quad2p (problem 3.2.1, positive)

Percentage Accurate: 51.7% → 85.7%

Time: 8.2s

Alternatives: 6

Speedup: 1.7×

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: 51.7% 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: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{elif}\;b\_2 \leq 5.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{b\_2 \cdot b\_2 - c \cdot a} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -3.5e+149)
   (* (/ b_2 a) -2.0)
   (if (<= b_2 5.2e-107)
     (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
     (* -0.5 (/ c b_2)))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -3.5e+149) {
		tmp = (b_2 / a) * -2.0;
	} else if (b_2 <= 5.2e-107) {
		tmp = (sqrt(((b_2 * b_2) - (c * a))) - b_2) / a;
	} else {
		tmp = -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 <= (-3.5d+149)) then
        tmp = (b_2 / a) * (-2.0d0)
    else if (b_2 <= 5.2d-107) then
        tmp = (sqrt(((b_2 * b_2) - (c * a))) - b_2) / a
    else
        tmp = (-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 <= -3.5e+149) {
		tmp = (b_2 / a) * -2.0;
	} else if (b_2 <= 5.2e-107) {
		tmp = (Math.sqrt(((b_2 * b_2) - (c * a))) - b_2) / a;
	} else {
		tmp = -0.5 * (c / b_2);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -3.5e+149:
		tmp = (b_2 / a) * -2.0
	elif b_2 <= 5.2e-107:
		tmp = (math.sqrt(((b_2 * b_2) - (c * a))) - b_2) / a
	else:
		tmp = -0.5 * (c / b_2)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -3.5e+149)
		tmp = Float64(Float64(b_2 / a) * -2.0);
	elseif (b_2 <= 5.2e-107)
		tmp = Float64(Float64(sqrt(Float64(Float64(b_2 * b_2) - Float64(c * a))) - b_2) / a);
	else
		tmp = 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 <= -3.5e+149)
		tmp = (b_2 / a) * -2.0;
	elseif (b_2 <= 5.2e-107)
		tmp = (sqrt(((b_2 * b_2) - (c * a))) - b_2) / a;
	else
		tmp = -0.5 * (c / b_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -3.5e+149], N[(N[(b$95$2 / a), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[b$95$2, 5.2e-107], N[(N[(N[Sqrt[N[(N[(b$95$2 * b$95$2), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b$95$2), $MachinePrecision] / a), $MachinePrecision], N[(-0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -3.50000000000000011e149

   1. Initial program 37.0%

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

   3. Taylor expanded in b_2 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -3.50000000000000011e149 < b_2 < 5.2000000000000001e-107

   1. Initial program 85.1%

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

   if 5.2000000000000001e-107 < b_2

   1. Initial program 13.4%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 86.4

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

   5. Applied rewrites 86.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{elif}\;b\_2 \leq 5.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{b\_2 \cdot b\_2 - c \cdot a} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{elif}\;b\_2 \leq 5.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{\left(-a\right) \cdot c} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 -4.2e-51)
   (* (/ b_2 a) -2.0)
   (if (<= b_2 5.2e-107) (/ (- (sqrt (* (- a) c)) b_2) a) (* -0.5 (/ c b_2)))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= -4.2e-51) {
		tmp = (b_2 / a) * -2.0;
	} else if (b_2 <= 5.2e-107) {
		tmp = (sqrt((-a * c)) - b_2) / a;
	} else {
		tmp = -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 <= (-4.2d-51)) then
        tmp = (b_2 / a) * (-2.0d0)
    else if (b_2 <= 5.2d-107) then
        tmp = (sqrt((-a * c)) - b_2) / a
    else
        tmp = (-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 <= -4.2e-51) {
		tmp = (b_2 / a) * -2.0;
	} else if (b_2 <= 5.2e-107) {
		tmp = (Math.sqrt((-a * c)) - b_2) / a;
	} else {
		tmp = -0.5 * (c / b_2);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= -4.2e-51:
		tmp = (b_2 / a) * -2.0
	elif b_2 <= 5.2e-107:
		tmp = (math.sqrt((-a * c)) - b_2) / a
	else:
		tmp = -0.5 * (c / b_2)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= -4.2e-51)
		tmp = Float64(Float64(b_2 / a) * -2.0);
	elseif (b_2 <= 5.2e-107)
		tmp = Float64(Float64(sqrt(Float64(Float64(-a) * c)) - b_2) / a);
	else
		tmp = 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 <= -4.2e-51)
		tmp = (b_2 / a) * -2.0;
	elseif (b_2 <= 5.2e-107)
		tmp = (sqrt((-a * c)) - b_2) / a;
	else
		tmp = -0.5 * (c / b_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, -4.2e-51], N[(N[(b$95$2 / a), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[b$95$2, 5.2e-107], N[(N[(N[Sqrt[N[((-a) * c), $MachinePrecision]], $MachinePrecision] - b$95$2), $MachinePrecision] / a), $MachinePrecision], N[(-0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b_2 < -4.20000000000000003e-51

