quad2p (problem 3.2.1, positive)

Percentage Accurate: 51.9% → 85.6%

Time: 14.1s

Alternatives: 7

Speedup: 11.2×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))

C

double code(double a, double b_2, double c) {
	return (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a
end function

Java

public static double code(double a, double b_2, double c) {
	return (-b_2 + Math.sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Python

def code(a, b_2, c):
	return (-b_2 + math.sqrt(((b_2 * b_2) - (a * c)))) / a

Julia

function code(a, b_2, c)
	return Float64(Float64(Float64(-b_2) + sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c)))) / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[(N[((-b$95$2) + N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))

C

double code(double a, double b_2, double c) {
	return (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a
end function

Java

public static double code(double a, double b_2, double c) {
	return (-b_2 + Math.sqrt(((b_2 * b_2) - (a * c)))) / a;
}

Python

def code(a, b_2, c):
	return (-b_2 + math.sqrt(((b_2 * b_2) - (a * c)))) / a

Julia

function code(a, b_2, c)
	return Float64(Float64(Float64(-b_2) + sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c)))) / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = (-b_2 + sqrt(((b_2 * b_2) - (a * c)))) / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[(N[((-b$95$2) + N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq 1.65 \cdot 10^{-88}:\\ \;\;\;\;\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -5e+101)
   (/ (* b_2 -2.0) a)
   (if (<= b_2 1.65e-88)
     (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
     (/ (* c -0.5) b_2))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -5e+101) {
		tmp = (b_2 * -2.0) / a;
	} else if (b_2 <= 1.65e-88) {
		tmp = (sqrt(((b_2 * b_2) - (a * c))) - b_2) / a;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-5d+101)) then
        tmp = (b_2 * (-2.0d0)) / a
    else if (b_2 <= 1.65d-88) then
        tmp = (sqrt(((b_2 * b_2) - (a * c))) - b_2) / a
    else
        tmp = (c * (-0.5d0)) / b_2
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -5e+101) {
		tmp = (b_2 * -2.0) / a;
	} else if (b_2 <= 1.65e-88) {
		tmp = (Math.sqrt(((b_2 * b_2) - (a * c))) - b_2) / a;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -5e+101:
		tmp = (b_2 * -2.0) / a
	elif b_2 <= 1.65e-88:
		tmp = (math.sqrt(((b_2 * b_2) - (a * c))) - b_2) / a
	else:
		tmp = (c * -0.5) / b_2
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -5e+101)
		tmp = Float64(Float64(b_2 * -2.0) / a);
	elseif (b_2 <= 1.65e-88)
		tmp = Float64(Float64(sqrt(Float64(Float64(b_2 * b_2) - Float64(a * c))) - b_2) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -5e+101)
		tmp = (b_2 * -2.0) / a;
	elseif (b_2 <= 1.65e-88)
		tmp = (sqrt(((b_2 * b_2) - (a * c))) - b_2) / a;
	else
		tmp = (c * -0.5) / b_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -5e+101], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b$95$2, 1.65e-88], N[(N[(N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b$95$2), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -4.99999999999999989e101

   1. Initial program 45.9%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 45.9%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 45.9%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 45.9%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around -inf 96.4%

      \[\leadsto \frac{\color{blue}{-2 \cdot b\_2}}{a} \]
   6. Step-by-step derivation

      1. *-commutative 96.4%

         \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   7. Simplified 96.4%

      \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   if -4.99999999999999989e101 < b_2 < 1.64999999999999997e-88

   1. Initial program 78.0%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 78.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 78.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   if 1.64999999999999997e-88 < b_2

   1. Initial program 15.0%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 15.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 15.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 15.0%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around inf 88.4%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b\_2}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.4%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot c}{b\_2}} \]

      2. *-commutative 88.4%

         \[\leadsto \frac{\color{blue}{c \cdot -0.5}}{b\_2} \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{c \cdot -0.5}{b\_2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq 1.65 \cdot 10^{-88}:\\ \;\;\;\;\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b\_2 \cdot -2}{a}\\ t_1 := \frac{\sqrt{a \cdot \left(-c\right)} - b\_2}{a}\\ \mathbf{if}\;b\_2 \leq -2.1 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;b\_2 \leq -6.4 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b\_2 \leq -1.05 \cdot 10^{-130}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;b\_2 \leq 4.9 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (let* ((t_0 (/ (* b_2 -2.0) a)) (t_1 (/ (- (sqrt (* a (- c))) b_2) a)))
   (if (<= b_2 -2.1e-54)
     t_0
     (if (<= b_2 -6.4e-109)
       t_1
       (if (<= b_2 -1.05e-130)
         t_0
         (if (<= b_2 4.9e-89) t_1 (/ (* c -0.5) b_2)))))))

