quadp (p42, positive)

Percentage Accurate: 52.3% → 85.1%

Time: 12.3s

Alternatives: 9

Speedup: 19.1×

Specification

Math

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

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 52.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - (4.0d0 * (a * c))))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(a * c))))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - (4.0 * (a * c))))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+61}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -9e+61)
   (- (/ c b) (/ b a))
   (if (<= b 1.7e-120)
     (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) (* a 2.0))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -9e+61) {
		tmp = (c / b) - (b / a);
	} else if (b <= 1.7e-120) {
		tmp = (sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-9d+61)) then
        tmp = (c / b) - (b / a)
    else if (b <= 1.7d-120) then
        tmp = (sqrt(((b * b) - (4.0d0 * (c * a)))) - b) / (a * 2.0d0)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -9e+61) {
		tmp = (c / b) - (b / a);
	} else if (b <= 1.7e-120) {
		tmp = (Math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -9e+61:
		tmp = (c / b) - (b / a)
	elif b <= 1.7e-120:
		tmp = (math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -9e+61)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 1.7e-120)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a)))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -9e+61)
		tmp = (c / b) - (b / a);
	elseif (b <= 1.7e-120)
		tmp = (sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -9e+61], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-120], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9e61

   1. Initial program 65.1%

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

      1. neg-sub0 65.1%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 65.1%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 65.1%

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

      4. neg-mul-1 65.1%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 65.1%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 64.9%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 65.2%

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

   4. Taylor expanded in b around -inf 95.5%

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

      1. mul-1-neg 95.5%

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

      2. unsub-neg 95.5%

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

   6. Simplified 95.5%

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

   if -9e61 < b < 1.70000000000000005e-120

   1. Initial program 86.7%

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

   if 1.70000000000000005e-120 < b

   1. Initial program 13.2%

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

      1. neg-sub0 13.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 13.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 13.2%

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

      4. neg-mul-1 13.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 13.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 13.2%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 13.2%

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

   4. Taylor expanded in b around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+61}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 2: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-119}:\\ \;\;\;\;\left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -7.5e-64)
   (- (/ c b) (/ b a))
   (if (<= b 3.4e-119)
     (* (- b (sqrt (* (* c a) -4.0))) (/ -0.5 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-64) {
		tmp = (c / b) - (b / a);
	} else if (b <= 3.4e-119) {
		tmp = (b - sqrt(((c * a) * -4.0))) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-7.5d-64)) then
        tmp = (c / b) - (b / a)
    else if (b <= 3.4d-119) then
        tmp = (b - sqrt(((c * a) * (-4.0d0)))) * ((-0.5d0) / a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-64) {
		tmp = (c / b) - (b / a);
	} else if (b <= 3.4e-119) {
		tmp = (b - Math.sqrt(((c * a) * -4.0))) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -7.5e-64:
		tmp = (c / b) - (b / a)
	elif b <= 3.4e-119:
		tmp = (b - math.sqrt(((c * a) * -4.0))) * (-0.5 / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -7.5e-64)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 3.4e-119)
		tmp = Float64(Float64(b - sqrt(Float64(Float64(c * a) * -4.0))) * Float64(-0.5 / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -7.5e-64)
		tmp = (c / b) - (b / a);
	elseif (b <= 3.4e-119)
		tmp = (b - sqrt(((c * a) * -4.0))) * (-0.5 / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -7.5e-64], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-119], N[(N[(b - N[Sqrt[N[(N[(c * a), $MachinePrecision] * -4.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.49999999999999949e-64

   1. Initial program 74.2%

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

      1. neg-sub0 74.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 74.2%

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

      4. neg-mul-1 74.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 74.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 74.1%

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

   4. Taylor expanded in b around -inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   6. Simplified 85.4%

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

   if -7.49999999999999949e-64 < b < 3.40000000000000024e-119

   1. Initial program 82.5%

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

      1. neg-sub0 82.5%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 82.5%

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

      4. neg-mul-1 82.5%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 82.5%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 82.4%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 82.4%

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

      1. fma-udef 82.4%

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

      2. associate-*r* 82.4%

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

      3. metadata-eval 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      5. *-commutative 82.4%

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

      6. +-commutative 82.4%

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

      7. sub-neg 82.4%

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

      8. add-sqr-sqrt 81.8%

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

      9. pow2 81.8%

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

   5. Applied egg-rr 81.9%

      \[\leadsto \left(b - \color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \frac{-0.5}{a} \]

