quadp (p42, positive)

Percentage Accurate: 51.9% → 87.3%

Time: 11.9s

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: 51.9% 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: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-254}:\\ \;\;\;\;\frac{\left(b - \sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)}\right) \cdot -0.5}{a}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;\frac{0.5}{\frac{1}{\frac{a}{-a} \cdot \frac{c \cdot 4}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -4.8e+72)
   (- (/ c b) (/ b a))
   (if (<= b 2.3e-254)
     (/ (* (- b (sqrt (- (* b b) (* a (* c 4.0))))) -0.5) a)
     (if (<= b 1.75e-72)
       (/
        0.5
        (/
         1.0
         (*
          (/ a (- a))
          (/ (* c 4.0) (+ b (hypot (sqrt (* a (* c -4.0))) b))))))
       (/ (- c) b)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -4.8e+72) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.3e-254) {
		tmp = ((b - sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a;
	} else if (b <= 1.75e-72) {
		tmp = 0.5 / (1.0 / ((a / -a) * ((c * 4.0) / (b + hypot(sqrt((a * (c * -4.0))), b)))));
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -4.8e+72) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.3e-254) {
		tmp = ((b - Math.sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a;
	} else if (b <= 1.75e-72) {
		tmp = 0.5 / (1.0 / ((a / -a) * ((c * 4.0) / (b + Math.hypot(Math.sqrt((a * (c * -4.0))), b)))));
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -4.8e+72:
		tmp = (c / b) - (b / a)
	elif b <= 2.3e-254:
		tmp = ((b - math.sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a
	elif b <= 1.75e-72:
		tmp = 0.5 / (1.0 / ((a / -a) * ((c * 4.0) / (b + math.hypot(math.sqrt((a * (c * -4.0))), b)))))
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -4.8e+72)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 2.3e-254)
		tmp = Float64(Float64(Float64(b - sqrt(Float64(Float64(b * b) - Float64(a * Float64(c * 4.0))))) * -0.5) / a);
	elseif (b <= 1.75e-72)
		tmp = Float64(0.5 / Float64(1.0 / Float64(Float64(a / Float64(-a)) * Float64(Float64(c * 4.0) / Float64(b + hypot(sqrt(Float64(a * Float64(c * -4.0))), b))))));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -4.8e+72)
		tmp = (c / b) - (b / a);
	elseif (b <= 2.3e-254)
		tmp = ((b - sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a;
	elseif (b <= 1.75e-72)
		tmp = 0.5 / (1.0 / ((a / -a) * ((c * 4.0) / (b + hypot(sqrt((a * (c * -4.0))), b)))));
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -4.8e+72], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-254], N[(N[(N[(b - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(a * N[(c * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.75e-72], N[(0.5 / N[(1.0 / N[(N[(a / (-a)), $MachinePrecision] * N[(N[(c * 4.0), $MachinePrecision] / N[(b + N[Sqrt[N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] ^ 2 + b ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.8000000000000002e72

   1. Initial program 55.6%

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

      1. neg-sub0 55.6%

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

      2. associate-+l- 55.6%

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

      3. sub0-neg 55.6%

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

      4. neg-mul-1 55.6%

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

      5. *-commutative 55.6%

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

      6. associate-*r/ 55.5%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in b around -inf 96.9%

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

      1. mul-1-neg 96.9%

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

      2. unsub-neg 96.9%

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

   6. Simplified 96.9%

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

   if -4.8000000000000002e72 < b < 2.2999999999999999e-254

   1. Initial program 83.6%

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

      1. neg-sub0 83.6%

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

      2. associate-+l- 83.6%

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

      3. sub0-neg 83.6%

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

      4. neg-mul-1 83.6%

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

      5. *-commutative 83.6%

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

      6. associate-*r/ 83.3%

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

   3. Simplified 83.3%

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

      1. fma-udef 83.3%

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

      2. associate-*r* 83.3%

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

      3. metadata-eval 83.3%

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

      4. distribute-rgt-neg-in 83.3%

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

      5. *-commutative 83.3%

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

      6. +-commutative 83.3%

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

      7. sub-neg 83.3%

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

      8. *-commutative 83.3%

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

      9. associate-*l* 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. associate-*r/ 83.6%