C

double code(double a, double b_2, double c) {
	double t_0 = (b_2 * -2.0) / a;
	double t_1 = (sqrt((a * -c)) - b_2) / a;
	double tmp;
	if (b_2 <= -2.1e-54) {
		tmp = t_0;
	} else if (b_2 <= -6.4e-109) {
		tmp = t_1;
	} else if (b_2 <= -1.05e-130) {
		tmp = t_0;
	} else if (b_2 <= 4.9e-89) {
		tmp = t_1;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (b_2 * (-2.0d0)) / a
    t_1 = (sqrt((a * -c)) - b_2) / a
    if (b_2 <= (-2.1d-54)) then
        tmp = t_0
    else if (b_2 <= (-6.4d-109)) then
        tmp = t_1
    else if (b_2 <= (-1.05d-130)) then
        tmp = t_0
    else if (b_2 <= 4.9d-89) then
        tmp = t_1
    else
        tmp = (c * (-0.5d0)) / b_2
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double t_0 = (b_2 * -2.0) / a;
	double t_1 = (Math.sqrt((a * -c)) - b_2) / a;
	double tmp;
	if (b_2 <= -2.1e-54) {
		tmp = t_0;
	} else if (b_2 <= -6.4e-109) {
		tmp = t_1;
	} else if (b_2 <= -1.05e-130) {
		tmp = t_0;
	} else if (b_2 <= 4.9e-89) {
		tmp = t_1;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	t_0 = (b_2 * -2.0) / a
	t_1 = (math.sqrt((a * -c)) - b_2) / a
	tmp = 0
	if b_2 <= -2.1e-54:
		tmp = t_0
	elif b_2 <= -6.4e-109:
		tmp = t_1
	elif b_2 <= -1.05e-130:
		tmp = t_0
	elif b_2 <= 4.9e-89:
		tmp = t_1
	else:
		tmp = (c * -0.5) / b_2
	return tmp

Julia

function code(a, b_2, c)
	t_0 = Float64(Float64(b_2 * -2.0) / a)
	t_1 = Float64(Float64(sqrt(Float64(a * Float64(-c))) - b_2) / a)
	tmp = 0.0
	if (b_2 <= -2.1e-54)
		tmp = t_0;
	elseif (b_2 <= -6.4e-109)
		tmp = t_1;
	elseif (b_2 <= -1.05e-130)
		tmp = t_0;
	elseif (b_2 <= 4.9e-89)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * -0.5) / b_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	t_0 = (b_2 * -2.0) / a;
	t_1 = (sqrt((a * -c)) - b_2) / a;
	tmp = 0.0;
	if (b_2 <= -2.1e-54)
		tmp = t_0;
	elseif (b_2 <= -6.4e-109)
		tmp = t_1;
	elseif (b_2 <= -1.05e-130)
		tmp = t_0;
	elseif (b_2 <= 4.9e-89)
		tmp = t_1;
	else
		tmp = (c * -0.5) / b_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := Block[{t$95$0 = N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Sqrt[N[(a * (-c)), $MachinePrecision]], $MachinePrecision] - b$95$2), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b$95$2, -2.1e-54], t$95$0, If[LessEqual[b$95$2, -6.4e-109], t$95$1, If[LessEqual[b$95$2, -1.05e-130], t$95$0, If[LessEqual[b$95$2, 4.9e-89], t$95$1, N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -2.1e-54 or -6.4000000000000003e-109 < b_2 < -1.05000000000000001e-130

   1. Initial program 67.2%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 67.2%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 67.2%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around -inf 90.1%

      \[\leadsto \frac{\color{blue}{-2 \cdot b\_2}}{a} \]
   6. Step-by-step derivation

      1. *-commutative 90.1%

         \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   7. Simplified 90.1%

      \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   if -2.1e-54 < b_2 < -6.4000000000000003e-109 or -1.05000000000000001e-130 < b_2 < 4.9e-89

   1. Initial program 68.8%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 68.8%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around 0 65.4%

      \[\leadsto \frac{\sqrt{\color{blue}{-1 \cdot \left(a \cdot c\right)}} - b\_2}{a} \]
   6. Step-by-step derivation

      1. associate-*r* 65.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(-1 \cdot a\right) \cdot c}} - b\_2}{a} \]

      2. neg-mul-1 65.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(-a\right)} \cdot c} - b\_2}{a} \]

      3. *-commutative 65.4%

         \[\leadsto \frac{\sqrt{\color{blue}{c \cdot \left(-a\right)}} - b\_2}{a} \]

   7. Simplified 65.4%

      \[\leadsto \frac{\sqrt{\color{blue}{c \cdot \left(-a\right)}} - b\_2}{a} \]

   if 4.9e-89 < b_2

   1. Initial program 15.0%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 15.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 15.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 15.0%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around inf 88.4%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b\_2}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.4%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot c}{b\_2}} \]