   6. Taylor expanded in a around inf 42.0%

      \[\leadsto \color{blue}{\left(b - {\left(e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right)}^{2}\right)} \cdot \frac{-0.5}{a} \]
   7. Step-by-step derivation

      1. unpow2 42.0%

         \[\leadsto \left(b - \color{blue}{e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}}\right) \cdot \frac{-0.5}{a} \]

      2. *-commutative 42.0%

         \[\leadsto \left(b - e^{\color{blue}{\left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right) \cdot 0.25}} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      3. exp-prod 33.8%

         \[\leadsto \left(b - \color{blue}{{\left(e^{-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)}\right)}^{0.25}} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      4. mul-1-neg 33.8%

         \[\leadsto \left(b - {\left(e^{\color{blue}{\left(-\log \left(\frac{1}{a}\right)\right)} + \log \left(-4 \cdot c\right)}\right)}^{0.25} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      5. log-rec 33.8%

         \[\leadsto \left(b - {\left(e^{\left(-\color{blue}{\left(-\log a\right)}\right) + \log \left(-4 \cdot c\right)}\right)}^{0.25} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      6. remove-double-neg 33.8%

         \[\leadsto \left(b - {\left(e^{\color{blue}{\log a} + \log \left(-4 \cdot c\right)}\right)}^{0.25} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      7. *-commutative 33.8%

         \[\leadsto \left(b - {\left(e^{\log a + \log \color{blue}{\left(c \cdot -4\right)}}\right)}^{0.25} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      8. log-prod 34.3%

         \[\leadsto \left(b - {\left(e^{\color{blue}{\log \left(a \cdot \left(c \cdot -4\right)\right)}}\right)}^{0.25} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      9. rem-exp-log 34.3%

         \[\leadsto \left(b - {\color{blue}{\left(a \cdot \left(c \cdot -4\right)\right)}}^{0.25} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      10. metadata-eval 34.3%

          \[\leadsto \left(b - {\left(a \cdot \left(c \cdot -4\right)\right)}^{\color{blue}{\left(\frac{0.5}{2}\right)}} \cdot e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right) \cdot \frac{-0.5}{a} \]

      11. *-commutative 34.3%

          \[\leadsto \left(b - {\left(a \cdot \left(c \cdot -4\right)\right)}^{\left(\frac{0.5}{2}\right)} \cdot e^{\color{blue}{\left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right) \cdot 0.25}}\right) \cdot \frac{-0.5}{a} \]

      12. exp-prod 34.3%

          \[\leadsto \left(b - {\left(a \cdot \left(c \cdot -4\right)\right)}^{\left(\frac{0.5}{2}\right)} \cdot \color{blue}{{\left(e^{-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)}\right)}^{0.25}}\right) \cdot \frac{-0.5}{a} \]

   8. Simplified 76.8%

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

   if 3.40000000000000024e-119 < b

   1. Initial program 13.2%

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

      1. neg-sub0 13.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 13.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 13.2%

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

      4. neg-mul-1 13.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 13.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 13.2%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 13.2%

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

   4. Taylor expanded in b around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-119}:\\ \;\;\;\;\left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 3: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-119}:\\ \;\;\;\;\frac{-0.5}{\frac{a}{b - \sqrt{c \cdot \left(a \cdot -4\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6.2e-66)
   (- (/ c b) (/ b a))
   (if (<= b 1.02e-119)
     (/ -0.5 (/ a (- b (sqrt (* c (* a -4.0))))))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.2e-66) {
		tmp = (c / b) - (b / a);
	} else if (b <= 1.02e-119) {
		tmp = -0.5 / (a / (b - sqrt((c * (a * -4.0)))));
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-6.2d-66)) then
        tmp = (c / b) - (b / a)
    else if (b <= 1.02d-119) then
        tmp = (-0.5d0) / (a / (b - sqrt((c * (a * (-4.0d0))))))
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.2e-66) {
		tmp = (c / b) - (b / a);
	} else if (b <= 1.02e-119) {
		tmp = -0.5 / (a / (b - Math.sqrt((c * (a * -4.0)))));
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6.2e-66:
		tmp = (c / b) - (b / a)
	elif b <= 1.02e-119:
		tmp = -0.5 / (a / (b - math.sqrt((c * (a * -4.0)))))
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6.2e-66)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 1.02e-119)
		tmp = Float64(-0.5 / Float64(a / Float64(b - sqrt(Float64(c * Float64(a * -4.0))))));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6.2e-66)
		tmp = (c / b) - (b / a);
	elseif (b <= 1.02e-119)
		tmp = -0.5 / (a / (b - sqrt((c * (a * -4.0)))));
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6.2e-66], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-119], N[(-0.5 / N[(a / N[(b - N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.1999999999999995e-66

