quad2m (problem 3.2.1, negative)

Percentage Accurate: 51.8% → 84.9%

Time: 13.0s

Alternatives: 10

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: 51.8% 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: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{elif}\;b\_2 \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - c \cdot a}}{a}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a} + 0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1.55e-53)
   (/ (* -0.5 c) b_2)
   (if (<= b_2 1.2e+67)
     (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a)
     (+ (* -2.0 (/ b_2 a)) (* 0.5 (/ c b_2))))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.55e-53) {
		tmp = (-0.5 * c) / b_2;
	} else if (b_2 <= 1.2e+67) {
		tmp = (-b_2 - sqrt(((b_2 * b_2) - (c * a)))) / a;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / 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 <= (-1.55d-53)) then
        tmp = ((-0.5d0) * c) / b_2
    else if (b_2 <= 1.2d+67) then
        tmp = (-b_2 - sqrt(((b_2 * b_2) - (c * a)))) / a
    else
        tmp = ((-2.0d0) * (b_2 / a)) + (0.5d0 * (c / 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 <= -1.55e-53) {
		tmp = (-0.5 * c) / b_2;
	} else if (b_2 <= 1.2e+67) {
		tmp = (-b_2 - Math.sqrt(((b_2 * b_2) - (c * a)))) / a;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1.55e-53:
		tmp = (-0.5 * c) / b_2
	elif b_2 <= 1.2e+67:
		tmp = (-b_2 - math.sqrt(((b_2 * b_2) - (c * a)))) / a
	else:
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2))
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1.55e-53)
		tmp = Float64(Float64(-0.5 * c) / b_2);
	elseif (b_2 <= 1.2e+67)
		tmp = Float64(Float64(Float64(-b_2) - sqrt(Float64(Float64(b_2 * b_2) - Float64(c * a)))) / a);
	else
		tmp = Float64(Float64(-2.0 * Float64(b_2 / a)) + Float64(0.5 * Float64(c / b_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1.55e-53)
		tmp = (-0.5 * c) / b_2;
	elseif (b_2 <= 1.2e+67)
		tmp = (-b_2 - sqrt(((b_2 * b_2) - (c * a)))) / a;
	else
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1.55e-53], N[(N[(-0.5 * c), $MachinePrecision] / b$95$2), $MachinePrecision], If[LessEqual[b$95$2, 1.2e+67], N[(N[((-b$95$2) - N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(-2.0 * N[(b$95$2 / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -1.55000000000000008e-53