      2. *-commutative 88.4%

         \[\leadsto \frac{\color{blue}{c \cdot -0.5}}{b\_2} \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{c \cdot -0.5}{b\_2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -2.1 \cdot 10^{-54}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq -6.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(-c\right)} - b\_2}{a}\\ \mathbf{elif}\;b\_2 \leq -1.05 \cdot 10^{-130}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq 4.9 \cdot 10^{-89}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(-c\right)} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b\_2 \cdot -2}{a}\\ t_1 := \frac{\sqrt{a \cdot \left(-c\right)}}{a}\\ \mathbf{if}\;b\_2 \leq -8.2 \cdot 10^{-57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;b\_2 \leq -4.2 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b\_2 \leq -4 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;b\_2 \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (let* ((t_0 (/ (* b_2 -2.0) a)) (t_1 (/ (sqrt (* a (- c))) a)))
   (if (<= b_2 -8.2e-57)
     t_0
     (if (<= b_2 -4.2e-109)
       t_1
       (if (<= b_2 -4e-147)
         t_0
         (if (<= b_2 4.5e-89) t_1 (/ (* c -0.5) b_2)))))))

C

double code(double a, double b_2, double c) {
	double t_0 = (b_2 * -2.0) / a;
	double t_1 = sqrt((a * -c)) / a;
	double tmp;
	if (b_2 <= -8.2e-57) {
		tmp = t_0;
	} else if (b_2 <= -4.2e-109) {
		tmp = t_1;
	} else if (b_2 <= -4e-147) {
		tmp = t_0;
	} else if (b_2 <= 4.5e-89) {
		tmp = t_1;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (b_2 * (-2.0d0)) / a
    t_1 = sqrt((a * -c)) / a
    if (b_2 <= (-8.2d-57)) then
        tmp = t_0
    else if (b_2 <= (-4.2d-109)) then
        tmp = t_1
    else if (b_2 <= (-4d-147)) then
        tmp = t_0
    else if (b_2 <= 4.5d-89) then
        tmp = t_1
    else
        tmp = (c * (-0.5d0)) / b_2
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double t_0 = (b_2 * -2.0) / a;
	double t_1 = Math.sqrt((a * -c)) / a;
	double tmp;
	if (b_2 <= -8.2e-57) {
		tmp = t_0;
	} else if (b_2 <= -4.2e-109) {
		tmp = t_1;
	} else if (b_2 <= -4e-147) {
		tmp = t_0;
	} else if (b_2 <= 4.5e-89) {
		tmp = t_1;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	t_0 = (b_2 * -2.0) / a
	t_1 = math.sqrt((a * -c)) / a
	tmp = 0
	if b_2 <= -8.2e-57:
		tmp = t_0
	elif b_2 <= -4.2e-109:
		tmp = t_1
	elif b_2 <= -4e-147:
		tmp = t_0
	elif b_2 <= 4.5e-89:
		tmp = t_1
	else:
		tmp = (c * -0.5) / b_2
	return tmp

Julia

function code(a, b_2, c)
	t_0 = Float64(Float64(b_2 * -2.0) / a)
	t_1 = Float64(sqrt(Float64(a * Float64(-c))) / a)
	tmp = 0.0
	if (b_2 <= -8.2e-57)
		tmp = t_0;
	elseif (b_2 <= -4.2e-109)
		tmp = t_1;
	elseif (b_2 <= -4e-147)
		tmp = t_0;
	elseif (b_2 <= 4.5e-89)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * -0.5) / b_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	t_0 = (b_2 * -2.0) / a;
	t_1 = sqrt((a * -c)) / a;
	tmp = 0.0;
	if (b_2 <= -8.2e-57)
		tmp = t_0;
	elseif (b_2 <= -4.2e-109)
		tmp = t_1;
	elseif (b_2 <= -4e-147)
		tmp = t_0;
	elseif (b_2 <= 4.5e-89)
		tmp = t_1;
	else
		tmp = (c * -0.5) / b_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := Block[{t$95$0 = N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[N[(a * (-c)), $MachinePrecision]], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b$95$2, -8.2e-57], t$95$0, If[LessEqual[b$95$2, -4.2e-109], t$95$1, If[LessEqual[b$95$2, -4e-147], t$95$0, If[LessEqual[b$95$2, 4.5e-89], t$95$1, N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -8.2000000000000003e-57 or -4.19999999999999992e-109 < b_2 < -3.9999999999999999e-147

   1. Initial program 67.9%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 67.9%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 67.9%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around -inf 89.3%

      \[\leadsto \frac{\color{blue}{-2 \cdot b\_2}}{a} \]
   6. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   7. Simplified 89.3%