   1. Initial program 74.2%

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

      1. neg-sub0 74.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 74.2%

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

      4. neg-mul-1 74.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 74.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 74.1%

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

   4. Taylor expanded in b around -inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   6. Simplified 85.4%

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

   if -6.1999999999999995e-66 < b < 1.02e-119

   1. Initial program 82.5%

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

      1. neg-sub0 82.5%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 82.5%

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

      4. neg-mul-1 82.5%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 82.5%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 82.4%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 82.4%

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

      1. fma-udef 82.4%

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

      2. associate-*r* 82.4%

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

      3. metadata-eval 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      5. *-commutative 82.4%

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

      6. +-commutative 82.4%

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

      7. sub-neg 82.4%

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

      8. add-sqr-sqrt 81.8%

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

      9. pow2 81.8%

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

   5. Applied egg-rr 81.9%

      \[\leadsto \left(b - \color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \frac{-0.5}{a} \]

   6. Taylor expanded in a around inf 42.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{b - {\left(e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right)}^{2}}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 42.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(b - {\left(e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right)}^{2}\right)}{a}} \]

   8. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right)}{a}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 52.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-0.5 \cdot \left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right)}{a}\right)\right)} \]

      2. expm1-udef 22.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-0.5 \cdot \left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right)}{a}\right)} - 1} \]

      3. *-commutative 22.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{-0.5 \cdot \left(b - \sqrt{\color{blue}{-4 \cdot \left(c \cdot a\right)}}\right)}{a}\right)} - 1 \]

      4. *-commutative 22.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{-0.5 \cdot \left(b - \sqrt{-4 \cdot \color{blue}{\left(a \cdot c\right)}}\right)}{a}\right)} - 1 \]

   10. Applied egg-rr 22.6%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-0.5 \cdot \left(b - \sqrt{-4 \cdot \left(a \cdot c\right)}\right)}{a}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 52.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-0.5 \cdot \left(b - \sqrt{-4 \cdot \left(a \cdot c\right)}\right)}{a}\right)\right)} \]

       2. expm1-log1p 76.9%

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

       3. associate-/l* 76.8%

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

       4. *-commutative 76.8%

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

       5. *-commutative 76.8%

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

       6. associate-*r* 76.8%

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

   12. Simplified 76.8%

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

   if 1.02e-119 < b

   1. Initial program 13.2%

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

      1. neg-sub0 13.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 13.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 13.2%

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

      4. neg-mul-1 13.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 13.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 13.2%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 13.2%

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

   4. Taylor expanded in b around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-119}:\\ \;\;\;\;\frac{-0.5}{\frac{a}{b - \sqrt{c \cdot \left(a \cdot -4\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 4: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{-0.5 \cdot \left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -9.2e-64)
   (- (/ c b) (/ b a))
   (if (<= b 1.3e-119)
     (/ (* -0.5 (- b (sqrt (* (* c a) -4.0)))) a)
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -9.2e-64) {
		tmp = (c / b) - (b / a);
	} else if (b <= 1.3e-119) {
		tmp = (-0.5 * (b - sqrt(((c * a) * -4.0)))) / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-9.2d-64)) then
        tmp = (c / b) - (b / a)
    else if (b <= 1.3d-119) then
        tmp = ((-0.5d0) * (b - sqrt(((c * a) * (-4.0d0))))) / a
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -9.2e-64) {
		tmp = (c / b) - (b / a);
	} else if (b <= 1.3e-119) {
		tmp = (-0.5 * (b - Math.sqrt(((c * a) * -4.0)))) / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -9.2e-64:
		tmp = (c / b) - (b / a)
	elif b <= 1.3e-119:
		tmp = (-0.5 * (b - math.sqrt(((c * a) * -4.0)))) / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -9.2e-64)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 1.3e-119)
		tmp = Float64(Float64(-0.5 * Float64(b - sqrt(Float64(Float64(c * a) * -4.0)))) / a);
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -9.2e-64)
		tmp = (c / b) - (b / a);
	elseif (b <= 1.3e-119)
		tmp = (-0.5 * (b - sqrt(((c * a) * -4.0)))) / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -9.2e-64], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-119], N[(N[(-0.5 * N[(b - N[Sqrt[N[(N[(c * a), $MachinePrecision] * -4.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.2000000000000006e-64