   1. Initial program 8.1%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around -inf 92.1%

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

      1. associate-*r/ 92.1%

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

   5. Simplified 92.1%

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

   if -1.55000000000000008e-53 < b_2 < 1.20000000000000001e67

   1. Initial program 83.4%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   if 1.20000000000000001e67 < b_2

   1. Initial program 58.4%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 95.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{elif}\;b\_2 \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - c \cdot a}}{a}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a} + 0.5 \cdot \frac{c}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -1.15 \cdot 10^{-58}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{elif}\;b\_2 \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;\frac{\left(-b\_2\right) - \sqrt{c \cdot \left(-a\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a} + 0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -1.15e-58)
   (/ (* -0.5 c) b_2)
   (if (<= b_2 2.55e-89)
     (/ (- (- b_2) (sqrt (* c (- a)))) a)
     (+ (* -2.0 (/ b_2 a)) (* 0.5 (/ c b_2))))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -1.15e-58) {
		tmp = (-0.5 * c) / b_2;
	} else if (b_2 <= 2.55e-89) {
		tmp = (-b_2 - sqrt((c * -a))) / a;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / 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 <= (-1.15d-58)) then
        tmp = ((-0.5d0) * c) / b_2
    else if (b_2 <= 2.55d-89) then
        tmp = (-b_2 - sqrt((c * -a))) / a
    else
        tmp = ((-2.0d0) * (b_2 / a)) + (0.5d0 * (c / 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 <= -1.15e-58) {
		tmp = (-0.5 * c) / b_2;
	} else if (b_2 <= 2.55e-89) {
		tmp = (-b_2 - Math.sqrt((c * -a))) / a;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -1.15e-58:
		tmp = (-0.5 * c) / b_2
	elif b_2 <= 2.55e-89:
		tmp = (-b_2 - math.sqrt((c * -a))) / a
	else:
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2))
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -1.15e-58)
		tmp = Float64(Float64(-0.5 * c) / b_2);
	elseif (b_2 <= 2.55e-89)
		tmp = Float64(Float64(Float64(-b_2) - sqrt(Float64(c * Float64(-a)))) / a);
	else
		tmp = Float64(Float64(-2.0 * Float64(b_2 / a)) + Float64(0.5 * Float64(c / b_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -1.15e-58)
		tmp = (-0.5 * c) / b_2;
	elseif (b_2 <= 2.55e-89)
		tmp = (-b_2 - sqrt((c * -a))) / a;
	else
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -1.15e-58], N[(N[(-0.5 * c), $MachinePrecision] / b$95$2), $MachinePrecision], If[LessEqual[b$95$2, 2.55e-89], N[(N[((-b$95$2) - N[Sqrt[N[(c * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(-2.0 * N[(b$95$2 / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -1.1499999999999999e-58

   1. Initial program 8.1%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around -inf 92.1%

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

      1. associate-*r/ 92.1%

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

   5. Simplified 92.1%

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

   if -1.1499999999999999e-58 < b_2 < 2.55000000000000002e-89

   1. Initial program 77.2%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around 0 74.7%

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

      1. associate-*r* 74.7%

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

      2. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   if 2.55000000000000002e-89 < b_2

   1. Initial program 72.1%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 89.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -1.15 \cdot 10^{-58}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{elif}\;b\_2 \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;\frac{\left(-b\_2\right) - \sqrt{c \cdot \left(-a\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a} + 0.5 \cdot \frac{c}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a} + 0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -4e-310)
   (/ (* -0.5 c) b_2)
   (+ (* -2.0 (/ b_2 a)) (* 0.5 (/ c b_2)))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -4e-310) {
		tmp = (-0.5 * c) / b_2;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / 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 <= (-4d-310)) then
        tmp = ((-0.5d0) * c) / b_2
    else
        tmp = ((-2.0d0) * (b_2 / a)) + (0.5d0 * (c / 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 <= -4e-310) {
		tmp = (-0.5 * c) / b_2;
	} else {
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -4e-310:
		tmp = (-0.5 * c) / b_2
	else:
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2))
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -4e-310)
		tmp = Float64(Float64(-0.5 * c) / b_2);
	else
		tmp = Float64(Float64(-2.0 * Float64(b_2 / a)) + Float64(0.5 * Float64(c / b_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -4e-310)
		tmp = (-0.5 * c) / b_2;
	else
		tmp = (-2.0 * (b_2 / a)) + (0.5 * (c / b_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -4e-310], N[(N[(-0.5 * c), $MachinePrecision] / b$95$2), $MachinePrecision], N[(N[(-2.0 * N[(b$95$2 / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < -3.999999999999988e-310