      \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   if -8.2000000000000003e-57 < b_2 < -4.19999999999999992e-109 or -3.9999999999999999e-147 < b_2 < 4.4999999999999999e-89

   1. Initial program 67.8%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 67.8%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. prod-diff 67.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\mathsf{fma}\left(b\_2, b\_2, -c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)}} - b\_2}{a} \]

      2. *-commutative 67.4%

         \[\leadsto \frac{\sqrt{\mathsf{fma}\left(b\_2, b\_2, -\color{blue}{a \cdot c}\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      3. fmm-def 67.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(b\_2 \cdot b\_2 - a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      4. prod-diff 67.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(\mathsf{fma}\left(b\_2, b\_2, -c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      5. *-commutative 67.4%

         \[\leadsto \frac{\sqrt{\left(\mathsf{fma}\left(b\_2, b\_2, -\color{blue}{a \cdot c}\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      6. fmm-def 67.4%

         \[\leadsto \frac{\sqrt{\left(\color{blue}{\left(b\_2 \cdot b\_2 - a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      7. associate-+l+ 67.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(b\_2 \cdot b\_2 - a \cdot c\right) + \left(\mathsf{fma}\left(-c, a, c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)}} - b\_2}{a} \]

      8. pow2 67.4%

         \[\leadsto \frac{\sqrt{\left(\color{blue}{{b\_2}^{2}} - a \cdot c\right) + \left(\mathsf{fma}\left(-c, a, c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      9. *-commutative 67.4%

         \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(-c, a, \color{blue}{a \cdot c}\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      10. fma-undefine 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\color{blue}{\left(\left(-c\right) \cdot a + a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      11. distribute-lft-neg-in 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\left(\color{blue}{\left(-c \cdot a\right)} + a \cdot c\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      12. *-commutative 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\left(\left(-\color{blue}{a \cdot c}\right) + a \cdot c\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      13. distribute-rgt-neg-in 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\left(\color{blue}{a \cdot \left(-c\right)} + a \cdot c\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      14. fma-define 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\color{blue}{\mathsf{fma}\left(a, -c, a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      15. *-commutative 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \mathsf{fma}\left(-c, a, \color{blue}{a \cdot c}\right)\right)} - b\_2}{a} \]

      16. fma-undefine 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \color{blue}{\left(\left(-c\right) \cdot a + a \cdot c\right)}\right)} - b\_2}{a} \]

      17. distribute-lft-neg-in 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \left(\color{blue}{\left(-c \cdot a\right)} + a \cdot c\right)\right)} - b\_2}{a} \]

      18. *-commutative 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \left(\left(-\color{blue}{a \cdot c}\right) + a \cdot c\right)\right)} - b\_2}{a} \]

      19. distribute-rgt-neg-in 67.4%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \left(\color{blue}{a \cdot \left(-c\right)} + a \cdot c\right)\right)} - b\_2}{a} \]

   6. Applied egg-rr 67.4%

      \[\leadsto \frac{\sqrt{\color{blue}{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \mathsf{fma}\left(a, -c, a \cdot c\right)\right)}} - b\_2}{a} \]
   7. Step-by-step derivation

      1. associate-+l- 67.4%

         \[\leadsto \frac{\sqrt{\color{blue}{{b\_2}^{2} - \left(a \cdot c - \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \mathsf{fma}\left(a, -c, a \cdot c\right)\right)\right)}} - b\_2}{a} \]

      2. count-2 67.4%

         \[\leadsto \frac{\sqrt{{b\_2}^{2} - \left(a \cdot c - \color{blue}{2 \cdot \mathsf{fma}\left(a, -c, a \cdot c\right)}\right)} - b\_2}{a} \]

   8. Simplified 67.4%

      \[\leadsto \frac{\sqrt{\color{blue}{{b\_2}^{2} - \left(a \cdot c - 2 \cdot \mathsf{fma}\left(a, -c, a \cdot c\right)\right)}} - b\_2}{a} \]

   9. Taylor expanded in b_2 around 0 63.6%

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

       1. associate-*l/ 63.7%

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

       2. *-lft-identity 63.7%

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

       3. distribute-lft1-in 63.7%

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

       4. metadata-eval 63.7%

          \[\leadsto \frac{\sqrt{2 \cdot \left(\color{blue}{0} \cdot \left(a \cdot c\right)\right) - a \cdot c}}{a} \]

       5. mul0-lft 64.1%

          \[\leadsto \frac{\sqrt{2 \cdot \color{blue}{0} - a \cdot c}}{a} \]

       6. metadata-eval 64.1%

          \[\leadsto \frac{\sqrt{\color{blue}{0} - a \cdot c}}{a} \]