   1. Initial program 63.8%

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

   3. Taylor expanded in b_2 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -4.20000000000000003e-51 < b_2 < 5.2000000000000001e-107

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 70.5

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

   5. Applied rewrites 70.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-neg.f64 N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 70.5

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

   7. Applied rewrites 70.5%

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

   if 5.2000000000000001e-107 < b_2

   1. Initial program 13.4%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 86.4

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

   5. Applied rewrites 86.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{elif}\;b\_2 \leq 5.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{\sqrt{\left(-a\right) \cdot c} - b\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq 1.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 1.45e-256) (* (/ b_2 a) -2.0) (* -0.5 (/ c b_2))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= 1.45e-256) {
		tmp = (b_2 / a) * -2.0;
	} else {
		tmp = -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 <= 1.45d-256) then
        tmp = (b_2 / a) * (-2.0d0)
    else
        tmp = (-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 <= 1.45e-256) {
		tmp = (b_2 / a) * -2.0;
	} else {
		tmp = -0.5 * (c / b_2);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= 1.45e-256:
		tmp = (b_2 / a) * -2.0
	else:
		tmp = -0.5 * (c / b_2)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= 1.45e-256)
		tmp = Float64(Float64(b_2 / a) * -2.0);
	else
		tmp = 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 <= 1.45e-256)
		tmp = (b_2 / a) * -2.0;
	else
		tmp = -0.5 * (c / b_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, 1.45e-256], N[(N[(b$95$2 / a), $MachinePrecision] * -2.0), $MachinePrecision], N[(-0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < 1.44999999999999986e-256

   1. Initial program 71.0%

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

   3. Taylor expanded in b_2 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 64.6

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

   5. Applied rewrites 64.6%

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

   if 1.44999999999999986e-256 < b_2

   1. Initial program 21.2%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 77.4

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

   5. Applied rewrites 77.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq 1.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq 1.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{b\_2} \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 1.45e-256) (* (/ b_2 a) -2.0) (* (/ -0.5 b_2) c)))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= 1.45e-256) {
		tmp = (b_2 / a) * -2.0;
	} else {
		tmp = (-0.5 / b_2) * c;
	}
	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 <= 1.45d-256) then
        tmp = (b_2 / a) * (-2.0d0)
    else
        tmp = ((-0.5d0) / b_2) * c
    end if
    code = tmp
end function

Java

public static double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= 1.45e-256) {
		tmp = (b_2 / a) * -2.0;
	} else {
		tmp = (-0.5 / b_2) * c;
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= 1.45e-256:
		tmp = (b_2 / a) * -2.0
	else:
		tmp = (-0.5 / b_2) * c
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= 1.45e-256)
		tmp = Float64(Float64(b_2 / a) * -2.0);
	else
		tmp = Float64(Float64(-0.5 / b_2) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b_2, c)
	tmp = 0.0;
	if (b_2 <= 1.45e-256)
		tmp = (b_2 / a) * -2.0;
	else
		tmp = (-0.5 / b_2) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, 1.45e-256], N[(N[(b$95$2 / a), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(-0.5 / b$95$2), $MachinePrecision] * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < 1.44999999999999986e-256

   1. Initial program 71.0%

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

   3. Taylor expanded in b_2 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 64.6

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

   5. Applied rewrites 64.6%

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

   if 1.44999999999999986e-256 < b_2

   1. Initial program 21.2%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 77.4

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

   5. Applied rewrites 77.4%

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

   7. Applied rewrites 77.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq 1.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{b\_2} \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b\_2 \leq 3.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b_2 c)
 :precision binary64
 (if (<= b_2 3.8e+42) (* (/ b_2 a) -2.0) (* 0.5 (/ c b_2))))

C

double code(double a, double b_2, double c) {
	double tmp;
	if (b_2 <= 3.8e+42) {
		tmp = (b_2 / a) * -2.0;
	} else {
		tmp = 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 <= 3.8d+42) then
        tmp = (b_2 / a) * (-2.0d0)
    else
        tmp = 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 <= 3.8e+42) {
		tmp = (b_2 / a) * -2.0;
	} else {
		tmp = 0.5 * (c / b_2);
	}
	return tmp;
}

Python

def code(a, b_2, c):
	tmp = 0
	if b_2 <= 3.8e+42:
		tmp = (b_2 / a) * -2.0
	else:
		tmp = 0.5 * (c / b_2)
	return tmp