   1. Initial program 23.9%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around -inf 74.7%

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

      1. associate-*r/ 74.7%

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

   5. Simplified 74.7%

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

   if -3.999999999999988e-310 < b_2

   1. Initial program 74.5%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 69.5%

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

Alternative 4: 68.2% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -3.4e-303) (/ (* -0.5 c) b_2) (* -2.0 (/ b_2 a))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.4e-303) {
		tmp = (-0.5 * c) / b_2;
	} else {
		tmp = -2.0 * (b_2 / a);
	}
	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 <= (-3.4d-303)) then
        tmp = ((-0.5d0) * c) / b_2
    else
        tmp = (-2.0d0) * (b_2 / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.4e-303) {
		tmp = (-0.5 * c) / b_2;
	} else {
		tmp = -2.0 * (b_2 / a);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -3.4e-303:
		tmp = (-0.5 * c) / b_2
	else:
		tmp = -2.0 * (b_2 / a)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -3.4e-303)
		tmp = Float64(Float64(-0.5 * c) / b_2);
	else
		tmp = Float64(-2.0 * Float64(b_2 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -3.4e-303)
		tmp = (-0.5 * c) / b_2;
	else
		tmp = -2.0 * (b_2 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -3.4e-303], N[(N[(-0.5 * c), $MachinePrecision] / b$95$2), $MachinePrecision], N[(-2.0 * N[(b$95$2 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < -3.4e-303

   1. Initial program 22.7%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

   5. Simplified 75.8%

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

   if -3.4e-303 < b_2

   1. Initial program 74.8%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around inf 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{-0.5 \cdot c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.9% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -3.8e+80) (* 0.5 (/ c b_2)) (* -2.0 (/ b_2 a))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.8e+80) {
		tmp = 0.5 * (c / b_2);
	} else {
		tmp = -2.0 * (b_2 / a);
	}
	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 <= (-3.8d+80)) then
        tmp = 0.5d0 * (c / b_2)
    else
        tmp = (-2.0d0) * (b_2 / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.8e+80) {
		tmp = 0.5 * (c / b_2);
	} else {
		tmp = -2.0 * (b_2 / a);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -3.8e+80:
		tmp = 0.5 * (c / b_2)
	else:
		tmp = -2.0 * (b_2 / a)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -3.8e+80)
		tmp = Float64(0.5 * Float64(c / b_2));
	else
		tmp = Float64(-2.0 * Float64(b_2 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -3.8e+80)
		tmp = 0.5 * (c / b_2);
	else
		tmp = -2.0 * (b_2 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -3.8e+80], N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(b$95$2 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < -3.79999999999999997e80

   1. Initial program 5.3%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 1.8%

      \[\leadsto \frac{\color{blue}{0.5 \cdot \frac{a \cdot c}{b\_2} - 2 \cdot b\_2}}{a} \]

   4. Taylor expanded in a around inf 32.0%

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

   if -3.79999999999999997e80 < b_2

   1. Initial program 65.0%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around inf 48.2%

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

      1. *-commutative 48.2%

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

   5. Simplified 48.2%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b\_2}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.8% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;b\_2 \cdot \frac{-2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -3.8e+80) (* 0.5 (/ c b_2)) (* b_2 (/ -2.0 a))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.8e+80) {
		tmp = 0.5 * (c / b_2);
	} else {
		tmp = b_2 * (-2.0 / a);
	}
	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 <= (-3.8d+80)) then
        tmp = 0.5d0 * (c / b_2)
    else
        tmp = b_2 * ((-2.0d0) / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.8e+80) {
		tmp = 0.5 * (c / b_2);
	} else {
		tmp = b_2 * (-2.0 / a);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -3.8e+80:
		tmp = 0.5 * (c / b_2)
	else:
		tmp = b_2 * (-2.0 / a)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -3.8e+80)
		tmp = Float64(0.5 * Float64(c / b_2));
	else
		tmp = Float64(b_2 * Float64(-2.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -3.8e+80)
		tmp = 0.5 * (c / b_2);
	else
		tmp = b_2 * (-2.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -3.8e+80], N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision], N[(b$95$2 * N[(-2.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < -3.79999999999999997e80

   1. Initial program 5.3%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 1.8%

      \[\leadsto \frac{\color{blue}{0.5 \cdot \frac{a \cdot c}{b\_2} - 2 \cdot b\_2}}{a} \]