       7. neg-sub0 64.1%

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

       8. distribute-rgt-neg-out 64.1%

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

   11. Simplified 64.1%

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

   if 4.4999999999999999e-89 < b_2

   1. Initial program 15.0%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 15.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 15.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 15.0%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around inf 88.4%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b\_2}} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.4%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot c}{b\_2}} \]

      2. *-commutative 88.4%

         \[\leadsto \frac{\color{blue}{c \cdot -0.5}}{b\_2} \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{c \cdot -0.5}{b\_2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -8.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq -4.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(-c\right)}}{a}\\ \mathbf{elif}\;b\_2 \leq -4 \cdot 10^{-147}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(-c\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -7 \cdot 10^{-224}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;\sqrt{\frac{c}{-a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -7e-224)
   (/ (* b_2 -2.0) a)
   (if (<= b_2 1.7e-132) (sqrt (/ c (- a))) (/ (* c -0.5) b_2))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -7e-224) {
		tmp = (b_2 * -2.0) / a;
	} else if (b_2 <= 1.7e-132) {
		tmp = sqrt((c / -a));
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= (-7d-224)) then
        tmp = (b_2 * (-2.0d0)) / a
    else if (b_2 <= 1.7d-132) then
        tmp = sqrt((c / -a))
    else
        tmp = (c * (-0.5d0)) / b_2
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -7e-224) {
		tmp = (b_2 * -2.0) / a;
	} else if (b_2 <= 1.7e-132) {
		tmp = Math.sqrt((c / -a));
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -7e-224:
		tmp = (b_2 * -2.0) / a
	elif b_2 <= 1.7e-132:
		tmp = math.sqrt((c / -a))
	else:
		tmp = (c * -0.5) / b_2
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -7e-224)
		tmp = Float64(Float64(b_2 * -2.0) / a);
	elseif (b_2 <= 1.7e-132)
		tmp = sqrt(Float64(c / Float64(-a)));
	else
		tmp = Float64(Float64(c * -0.5) / b_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -7e-224)
		tmp = (b_2 * -2.0) / a;
	elseif (b_2 <= 1.7e-132)
		tmp = sqrt((c / -a));
	else
		tmp = (c * -0.5) / b_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -7e-224], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b$95$2, 1.7e-132], N[Sqrt[N[(c / (-a)), $MachinePrecision]], $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -7.00000000000000037e-224

   1. Initial program 67.8%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 67.8%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around -inf 81.3%

      \[\leadsto \frac{\color{blue}{-2 \cdot b\_2}}{a} \]
   6. Step-by-step derivation

      1. *-commutative 81.3%

         \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   7. Simplified 81.3%

      \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   if -7.00000000000000037e-224 < b_2 < 1.69999999999999991e-132

   1. Initial program 67.3%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 67.3%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. prod-diff 66.8%

         \[\leadsto \frac{\sqrt{\color{blue}{\mathsf{fma}\left(b\_2, b\_2, -c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)}} - b\_2}{a} \]

      2. *-commutative 66.8%

         \[\leadsto \frac{\sqrt{\mathsf{fma}\left(b\_2, b\_2, -\color{blue}{a \cdot c}\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      3. fmm-def 66.8%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(b\_2 \cdot b\_2 - a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      4. prod-diff 66.8%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(\mathsf{fma}\left(b\_2, b\_2, -c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      5. *-commutative 66.8%

         \[\leadsto \frac{\sqrt{\left(\mathsf{fma}\left(b\_2, b\_2, -\color{blue}{a \cdot c}\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      6. fmm-def 66.8%

         \[\leadsto \frac{\sqrt{\left(\color{blue}{\left(b\_2 \cdot b\_2 - a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)} - b\_2}{a} \]

      7. associate-+l+ 67.0%

         \[\leadsto \frac{\sqrt{\color{blue}{\left(b\_2 \cdot b\_2 - a \cdot c\right) + \left(\mathsf{fma}\left(-c, a, c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)}} - b\_2}{a} \]

      8. pow2 67.0%

         \[\leadsto \frac{\sqrt{\left(\color{blue}{{b\_2}^{2}} - a \cdot c\right) + \left(\mathsf{fma}\left(-c, a, c \cdot a\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      9. *-commutative 67.0%

         \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(-c, a, \color{blue}{a \cdot c}\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      10. fma-undefine 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\color{blue}{\left(\left(-c\right) \cdot a + a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      11. distribute-lft-neg-in 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\left(\color{blue}{\left(-c \cdot a\right)} + a \cdot c\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      12. *-commutative 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\left(\left(-\color{blue}{a \cdot c}\right) + a \cdot c\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      13. distribute-rgt-neg-in 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\left(\color{blue}{a \cdot \left(-c\right)} + a \cdot c\right) + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      14. fma-define 67.0%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\color{blue}{\mathsf{fma}\left(a, -c, a \cdot c\right)} + \mathsf{fma}\left(-c, a, c \cdot a\right)\right)} - b\_2}{a} \]