Julia

function code(a, b_2, c)
	tmp = 0.0
	if (b_2 <= 3.8e+42)
		tmp = Float64(Float64(b_2 / a) * -2.0);
	else
		tmp = 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 <= 3.8e+42)
		tmp = (b_2 / a) * -2.0;
	else
		tmp = 0.5 * (c / b_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b$95$2_, c_] := If[LessEqual[b$95$2, 3.8e+42], N[(N[(b$95$2 / a), $MachinePrecision] * -2.0), $MachinePrecision], N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b_2 < 3.7999999999999998e42

   1. Initial program 65.5%

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

   3. Taylor expanded in b_2 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 52.5

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

   5. Applied rewrites 52.5%

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

   if 3.7999999999999998e42 < b_2

   1. Initial program 9.3%

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

   3. Taylor expanded in b_2 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 2.4

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

   5. Applied rewrites 2.4%

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

   7. Applied rewrites 2.4%

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

   8. Taylor expanded in b_2 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(\frac{c}{\color{blue}{b\_2 \cdot b\_2}}, \frac{-1}{2}, 2 \cdot \frac{1}{a}\right) \cdot \left(-1 \cdot b\_2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{c}{\color{blue}{b\_2 \cdot b\_2}}, \frac{-1}{2}, 2 \cdot \frac{1}{a}\right) \cdot \left(-1 \cdot b\_2\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \color{blue}{\frac{2 \cdot 1}{a}}\right) \cdot \left(-1 \cdot b\_2\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \frac{\color{blue}{2}}{a}\right) \cdot \left(-1 \cdot b\_2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \color{blue}{\frac{2}{a}}\right) \cdot \left(-1 \cdot b\_2\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \frac{2}{a}\right) \cdot \color{blue}{\left(\mathsf{neg}\left(b\_2\right)\right)} \]

      15. lower-neg.f64 2.3

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

   10. Applied rewrites 2.3%

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

   11. Taylor expanded in a around inf

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

   13. Applied rewrites 17.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b\_2 \leq 3.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{b\_2}{a} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{c}{b\_2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 11.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \frac{c}{b\_2} \end{array} \]

FPCore

(FPCore (a b_2 c) :precision binary64 (* 0.5 (/ c b_2)))

C

double code(double a, double b_2, double c) {
	return 0.5 * (c / b_2);
}

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 = 0.5d0 * (c / b_2)
end function

Java

public static double code(double a, double b_2, double c) {
	return 0.5 * (c / b_2);
}

Python

def code(a, b_2, c):
	return 0.5 * (c / b_2)

Julia

function code(a, b_2, c)
	return Float64(0.5 * Float64(c / b_2))
end

MATLAB

function tmp = code(a, b_2, c)
	tmp = 0.5 * (c / b_2);
end

Wolfram

code[a_, b$95$2_, c_] := N[(0.5 * N[(c / b$95$2), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 50.8%

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

3. Taylor expanded in b_2 around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 39.4

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

5. Applied rewrites 39.4%

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

7. Applied rewrites 39.3%

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

8. Taylor expanded in b_2 around -inf

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

   1. mul-1-neg N/A

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

   2. *-commutative N/A

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

   3. distribute-rgt-neg-in N/A

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

   4. mul-1-neg N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. unpow2 N/A

      \[\leadsto \mathsf{fma}\left(\frac{c}{\color{blue}{b\_2 \cdot b\_2}}, \frac{-1}{2}, 2 \cdot \frac{1}{a}\right) \cdot \left(-1 \cdot b\_2\right) \]

   10. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{c}{\color{blue}{b\_2 \cdot b\_2}}, \frac{-1}{2}, 2 \cdot \frac{1}{a}\right) \cdot \left(-1 \cdot b\_2\right) \]

   11. associate-*r/ N/A

       \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \color{blue}{\frac{2 \cdot 1}{a}}\right) \cdot \left(-1 \cdot b\_2\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \frac{\color{blue}{2}}{a}\right) \cdot \left(-1 \cdot b\_2\right) \]

   13. lower-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \color{blue}{\frac{2}{a}}\right) \cdot \left(-1 \cdot b\_2\right) \]

   14. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{c}{b\_2 \cdot b\_2}, \frac{-1}{2}, \frac{2}{a}\right) \cdot \color{blue}{\left(\mathsf{neg}\left(b\_2\right)\right)} \]

   15. lower-neg.f64 38.9

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

10. Applied rewrites 38.9%

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

11. Taylor expanded in a around inf

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

13. Applied rewrites 6.8%

    \[\leadsto 0.5 \cdot \color{blue}{\frac{c}{b\_2}} \]
14. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.2× 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 2024248 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  :precision binary64
  :herbie-expected 10

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

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