   4. Taylor expanded in a around inf 32.0%

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

   if -3.79999999999999997e80 < b_2

   1. Initial program 65.0%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in b_2 around inf 48.2%

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

      1. *-commutative 48.2%

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

   5. Simplified 48.2%

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

      1. associate-*l/ 48.2%

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

   7. Applied egg-rr 48.2%

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

      1. associate-/l* 48.1%

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

   9. Simplified 48.1%

      \[\leadsto \color{blue}{b\_2 \cdot \frac{-2}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 22.5% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b\_2}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -3.8e+80) (* 0.5 (/ c b_2)) (/ b_2 (- a))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.8e+80) {
		tmp = 0.5 * (c / b_2);
	} else {
		tmp = b_2 / -a;
	}
	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 <= (-3.8d+80)) then
        tmp = 0.5d0 * (c / b_2)
    else
        tmp = b_2 / -a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.8e+80) {
		tmp = 0.5 * (c / b_2);
	} else {
		tmp = b_2 / -a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -3.8e+80:
		tmp = 0.5 * (c / b_2)
	else:
		tmp = b_2 / -a
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -3.8e+80)
		tmp = Float64(0.5 * Float64(c / b_2));
	else
		tmp = Float64(b_2 / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -3.8e+80)
		tmp = 0.5 * (c / b_2);
	else
		tmp = b_2 / -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -3.8e+80], N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision], N[(b$95$2 / (-a)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < -3.79999999999999997e80

   1. Initial program 5.3%

      \[\frac{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 1.8%

      \[\leadsto \frac{\color{blue}{0.5 \cdot \frac{a \cdot c}{b\_2} - 2 \cdot b\_2}}{a} \]

   4. Taylor expanded in a around inf 32.0%

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

   if -3.79999999999999997e80 < b_2

   1. Initial program 65.0%

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

      1. add-sqr-sqrt 64.7%

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

      2. pow2 64.7%

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

      3. pow1/2 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\left(\sqrt{\color{blue}{{\left(b\_2 \cdot b\_2 - a \cdot c\right)}^{0.5}}}\right)}^{2}}{a} \]

      4. sqrt-pow1 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(b\_2 \cdot b\_2 - a \cdot c\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2}}{a} \]

      5. sub-neg 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(b\_2 \cdot b\_2 + \left(-a \cdot c\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      6. +-commutative 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(\left(-a \cdot c\right) + b\_2 \cdot b\_2\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      7. distribute-rgt-neg-in 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\color{blue}{a \cdot \left(-c\right)} + b\_2 \cdot b\_2\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      8. fma-define 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(\mathsf{fma}\left(a, -c, b\_2 \cdot b\_2\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      9. pow2 64.7%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\mathsf{fma}\left(a, -c, \color{blue}{{b\_2}^{2}}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      10. metadata-eval 64.7%

          \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\mathsf{fma}\left(a, -c, {b\_2}^{2}\right)\right)}^{\color{blue}{0.25}}\right)}^{2}}{a} \]

   4. Applied egg-rr 64.7%

      \[\leadsto \frac{\left(-b\_2\right) - \color{blue}{{\left({\left(\mathsf{fma}\left(a, -c, {b\_2}^{2}\right)\right)}^{0.25}\right)}^{2}}}{a} \]

   5. Taylor expanded in b_2 around 0 39.9%

      \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(-1 \cdot \left(a \cdot c\right)\right)}^{0.25}\right)}}^{2}}{a} \]
   6. Step-by-step derivation

      1. neg-mul-1 39.9%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(-a \cdot c\right)}}^{0.25}\right)}^{2}}{a} \]

   7. Simplified 39.9%

      \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(-a \cdot c\right)}^{0.25}\right)}}^{2}}{a} \]

   8. Taylor expanded in b_2 around inf 17.0%

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

      1. associate-*r/ 17.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot b\_2}{a}} \]