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

   7. Applied egg-rr 83.6%

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

   if 2.2999999999999999e-254 < b < 1.75e-72

   1. Initial program 61.3%

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

      1. neg-sub0 61.3%

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

      2. associate-+l- 61.3%

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

      3. sub0-neg 61.3%

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

      4. neg-mul-1 61.3%

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

      5. *-commutative 61.3%

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

      6. associate-*r/ 61.0%

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

   3. Simplified 61.2%

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

      1. associate-*r/ 61.5%

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

      2. frac-2neg 61.5%

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

   5. Applied egg-rr 61.5%

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

      1. distribute-rgt-neg-in 61.5%

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

      2. metadata-eval 61.5%

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

      3. *-commutative 61.5%

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

      4. associate-/l* 61.1%

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

      5. fma-def 61.1%

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

      6. +-commutative 61.1%

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

      7. fma-def 61.1%

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

   7. Simplified 61.1%

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

      1. flip-- 60.6%

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

      2. add-sqr-sqrt 60.7%

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

   9. Applied egg-rr 60.7%

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

       1. metadata-eval 60.7%

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

       2. distribute-rgt-neg-in 60.7%

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

       3. distribute-rgt-neg-in 60.7%

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

       4. fma-def 60.7%

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

       5. associate--r+ 67.1%

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

       6. +-inverses 67.1%

          \[\leadsto \frac{0.5}{\frac{-a}{\frac{\color{blue}{0} - \left(-a \cdot \left(c \cdot 4\right)\right)}{b + \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}}}} \]

       7. associate-*r* 66.8%

          \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - \left(-\color{blue}{\left(a \cdot c\right) \cdot 4}\right)}{b + \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}}}} \]

       8. *-commutative 66.8%

          \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - \left(-\color{blue}{\left(c \cdot a\right)} \cdot 4\right)}{b + \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}}}} \]

       9. distribute-rgt-neg-in 66.8%

          \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - \color{blue}{\left(c \cdot a\right) \cdot \left(-4\right)}}{b + \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}}}} \]

       10. metadata-eval 66.8%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - \left(c \cdot a\right) \cdot \color{blue}{-4}}{b + \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}}}} \]

       11. associate-*l* 67.1%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - \color{blue}{c \cdot \left(a \cdot -4\right)}}{b + \sqrt{\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)}}}} \]

       12. fma-def 67.1%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\color{blue}{b \cdot b + a \cdot \left(c \cdot -4\right)}}}}} \]

       13. +-commutative 67.1%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\color{blue}{a \cdot \left(c \cdot -4\right) + b \cdot b}}}}} \]

       14. associate-*r* 67.0%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\color{blue}{\left(a \cdot c\right) \cdot -4} + b \cdot b}}}} \]

       15. *-commutative 67.0%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\color{blue}{\left(c \cdot a\right)} \cdot -4 + b \cdot b}}}} \]

       16. fma-def 67.0%

           \[\leadsto \frac{0.5}{\frac{-a}{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\color{blue}{\mathsf{fma}\left(c \cdot a, -4, b \cdot b\right)}}}}} \]

   11. Simplified 67.0%

       \[\leadsto \frac{0.5}{\frac{-a}{\color{blue}{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\mathsf{fma}\left(c \cdot a, -4, b \cdot b\right)}}}}} \]
   12. Step-by-step derivation

       1. clear-num 67.1%

          \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{\frac{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\mathsf{fma}\left(c \cdot a, -4, b \cdot b\right)}}}{-a}}}} \]

       2. inv-pow 67.1%

          \[\leadsto \frac{0.5}{\color{blue}{{\left(\frac{\frac{0 - c \cdot \left(a \cdot -4\right)}{b + \sqrt{\mathsf{fma}\left(c \cdot a, -4, b \cdot b\right)}}}{-a}\right)}^{-1}}} \]

       3. sub0-neg 67.1%

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

       4. associate-*r* 67.0%

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

       5. *-commutative 67.0%

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

       6. associate-*r* 67.1%

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

       7. fma-udef 67.1%

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

       8. *-commutative 67.1%

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

       9. associate-*r* 67.3%

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

       10. add-sqr-sqrt 67.3%

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

       11. hypot-def 67.3%

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

   13. Applied egg-rr 67.3%

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

       1. unpow-1 67.3%

          \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{\frac{\frac{-a \cdot \left(c \cdot -4\right)}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}{-a}}}} \]

       2. associate-/l/ 66.5%

          \[\leadsto \frac{0.5}{\frac{1}{\color{blue}{\frac{-a \cdot \left(c \cdot -4\right)}{\left(-a\right) \cdot \left(b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)\right)}}}} \]