      15. *-commutative 67.0%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \mathsf{fma}\left(-c, a, \color{blue}{a \cdot c}\right)\right)} - b\_2}{a} \]

      16. fma-undefine 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \color{blue}{\left(\left(-c\right) \cdot a + a \cdot c\right)}\right)} - b\_2}{a} \]

      17. distribute-lft-neg-in 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \left(\color{blue}{\left(-c \cdot a\right)} + a \cdot c\right)\right)} - b\_2}{a} \]

      18. *-commutative 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \left(\left(-\color{blue}{a \cdot c}\right) + a \cdot c\right)\right)} - b\_2}{a} \]

      19. distribute-rgt-neg-in 66.8%

          \[\leadsto \frac{\sqrt{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \left(\color{blue}{a \cdot \left(-c\right)} + a \cdot c\right)\right)} - b\_2}{a} \]

   6. Applied egg-rr 67.0%

      \[\leadsto \frac{\sqrt{\color{blue}{\left({b\_2}^{2} - a \cdot c\right) + \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \mathsf{fma}\left(a, -c, a \cdot c\right)\right)}} - b\_2}{a} \]
   7. Step-by-step derivation

      1. associate-+l- 67.0%

         \[\leadsto \frac{\sqrt{\color{blue}{{b\_2}^{2} - \left(a \cdot c - \left(\mathsf{fma}\left(a, -c, a \cdot c\right) + \mathsf{fma}\left(a, -c, a \cdot c\right)\right)\right)}} - b\_2}{a} \]

      2. count-2 67.0%

         \[\leadsto \frac{\sqrt{{b\_2}^{2} - \left(a \cdot c - \color{blue}{2 \cdot \mathsf{fma}\left(a, -c, a \cdot c\right)}\right)} - b\_2}{a} \]

   8. Simplified 67.0%

      \[\leadsto \frac{\sqrt{\color{blue}{{b\_2}^{2} - \left(a \cdot c - 2 \cdot \mathsf{fma}\left(a, -c, a \cdot c\right)\right)}} - b\_2}{a} \]

   9. Taylor expanded in a around inf 37.5%

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

       1. distribute-rgt1-in 37.5%

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

       2. metadata-eval 37.5%

          \[\leadsto \sqrt{\frac{2 \cdot \left(\color{blue}{0} \cdot c\right) - c}{a}} \]

       3. mul0-lft 37.5%

          \[\leadsto \sqrt{\frac{2 \cdot \color{blue}{0} - c}{a}} \]

       4. metadata-eval 37.5%

          \[\leadsto \sqrt{\frac{\color{blue}{0} - c}{a}} \]

       5. neg-sub0 37.5%

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

   11. Simplified 37.5%

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

   if 1.69999999999999991e-132 < b_2

   1. Initial program 19.0%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 19.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 19.0%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 19.0%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around inf 84.5%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b\_2}} \]
   6. Step-by-step derivation

      1. associate-*r/ 84.5%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot c}{b\_2}} \]

      2. *-commutative 84.5%

         \[\leadsto \frac{\color{blue}{c \cdot -0.5}}{b\_2} \]

   7. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{c \cdot -0.5}{b\_2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -7 \cdot 10^{-224}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{elif}\;b\_2 \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;\sqrt{\frac{c}{-a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.1% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq 4.4 \cdot 10^{-283}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 4.4e-283) (/ (* b_2 -2.0) a) (/ (* c -0.5) b_2)))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= 4.4e-283) {
		tmp = (b_2 * -2.0) / a;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b_2 <= 4.4d-283) then
        tmp = (b_2 * (-2.0d0)) / a
    else
        tmp = (c * (-0.5d0)) / b_2
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= 4.4e-283) {
		tmp = (b_2 * -2.0) / a;
	} else {
		tmp = (c * -0.5) / b_2;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= 4.4e-283:
		tmp = (b_2 * -2.0) / a
	else:
		tmp = (c * -0.5) / b_2
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= 4.4e-283)
		tmp = Float64(Float64(b_2 * -2.0) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= 4.4e-283)
		tmp = (b_2 * -2.0) / a;
	else
		tmp = (c * -0.5) / b_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, 4.4e-283], N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b$95$2), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < 4.3999999999999996e-283

   1. Initial program 67.9%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 67.9%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 67.9%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around -inf 72.4%

      \[\leadsto \frac{\color{blue}{-2 \cdot b\_2}}{a} \]
   6. Step-by-step derivation