      2. mul-1-neg 17.0%

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

   10. Simplified 17.0%

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

4. Final simplification 20.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b\_2}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 18.7% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -4.6 \cdot 10^{-256}:\\ \;\;\;\;0.5 \cdot \frac{a}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b\_2}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -4.6e-256) (* 0.5 (/ a b_2)) (/ b_2 (- a))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -4.6e-256) {
		tmp = 0.5 * (a / b_2);
	} else {
		tmp = b_2 / -a;
	}
	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 <= (-4.6d-256)) then
        tmp = 0.5d0 * (a / b_2)
    else
        tmp = b_2 / -a
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -4.6e-256) {
		tmp = 0.5 * (a / b_2);
	} else {
		tmp = b_2 / -a;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -4.6e-256:
		tmp = 0.5 * (a / b_2)
	else:
		tmp = b_2 / -a
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -4.6e-256)
		tmp = Float64(0.5 * Float64(a / b_2));
	else
		tmp = Float64(b_2 / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= -4.6e-256)
		tmp = 0.5 * (a / b_2);
	else
		tmp = b_2 / -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -4.6e-256], N[(0.5 * N[(a / b$95$2), $MachinePrecision]), $MachinePrecision], N[(b$95$2 / (-a)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < -4.6e-256

   1. Initial program 22.8%

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

      1. add-cube-cbrt 22.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}} \cdot \sqrt[3]{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right) \cdot \sqrt[3]{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}}}{a} \]

      2. pow3 22.5%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(-b\_2\right) - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right)}^{3}}}{a} \]

      3. add-sqr-sqrt 21.4%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{\sqrt{-b\_2} \cdot \sqrt{-b\_2}} - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right)}^{3}}{a} \]

      4. sqrt-unprod 21.5%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{\sqrt{\left(-b\_2\right) \cdot \left(-b\_2\right)}} - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right)}^{3}}{a} \]

      5. sqr-neg 21.5%

         \[\leadsto \frac{{\left(\sqrt[3]{\sqrt{\color{blue}{b\_2 \cdot b\_2}} - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right)}^{3}}{a} \]

      6. sqrt-prod 0.0%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{\sqrt{b\_2} \cdot \sqrt{b\_2}} - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right)}^{3}}{a} \]

      7. add-sqr-sqrt 19.4%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{b\_2} - \sqrt{b\_2 \cdot b\_2 - a \cdot c}}\right)}^{3}}{a} \]

      8. sub-neg 19.4%

         \[\leadsto \frac{{\left(\sqrt[3]{b\_2 - \sqrt{\color{blue}{b\_2 \cdot b\_2 + \left(-a \cdot c\right)}}}\right)}^{3}}{a} \]

      9. add-sqr-sqrt 19.0%

         \[\leadsto \frac{{\left(\sqrt[3]{b\_2 - \sqrt{b\_2 \cdot b\_2 + \color{blue}{\sqrt{-a \cdot c} \cdot \sqrt{-a \cdot c}}}}\right)}^{3}}{a} \]

      10. hypot-define 19.1%

          \[\leadsto \frac{{\left(\sqrt[3]{b\_2 - \color{blue}{\mathsf{hypot}\left(b\_2, \sqrt{-a \cdot c}\right)}}\right)}^{3}}{a} \]

      11. distribute-rgt-neg-in 19.1%

          \[\leadsto \frac{{\left(\sqrt[3]{b\_2 - \mathsf{hypot}\left(b\_2, \sqrt{\color{blue}{a \cdot \left(-c\right)}}\right)}\right)}^{3}}{a} \]

   4. Applied egg-rr 19.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{b\_2 - \mathsf{hypot}\left(b\_2, \sqrt{a \cdot \left(-c\right)}\right)}\right)}^{3}}}{a} \]

   5. Taylor expanded in b_2 around -inf 3.1%

      \[\leadsto \frac{{\color{blue}{\left(-1 \cdot \left(\sqrt[3]{b\_2} \cdot \left(\sqrt[3]{-1} \cdot \sqrt[3]{2}\right)\right)\right)}}^{3}}{a} \]
   6. Step-by-step derivation