       3. distribute-rgt-neg-in 66.5%

          \[\leadsto \frac{0.5}{\frac{1}{\frac{\color{blue}{a \cdot \left(-c \cdot -4\right)}}{\left(-a\right) \cdot \left(b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)\right)}}} \]

       4. times-frac 80.3%

          \[\leadsto \frac{0.5}{\frac{1}{\color{blue}{\frac{a}{-a} \cdot \frac{-c \cdot -4}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}}} \]

       5. distribute-rgt-neg-in 80.3%

          \[\leadsto \frac{0.5}{\frac{1}{\frac{a}{-a} \cdot \frac{\color{blue}{c \cdot \left(--4\right)}}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}} \]

       6. metadata-eval 80.3%

          \[\leadsto \frac{0.5}{\frac{1}{\frac{a}{-a} \cdot \frac{c \cdot \color{blue}{4}}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}} \]

   15. Simplified 80.3%

       \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{\frac{a}{-a} \cdot \frac{c \cdot 4}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}}} \]

   if 1.75e-72 < b

   1. Initial program 10.0%

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

      1. neg-sub0 10.0%

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

      2. associate-+l- 10.0%

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

      3. sub0-neg 10.0%

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

      4. neg-mul-1 10.0%

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

      5. *-commutative 10.0%

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

      6. associate-*r/ 9.9%

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

   3. Simplified 9.9%

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

   4. Taylor expanded in b around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{-c}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-254}:\\ \;\;\;\;\frac{\left(b - \sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)}\right) \cdot -0.5}{a}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;\frac{0.5}{\frac{1}{\frac{a}{-a} \cdot \frac{c \cdot 4}{b + \mathsf{hypot}\left(\sqrt{a \cdot \left(c \cdot -4\right)}, b\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 2: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;\left(b - \sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5.2e+72)
   (- (/ c b) (/ b a))
   (if (<= b 2.4e-74)
     (* (- b (sqrt (- (* b b) (* a (* c 4.0))))) (/ -0.5 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5.2e+72) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.4e-74) {
		tmp = (b - sqrt(((b * b) - (a * (c * 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 <= (-5.2d+72)) then
        tmp = (c / b) - (b / a)
    else if (b <= 2.4d-74) then
        tmp = (b - sqrt(((b * b) - (a * (c * 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 <= -5.2e+72) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.4e-74) {
		tmp = (b - Math.sqrt(((b * b) - (a * (c * 4.0))))) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5.2e+72:
		tmp = (c / b) - (b / a)
	elif b <= 2.4e-74:
		tmp = (b - math.sqrt(((b * b) - (a * (c * 4.0))))) * (-0.5 / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5.2e+72)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 2.4e-74)
		tmp = Float64(Float64(b - sqrt(Float64(Float64(b * b) - Float64(a * Float64(c * 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 <= -5.2e+72)
		tmp = (c / b) - (b / a);
	elseif (b <= 2.4e-74)
		tmp = (b - sqrt(((b * b) - (a * (c * 4.0))))) * (-0.5 / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5.2e+72], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-74], N[(N[(b - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(a * N[(c * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.19999999999999963e72

   1. Initial program 55.6%

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

      1. neg-sub0 55.6%

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

      2. associate-+l- 55.6%

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

      3. sub0-neg 55.6%

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

      4. neg-mul-1 55.6%

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

      5. *-commutative 55.6%

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

      6. associate-*r/ 55.5%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in b around -inf 96.9%

