}{{\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right)}^{0.5}}}\right)}^{2}}{2 \cdot a} \]

      4. sqrt-pow1 9.0%

         \[\leadsto \frac{\left(-b\right) + {\color{blue}{\left({\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2}}{2 \cdot a} \]

      5. fma-neg 8.8%

         \[\leadsto \frac{\left(-b\right) + {\left({\color{blue}{\left(\mathsf{fma}\left(b, b, -4 \cdot \left(a \cdot c\right)\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      6. distribute-lft-neg-in 8.8%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \color{blue}{\left(-4\right) \cdot \left(a \cdot c\right)}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      7. *-commutative 8.8%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \left(-4\right) \cdot \color{blue}{\left(c \cdot a\right)}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      8. associate-*r* 8.8%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \color{blue}{\left(\left(-4\right) \cdot c\right) \cdot a}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      9. metadata-eval 8.8%

         \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \left(\color{blue}{-4} \cdot c\right) \cdot a\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{2 \cdot a} \]

      10. metadata-eval 8.8%

          \[\leadsto \frac{\left(-b\right) + {\left({\left(\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)\right)}^{\color{blue}{0.25}}\right)}^{2}}{2 \cdot a} \]

   3. Applied egg-rr 8.8%

      \[\leadsto \frac{\left(-b\right) + \color{blue}{{\left({\left(\mathsf{fma}\left(b, b, \left(-4 \cdot c\right) \cdot a\right)\right)}^{0.25}\right)}^{2}}}{2 \cdot a} \]

   4. Taylor expanded in b around -inf 2.2%

      \[\leadsto \frac{\color{blue}{2 \cdot \left(-1 \cdot b\right) + 2 \cdot \frac{a \cdot c}{b}}}{2 \cdot a} \]
   5. Step-by-step derivation

      1. mul-1-neg 2.2%

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

      2. distribute-lft-out 2.2%

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

      3. *-commutative 2.2%

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

      4. associate-*l/ 2.2%

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

      5. *-commutative 2.2%

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

   6. Simplified 2.2%

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

   7. Taylor expanded in b around 0 25.0%

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

4. Final simplification 10.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 7: 4.2% accurate, 38.7× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* b c))

C

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

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 * c
end function

Java

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

Python

def code(a, b, c):
	return b * c

Julia

function code(a, b, c)
	return Float64(b * c)
end

MATLAB

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

Wolfram

code[a_, b_, c_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 53.9%

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

2. Taylor expanded in b around inf 24.4%

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

   1. associate-/l* 27.0%

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

4. Simplified 27.0%

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

   1. add-cube-cbrt 26.8%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}} \cdot \sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}}\right) \cdot \sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}}} \]

   2. pow3 26.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{-2 \cdot \frac{a}{\frac{b}{c}}}{2 \cdot a}}\right)}^{3}} \]

   3. times-frac 26.8%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{-2}{2} \cdot \frac{\frac{a}{\frac{b}{c}}}{a}}}\right)}^{3} \]

   4. metadata-eval 26.8%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{-1} \cdot \frac{\frac{a}{\frac{b}{c}}}{a}}\right)}^{3} \]

   5. associate-/r/ 25.1%

      \[\leadsto {\left(\sqrt[3]{-1 \cdot \frac{\color{blue}{\frac{a}{b} \cdot c}}{a}}\right)}^{3} \]

6. Applied egg-rr 25.1%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{-1 \cdot \frac{\frac{a}{b} \cdot c}{a}}\right)}^{3}} \]

7. Taylor expanded in a around 0 17.3%

   \[\leadsto {\color{blue}{\left({\left(\frac{1 \cdot c}{b}\right)}^{0.3333333333333333} \cdot \sqrt[3]{-1}\right)}}^{3} \]

9. Applied egg-rr 4.7%

   \[\leadsto \color{blue}{b \cdot c} \]

10. Final simplification 4.7%

    \[\leadsto b \cdot c \]

Developer target: 99.7% accurate, 0.1× 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 2023312 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64
  :herbie-expected 10

  :herbie-target
  (if (< b 0.0) (/ (- (if (== (copysign a c) a) (* (sqrt (- (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot (/ b 2.0) (* (sqrt (fabs a)) (sqrt (fabs c))))) (/ b 2.0)) a) (/ (- c) (+ (/ b 2.0) (if (== (copysign a c) a) (* (sqrt (- (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot (/ b 2.0) (* (sqrt (fabs a)) (sqrt (fabs c))))))))

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