      1. mul-1-neg 3.1%

         \[\leadsto \frac{{\color{blue}{\left(-\sqrt[3]{b\_2} \cdot \left(\sqrt[3]{-1} \cdot \sqrt[3]{2}\right)\right)}}^{3}}{a} \]

   7. Simplified 3.1%

      \[\leadsto \frac{{\color{blue}{\left(-\sqrt[3]{b\_2} \cdot \left(\sqrt[3]{-1} \cdot \sqrt[3]{2}\right)\right)}}^{3}}{a} \]

   9. Applied egg-rr 11.6%

      \[\leadsto \color{blue}{a \cdot \frac{-1}{b\_2 \cdot -2}} \]
   10. Step-by-step derivation

       1. associate-*r/ 11.6%

          \[\leadsto \color{blue}{\frac{a \cdot -1}{b\_2 \cdot -2}} \]

       2. *-commutative 11.6%

          \[\leadsto \frac{\color{blue}{-1 \cdot a}}{b\_2 \cdot -2} \]

       3. *-commutative 11.6%

          \[\leadsto \frac{-1 \cdot a}{\color{blue}{-2 \cdot b\_2}} \]

       4. times-frac 11.6%

          \[\leadsto \color{blue}{\frac{-1}{-2} \cdot \frac{a}{b\_2}} \]

       5. metadata-eval 11.6%

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

   11. Simplified 11.6%

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

   if -4.6e-256 < b_2

   1. Initial program 74.4%

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

      1. add-sqr-sqrt 74.1%

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

      2. pow2 74.1%

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

      3. pow1/2 74.1%

         \[\leadsto \frac{\left(-b\_2\right) - {\left(\sqrt{\color{blue}{{\left(b\_2 \cdot b\_2 - a \cdot c\right)}^{0.5}}}\right)}^{2}}{a} \]

      4. sqrt-pow1 74.1%

         \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(b\_2 \cdot b\_2 - a \cdot c\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2}}{a} \]

      5. sub-neg 74.1%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(b\_2 \cdot b\_2 + \left(-a \cdot c\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      6. +-commutative 74.1%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(\left(-a \cdot c\right) + b\_2 \cdot b\_2\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      7. distribute-rgt-neg-in 74.1%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\color{blue}{a \cdot \left(-c\right)} + b\_2 \cdot b\_2\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      8. fma-define 74.2%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(\mathsf{fma}\left(a, -c, b\_2 \cdot b\_2\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      9. pow2 74.2%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\mathsf{fma}\left(a, -c, \color{blue}{{b\_2}^{2}}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

      10. metadata-eval 74.2%

          \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\mathsf{fma}\left(a, -c, {b\_2}^{2}\right)\right)}^{\color{blue}{0.25}}\right)}^{2}}{a} \]

   4. Applied egg-rr 74.2%

      \[\leadsto \frac{\left(-b\_2\right) - \color{blue}{{\left({\left(\mathsf{fma}\left(a, -c, {b\_2}^{2}\right)\right)}^{0.25}\right)}^{2}}}{a} \]

   5. Taylor expanded in b_2 around 0 39.6%

      \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(-1 \cdot \left(a \cdot c\right)\right)}^{0.25}\right)}}^{2}}{a} \]
   6. Step-by-step derivation

      1. neg-mul-1 39.6%

         \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(-a \cdot c\right)}}^{0.25}\right)}^{2}}{a} \]

   7. Simplified 39.6%

      \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(-a \cdot c\right)}^{0.25}\right)}}^{2}}{a} \]

   8. Taylor expanded in b_2 around inf 23.0%

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

      1. associate-*r/ 23.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot b\_2}{a}} \]

      2. mul-1-neg 23.0%

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

   10. Simplified 23.0%

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

4. Final simplification 17.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -4.6 \cdot 10^{-256}:\\ \;\;\;\;0.5 \cdot \frac{a}{b\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{b\_2}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 15.2% 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(b_2 / Float64(-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 49.4%