   1. Initial program 74.2%

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

      1. neg-sub0 74.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 74.2%

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

      4. neg-mul-1 74.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 74.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 74.1%

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

   4. Taylor expanded in b around -inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   6. Simplified 85.4%

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

   if -9.2000000000000006e-64 < b < 1.30000000000000006e-119

   1. Initial program 82.5%

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

      1. neg-sub0 82.5%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 82.5%

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

      4. neg-mul-1 82.5%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 82.5%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 82.4%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 82.4%

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

      1. fma-udef 82.4%

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

      2. associate-*r* 82.4%

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

      3. metadata-eval 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      5. *-commutative 82.4%

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

      6. +-commutative 82.4%

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

      7. sub-neg 82.4%

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

      8. add-sqr-sqrt 81.8%

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

      9. pow2 81.8%

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

   5. Applied egg-rr 81.9%

      \[\leadsto \left(b - \color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \frac{-0.5}{a} \]

   6. Taylor expanded in a around inf 42.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{b - {\left(e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right)}^{2}}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 42.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(b - {\left(e^{0.25 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}\right)}^{2}\right)}{a}} \]

   8. Simplified 76.9%

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

   if 1.30000000000000006e-119 < b

   1. Initial program 13.2%

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

      1. neg-sub0 13.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 13.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 13.2%

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

      4. neg-mul-1 13.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 13.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 13.2%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 13.2%

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

   4. Taylor expanded in b around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{-0.5 \cdot \left(b - \sqrt{\left(c \cdot a\right) \cdot -4}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 5: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-121}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -9.5e-65)
   (- (/ c b) (/ b a))
   (if (<= b 3.8e-121)
     (/ (- (sqrt (* a (* c -4.0))) b) (* a 2.0))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -9.5e-65) {
		tmp = (c / b) - (b / a);
	} else if (b <= 3.8e-121) {
		tmp = (sqrt((a * (c * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-9.5d-65)) then
        tmp = (c / b) - (b / a)
    else if (b <= 3.8d-121) then
        tmp = (sqrt((a * (c * (-4.0d0)))) - b) / (a * 2.0d0)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -9.5e-65) {
		tmp = (c / b) - (b / a);
	} else if (b <= 3.8e-121) {
		tmp = (Math.sqrt((a * (c * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -9.5e-65:
		tmp = (c / b) - (b / a)
	elif b <= 3.8e-121:
		tmp = (math.sqrt((a * (c * -4.0))) - b) / (a * 2.0)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -9.5e-65)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 3.8e-121)
		tmp = Float64(Float64(sqrt(Float64(a * Float64(c * -4.0))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -9.5e-65)
		tmp = (c / b) - (b / a);
	elseif (b <= 3.8e-121)
		tmp = (sqrt((a * (c * -4.0))) - b) / (a * 2.0);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -9.5e-65], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-121], N[(N[(N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5000000000000004e-65

   1. Initial program 74.2%

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

      1. neg-sub0 74.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 74.2%

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

      4. neg-mul-1 74.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 74.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 74.1%

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

   4. Taylor expanded in b around -inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   6. Simplified 85.4%

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

   if -9.5000000000000004e-65 < b < 3.8000000000000001e-121

   1. Initial program 82.5%

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

   2. Taylor expanded in b around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 77.0%

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

   4. Simplified 77.0%

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

   if 3.8000000000000001e-121 < b

   1. Initial program 13.2%

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

      1. neg-sub0 13.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 13.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 13.2%

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

      4. neg-mul-1 13.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 13.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 13.2%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 13.2%

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

   4. Taylor expanded in b around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-121}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 6: 68.1% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-311}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1e-311) (- (/ c b) (/ b a)) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1e-311) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1d-311)) then
        tmp = (c / b) - (b / a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1e-311) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1e-311:
		tmp = (c / b) - (b / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1e-311)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1e-311)
		tmp = (c / b) - (b / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1e-311], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.99999999999948e-312