      1. *-commutative 72.4%

         \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   7. Simplified 72.4%

      \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

   if 4.3999999999999996e-283 < b_2

   1. Initial program 29.3%

      \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Step-by-step derivation

      1. +-commutative 29.3%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

      2. unsub-neg 29.3%

         \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in b_2 around inf 67.3%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{c}{b\_2}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.3%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot c}{b\_2}} \]

      2. *-commutative 67.3%

         \[\leadsto \frac{\color{blue}{c \cdot -0.5}}{b\_2} \]

   7. Simplified 67.3%

      \[\leadsto \color{blue}{\frac{c \cdot -0.5}{b\_2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq 4.4 \cdot 10^{-283}:\\ \;\;\;\;\frac{b\_2 \cdot -2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.1% accurate, 22.4× speedup

Math

\[\begin{array}{l} \\ \frac{b\_2 \cdot -2}{a} \end{array} \]

FPCore

(FPCore (a b_2 c) :precision binary64 (/ (* b_2 -2.0) a))

C

double code(double a, double b_2, double c) {
	return (b_2 * -2.0) / a;
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = (b_2 * (-2.0d0)) / a
end function

Java

public static double code(double a, double b_2, double c) {
	return (b_2 * -2.0) / a;
}

Python

def code(a, b_2, c):
	return (b_2 * -2.0) / a

Julia

function code(a, b_2, c)
	return Float64(Float64(b_2 * -2.0) / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = (b_2 * -2.0) / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[(N[(b$95$2 * -2.0), $MachinePrecision] / a), $MachinePrecision]

Derivation

1. Initial program 48.4%

   \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
2. Step-by-step derivation

   1. +-commutative 48.4%

      \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

   2. unsub-neg 48.4%

      \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

3. Simplified 48.4%

   \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
4. Add Preprocessing

5. Taylor expanded in b_2 around -inf 37.3%

   \[\leadsto \frac{\color{blue}{-2 \cdot b\_2}}{a} \]
6. Step-by-step derivation

   1. *-commutative 37.3%

      \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

7. Simplified 37.3%

   \[\leadsto \frac{\color{blue}{b\_2 \cdot -2}}{a} \]

8. Final simplification 37.3%

   \[\leadsto \frac{b\_2 \cdot -2}{a} \]
9. Add Preprocessing

Alternative 7: 15.3% accurate, 28.0× speedup

Math

\[\begin{array}{l} \\ -\frac{b\_2}{a} \end{array} \]

FPCore

(FPCore (a b_2 c) :precision binary64 (- (/ b_2 a)))

C

double code(double a, double b_2, double c) {
	return -(b_2 / a);
}

Fortran

real(8) function code(a, b_2, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_2
    real(8), intent (in) :: c
    code = -(b_2 / a)
end function

Java

public static double code(double a, double b_2, double c) {
	return -(b_2 / a);
}

Python

def code(a, b_2, c):
	return -(b_2 / a)

Julia

function code(a, b_2, c)
	return Float64(-Float64(b_2 / a))
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = -(b_2 / a);
end

Wolfram

code[a_, b$95$2_, c_] := (-N[(b$95$2 / a), $MachinePrecision])

Derivation

1. Initial program 48.4%

   \[\frac{\left(-b\_2\right) + \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
2. Step-by-step derivation

   1. +-commutative 48.4%

      \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} + \left(-b\_2\right)}}{a} \]

   2. unsub-neg 48.4%

      \[\leadsto \frac{\color{blue}{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}}{a} \]

3. Simplified 48.4%

   \[\leadsto \color{blue}{\frac{\sqrt{b\_2 \cdot b\_2 - a \cdot c} - b\_2}{a}} \]
4. Add Preprocessing

5. Taylor expanded in b_2 around 0 28.8%

   \[\leadsto \frac{\sqrt{\color{blue}{-1 \cdot \left(a \cdot c\right)}} - b\_2}{a} \]
6. Step-by-step derivation

   1. associate-*r* 28.8%

      \[\leadsto \frac{\sqrt{\color{blue}{\left(-1 \cdot a\right) \cdot c}} - b\_2}{a} \]

   2. neg-mul-1 28.8%

      \[\leadsto \frac{\sqrt{\color{blue}{\left(-a\right)} \cdot c} - b\_2}{a} \]

   3. *-commutative 28.8%

      \[\leadsto \frac{\sqrt{\color{blue}{c \cdot \left(-a\right)}} - b\_2}{a} \]

7. Simplified 28.8%

   \[\leadsto \frac{\sqrt{\color{blue}{c \cdot \left(-a\right)}} - b\_2}{a} \]