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

   1. add-sqr-sqrt 48.8%

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

   2. pow2 48.8%

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

   3. pow1/2 48.8%

      \[\leadsto \frac{\left(-b\_2\right) - {\left(\sqrt{\color{blue}{{\left(b\_2 \cdot b\_2 - a \cdot c\right)}^{0.5}}}\right)}^{2}}{a} \]

   4. sqrt-pow1 48.7%

      \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(b\_2 \cdot b\_2 - a \cdot c\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2}}{a} \]

   5. sub-neg 48.7%

      \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(b\_2 \cdot b\_2 + \left(-a \cdot c\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

   6. +-commutative 48.7%

      \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(\left(-a \cdot c\right) + b\_2 \cdot b\_2\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

   7. distribute-rgt-neg-in 48.7%

      \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\color{blue}{a \cdot \left(-c\right)} + b\_2 \cdot b\_2\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

   8. fma-define 48.8%

      \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(\mathsf{fma}\left(a, -c, b\_2 \cdot b\_2\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

   9. pow2 48.8%

      \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\mathsf{fma}\left(a, -c, \color{blue}{{b\_2}^{2}}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2}}{a} \]

   10. metadata-eval 48.8%

       \[\leadsto \frac{\left(-b\_2\right) - {\left({\left(\mathsf{fma}\left(a, -c, {b\_2}^{2}\right)\right)}^{\color{blue}{0.25}}\right)}^{2}}{a} \]

4. Applied egg-rr 48.8%

   \[\leadsto \frac{\left(-b\_2\right) - \color{blue}{{\left({\left(\mathsf{fma}\left(a, -c, {b\_2}^{2}\right)\right)}^{0.25}\right)}^{2}}}{a} \]

5. Taylor expanded in b_2 around 0 29.8%

   \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(-1 \cdot \left(a \cdot c\right)\right)}^{0.25}\right)}}^{2}}{a} \]
6. Step-by-step derivation

   1. neg-mul-1 29.8%

      \[\leadsto \frac{\left(-b\_2\right) - {\left({\color{blue}{\left(-a \cdot c\right)}}^{0.25}\right)}^{2}}{a} \]

7. Simplified 29.8%

   \[\leadsto \frac{\left(-b\_2\right) - {\color{blue}{\left({\left(-a \cdot c\right)}^{0.25}\right)}}^{2}}{a} \]

8. Taylor expanded in b_2 around inf 13.1%

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

   1. associate-*r/ 13.1%

      \[\leadsto \color{blue}{\frac{-1 \cdot b\_2}{a}} \]

   2. mul-1-neg 13.1%

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

10. Simplified 13.1%

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

11. Final simplification 13.1%

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

Alternative 10: 5.3% accurate, 37.3× speedup

Math

\[\begin{array}{l} \\ \frac{-1}{a} \end{array} \]

FPCore

(FPCore (a b_2 c) :precision binary64 (/ -1.0 a))

C

double code(double a, double b_2, double c) {
	return -1.0 / 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 = (-1.0d0) / a
end function

Java

public static double code(double a, double b_2, double c) {
	return -1.0 / a;
}

Python

def code(a, b_2, c):
	return -1.0 / a

Julia

function code(a, b_2, c)
	return Float64(-1.0 / a)
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = -1.0 / a;
end

Wolfram

code[a_, b$95$2_, c_] := N[(-1.0 / a), $MachinePrecision]

Derivation

1. Initial program 49.4%

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

   1. clear-num 49.3%

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

   2. inv-pow 49.3%

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

   3. add-sqr-sqrt 11.3%

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

   4. sqrt-unprod 24.0%

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

   5. sqr-neg 24.0%

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

   6. sqrt-prod 18.6%

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

   7. add-sqr-sqrt 28.6%

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

   8. sub-neg 28.6%

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

   9. add-sqr-sqrt 27.5%

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

   10. hypot-define 22.8%

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

   11. distribute-rgt-neg-in 22.8%

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

4. Applied egg-rr 22.8%

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

   1. unpow-1 22.8%

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

   2. distribute-rgt-neg-out 22.8%

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

   3. distribute-lft-neg-in 22.8%

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

6. Simplified 22.8%

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

7. Taylor expanded in b_2 around inf 0.0%

   \[\leadsto \frac{1}{\frac{a}{\color{blue}{-0.5 \cdot \frac{a \cdot \left(c \cdot {\left(\sqrt{-1}\right)}^{2}\right)}{b\_2}}}} \]
8. Step-by-step derivation