   1. Initial program 77.9%

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

      1. neg-sub0 77.9%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 77.9%

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

      4. neg-mul-1 77.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 77.9%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 77.7%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 77.8%

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

   4. Taylor expanded in b around -inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   6. Simplified 70.2%

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

   if -9.99999999999948e-312 < b

   1. Initial program 22.7%

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

      1. neg-sub0 22.7%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 22.7%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 22.7%

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

      4. neg-mul-1 22.7%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 22.7%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 22.7%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 22.8%

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

   4. Taylor expanded in b around inf 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

   6. Simplified 77.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-311}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 7: 43.8% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 5.8e+44) (/ (- b) a) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 5.8e+44) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 5.8d+44) then
        tmp = -b / a
    else
        tmp = c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 5.8e+44) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 5.8e+44:
		tmp = -b / a
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 5.8e+44)
		tmp = Float64(Float64(-b) / a);
	else
		tmp = Float64(c / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 5.8e+44)
		tmp = -b / a;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 5.8e+44], N[((-b) / a), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.8000000000000004e44

   1. Initial program 68.9%

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

      1. neg-sub0 68.9%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 68.9%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 68.9%

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

      4. neg-mul-1 68.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 68.9%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 68.8%

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

   4. Taylor expanded in b around -inf 51.8%

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

      1. associate-*r/ 51.8%

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

      2. mul-1-neg 51.8%

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

   6. Simplified 51.8%

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

   if 5.8000000000000004e44 < b

   1. Initial program 10.3%

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

      1. neg-sub0 10.3%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 10.3%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 10.3%

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

      4. neg-mul-1 10.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 10.3%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 10.3%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 10.3%

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

   4. Taylor expanded in b around -inf 2.6%

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

      1. mul-1-neg 2.6%

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

      2. unsub-neg 2.6%

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

   6. Simplified 2.6%

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

   7. Taylor expanded in c around inf 26.1%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 8: 67.9% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-304}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.6e-304) (/ (- b) a) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-304) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 2.6d-304) then
        tmp = -b / a
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-304) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.6e-304:
		tmp = -b / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.6e-304)
		tmp = Float64(Float64(-b) / a);
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 2.6e-304)
		tmp = -b / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.6e-304], N[((-b) / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.59999999999999997e-304

   1. Initial program 78.2%

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

      1. neg-sub0 78.2%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 78.2%

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

      4. neg-mul-1 78.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 78.2%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 78.0%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 78.2%

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

   4. Taylor expanded in b around -inf 68.9%

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

      1. associate-*r/ 68.9%

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

      2. mul-1-neg 68.9%

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

   6. Simplified 68.9%

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

   if 2.59999999999999997e-304 < b

   1. Initial program 21.5%

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

      1. neg-sub0 21.5%

         \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

      2. associate-+l- 21.5%

         \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      3. sub0-neg 21.5%

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

      4. neg-mul-1 21.5%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

      5. *-commutative 21.5%

         \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

      6. associate-*r/ 21.5%

         \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

   3. Simplified 21.6%

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

   4. Taylor expanded in b around inf 78.9%

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

      1. associate-*r/ 78.9%

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

      2. neg-mul-1 78.9%

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

   6. Simplified 78.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-304}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 9: 11.0% accurate, 38.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 50.1%

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

   1. neg-sub0 50.1%

      \[\leadsto \frac{\color{blue}{\left(0 - b\right)} + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \]

   2. associate-+l- 50.1%

      \[\leadsto \frac{\color{blue}{0 - \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

   3. sub0-neg 50.1%

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

   4. neg-mul-1 50.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a} \]

   5. *-commutative 50.1%

      \[\leadsto \frac{\color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot -1}}{2 \cdot a} \]

   6. associate-*r/ 50.0%

      \[\leadsto \color{blue}{\left(b - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{-1}{2 \cdot a}} \]

3. Simplified 50.1%

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

4. Taylor expanded in b around -inf 36.0%

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

   1. mul-1-neg 36.0%

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

   2. unsub-neg 36.0%

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

6. Simplified 36.0%

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

7. Taylor expanded in c around inf 10.5%

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

8. Final simplification 10.5%

   \[\leadsto \frac{c}{b} \]

Developer target: 70.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023218 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64

  :herbie-target
  (if (< b 0.0) (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)) (/ c (* a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))))

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