8. Taylor expanded in b_2 around inf 14.9%

   \[\leadsto \color{blue}{-1 \cdot \frac{b\_2}{a}} \]
9. Step-by-step derivation

   1. neg-mul-1 14.9%

      \[\leadsto \color{blue}{-\frac{b\_2}{a}} \]

   2. distribute-neg-frac2 14.9%

      \[\leadsto \color{blue}{\frac{b\_2}{-a}} \]

10. Simplified 14.9%

    \[\leadsto \color{blue}{\frac{b\_2}{-a}} \]

11. Final simplification 14.9%

    \[\leadsto -\frac{b\_2}{a} \]
12. Add Preprocessing

Developer target: 99.7% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (let* ((t_0 (* (sqrt (fabs a)) (sqrt (fabs c))))
        (t_1
         (if (== (copysign a c) a)
           (* (sqrt (- (fabs b_2) t_0)) (sqrt (+ (fabs b_2) t_0)))
           (hypot b_2 t_0))))
   (if (< b_2 0.0) (/ (- t_1 b_2) a) (/ (- c) (+ b_2 t_1)))))

C

double code(double a, double b_2, double c) {
	double t_0 = sqrt(fabs(a)) * sqrt(fabs(c));
	double tmp;
	if (copysign(a, c) == a) {
		tmp = sqrt((fabs(b_2) - t_0)) * sqrt((fabs(b_2) + t_0));
	} else {
		tmp = hypot(b_2, t_0);
	}
	double t_1 = tmp;
	double tmp_1;
	if (b_2 < 0.0) {
		tmp_1 = (t_1 - b_2) / a;
	} else {
		tmp_1 = -c / (b_2 + t_1);
	}
	return tmp_1;
}

Java

public static double code(double a, double b_2, double c) {
	double t_0 = Math.sqrt(Math.abs(a)) * Math.sqrt(Math.abs(c));
	double tmp;
	if (Math.copySign(a, c) == a) {
		tmp = Math.sqrt((Math.abs(b_2) - t_0)) * Math.sqrt((Math.abs(b_2) + t_0));
	} else {
		tmp = Math.hypot(b_2, t_0);
	}
	double t_1 = tmp;
	double tmp_1;
	if (b_2 < 0.0) {
		tmp_1 = (t_1 - b_2) / a;
	} else {
		tmp_1 = -c / (b_2 + t_1);
	}
	return tmp_1;
}

Python

def code(a, b_2, c):
	t_0 = math.sqrt(math.fabs(a)) * math.sqrt(math.fabs(c))
	tmp = 0
	if math.copysign(a, c) == a:
		tmp = math.sqrt((math.fabs(b_2) - t_0)) * math.sqrt((math.fabs(b_2) + t_0))
	else:
		tmp = math.hypot(b_2, t_0)
	t_1 = tmp
	tmp_1 = 0
	if b_2 < 0.0:
		tmp_1 = (t_1 - b_2) / a
	else:
		tmp_1 = -c / (b_2 + t_1)
	return tmp_1

Julia

function code(a, b_2, c)
	t_0 = Float64(sqrt(abs(a)) * sqrt(abs(c)))
	tmp = 0.0
	if (copysign(a, c) == a)
		tmp = Float64(sqrt(Float64(abs(b_2) - t_0)) * sqrt(Float64(abs(b_2) + t_0)));
	else
		tmp = hypot(b_2, t_0);
	end
	t_1 = tmp
	tmp_1 = 0.0
	if (b_2 < 0.0)
		tmp_1 = Float64(Float64(t_1 - b_2) / a);
	else
		tmp_1 = Float64(Float64(-c) / Float64(b_2 + t_1));
	end
	return tmp_1
end

MATLAB

function tmp_3 = code(a, b_2, c)
	t_0 = sqrt(abs(a)) * sqrt(abs(c));
	tmp = 0.0;
	if ((sign(c) * abs(a)) == a)
		tmp = sqrt((abs(b_2) - t_0)) * sqrt((abs(b_2) + t_0));
	else
		tmp = hypot(b_2, t_0);
	end
	t_1 = tmp;
	tmp_2 = 0.0;
	if (b_2 < 0.0)
		tmp_2 = (t_1 - b_2) / a;
	else
		tmp_2 = -c / (b_2 + t_1);
	end
	tmp_3 = tmp_2;
end

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  :precision binary64
  :herbie-expected 10

  :alt
  (if (< b_2 0.0) (/ (- (if (== (copysign a c) a) (* (sqrt (- (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot b_2 (* (sqrt (fabs a)) (sqrt (fabs c))))) b_2) a) (/ (- c) (+ b_2 (if (== (copysign a c) a) (* (sqrt (- (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs b_2) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot b_2 (* (sqrt (fabs a)) (sqrt (fabs c))))))))

  (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))