   1. associate-/l* 0.0%

      \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \color{blue}{\left(a \cdot \frac{c \cdot {\left(\sqrt{-1}\right)}^{2}}{b\_2}\right)}}} \]

   2. associate-/l* 0.0%

      \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{{\left(\sqrt{-1}\right)}^{2}}{b\_2}\right)}\right)}} \]

   3. unpow2 0.0%

      \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{\color{blue}{\sqrt{-1} \cdot \sqrt{-1}}}{b\_2}\right)\right)}} \]

   4. rem-square-sqrt 10.8%

      \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{\color{blue}{-1}}{b\_2}\right)\right)}} \]

9. Simplified 10.8%

   \[\leadsto \frac{1}{\frac{a}{\color{blue}{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{-1}{b\_2}\right)\right)}}} \]

11. Applied egg-rr 4.6%

    \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(a \cdot \left(c \cdot b\_2\right)\right)} - -1\right)}}} \]
12. Step-by-step derivation

    1. sub-neg 4.6%

       \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(a \cdot \left(c \cdot b\_2\right)\right)} + \left(--1\right)\right)}}} \]

    2. log1p-undefine 4.6%

       \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \left(e^{\color{blue}{\log \left(1 + a \cdot \left(c \cdot b\_2\right)\right)}} + \left(--1\right)\right)}} \]

    3. rem-exp-log 5.0%

       \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \left(\color{blue}{\left(1 + a \cdot \left(c \cdot b\_2\right)\right)} + \left(--1\right)\right)}} \]

    4. metadata-eval 5.0%

       \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \left(\left(1 + a \cdot \left(c \cdot b\_2\right)\right) + \color{blue}{1}\right)}} \]

13. Simplified 5.0%

    \[\leadsto \frac{1}{\frac{a}{-0.5 \cdot \color{blue}{\left(\left(1 + a \cdot \left(c \cdot b\_2\right)\right) + 1\right)}}} \]

14. Taylor expanded in a around 0 5.1%

    \[\leadsto \color{blue}{\frac{-1}{a}} \]
15. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.1× speedup

Math

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

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) (/ c (- t_1 b_2)) (/ (+ b_2 t_1) (- a)))))

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 = c / (t_1 - b_2);
	} else {
		tmp_1 = (b_2 + t_1) / -a;
	}
	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 = c / (t_1 - b_2);
	} else {
		tmp_1 = (b_2 + t_1) / -a;
	}
	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 = c / (t_1 - b_2)
	else:
		tmp_1 = (b_2 + t_1) / -a
	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(c / Float64(t_1 - b_2));
	else
		tmp_1 = Float64(Float64(b_2 + t_1) / Float64(-a));
	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 = c / (t_1 - b_2);
	else
		tmp_2 = (b_2 + t_1) / -a;
	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[(c / N[(t$95$1 - b$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(b$95$2 + t$95$1), $MachinePrecision] / (-a)), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024136 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  :precision binary64
  :herbie-expected 10

  :alt
  (! :herbie-platform default (let ((sqtD (let ((x (* (sqrt (fabs a)) (sqrt (fabs c))))) (if (== (copysign a c) a) (* (sqrt (- (fabs b_2) x)) (sqrt (+ (fabs b_2) x))) (hypot b_2 x))))) (if (< b_2 0) (/ c (- sqtD b_2)) (/ (+ b_2 sqtD) (- a)))))

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