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

      1. mul-1-neg 96.9%

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

      2. unsub-neg 96.9%

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

   6. Simplified 96.9%

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

   if -5.19999999999999963e72 < b < 2.3999999999999999e-74

   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/ 77.9%

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

   3. Simplified 78.0%

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

      1. fma-udef 78.0%

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

      2. associate-*r* 77.9%

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

      3. metadata-eval 77.9%

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

      4. distribute-rgt-neg-in 77.9%

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

      5. *-commutative 77.9%

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

      6. +-commutative 77.9%

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

      7. sub-neg 77.9%

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

      8. *-commutative 77.9%

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

      9. associate-*l* 78.0%

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

   5. Applied egg-rr 78.0%

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

   if 2.3999999999999999e-74 < b

   1. Initial program 10.0%

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

      1. neg-sub0 10.0%

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

      2. associate-+l- 10.0%

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

      3. sub0-neg 10.0%

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

      4. neg-mul-1 10.0%

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

      5. *-commutative 10.0%

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

      6. associate-*r/ 9.9%

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

   3. Simplified 9.9%

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

   4. Taylor expanded in b around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;\left(b - \sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 3: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\left(b - \sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)}\right) \cdot -0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -7.5e+70)
   (- (/ c b) (/ b a))
   (if (<= b 8e-73)
     (/ (* (- b (sqrt (- (* b b) (* a (* c 4.0))))) -0.5) a)
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e+70) {
		tmp = (c / b) - (b / a);
	} else if (b <= 8e-73) {
		tmp = ((b - sqrt(((b * b) - (a * (c * 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+70)) then
        tmp = (c / b) - (b / a)
    else if (b <= 8d-73) then
        tmp = ((b - sqrt(((b * b) - (a * (c * 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+70) {
		tmp = (c / b) - (b / a);
	} else if (b <= 8e-73) {
		tmp = ((b - Math.sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -7.5e+70:
		tmp = (c / b) - (b / a)
	elif b <= 8e-73:
		tmp = ((b - math.sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -7.5e+70)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 8e-73)
		tmp = Float64(Float64(Float64(b - sqrt(Float64(Float64(b * b) - Float64(a * Float64(c * 4.0))))) * -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+70)
		tmp = (c / b) - (b / a);
	elseif (b <= 8e-73)
		tmp = ((b - sqrt(((b * b) - (a * (c * 4.0))))) * -0.5) / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -7.5e+70], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-73], N[(N[(N[(b - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(a * N[(c * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision] / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.50000000000000031e70

   1. Initial program 55.6%

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

      1. neg-sub0 55.6%

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

      2. associate-+l- 55.6%

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

      3. sub0-neg 55.6%

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

      4. neg-mul-1 55.6%

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

      5. *-commutative 55.6%

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

      6. associate-*r/ 55.5%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in b around -inf 96.9%

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

      1. mul-1-neg 96.9%

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

      2. unsub-neg 96.9%

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

   6. Simplified 96.9%

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

   if -7.50000000000000031e70 < b < 7.99999999999999998e-73

   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/ 77.9%

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

   3. Simplified 78.0%

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

      1. fma-udef 78.0%

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

      2. associate-*r* 77.9%

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

      3. metadata-eval 77.9%

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

      4. distribute-rgt-neg-in 77.9%

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

      5. *-commutative 77.9%

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

      6. +-commutative 77.9%

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

      7. sub-neg 77.9%

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

      8. *-commutative 77.9%

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

      9. associate-*l* 78.0%

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

   5. Applied egg-rr 78.0%

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

      1. associate-*r/ 78.3%

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

   7. Applied egg-rr 78.3%

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

   if 7.99999999999999998e-73 < b

   1. Initial program 10.0%

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

      1. neg-sub0 10.0%

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

      2. associate-+l- 10.0%

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

      3. sub0-neg 10.0%

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

      4. neg-mul-1 10.0%

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

      5. *-commutative 10.0%

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

      6. associate-*r/ 9.9%

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

   3. Simplified 9.9%

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

   4. Taylor expanded in b around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-73}:\\ \;\;\;\;\frac{\left(b - \sqrt{b \cdot b - a \cdot \left(c \cdot 4\right)}\right) \cdot -0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 4: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-54}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{a \cdot \left(c \cdot -4\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.8e-54)
   (/ (- b) a)
   (if (<= b 9.5e-75)
     (* (/ -0.5 a) (- b (sqrt (* a (* c -4.0)))))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.8e-54) {
		tmp = -b / a;
	} else if (b <= 9.5e-75) {
		tmp = (-0.5 / a) * (b - sqrt((a * (c * -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 <= (-1.8d-54)) then
        tmp = -b / a
    else if (b <= 9.5d-75) then
        tmp = ((-0.5d0) / a) * (b - sqrt((a * (c * (-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 <= -1.8e-54) {
		tmp = -b / a;
	} else if (b <= 9.5e-75) {
		tmp = (-0.5 / a) * (b - Math.sqrt((a * (c * -4.0))));
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.8e-54:
		tmp = -b / a
	elif b <= 9.5e-75:
		tmp = (-0.5 / a) * (b - math.sqrt((a * (c * -4.0))))
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.8e-54)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 9.5e-75)
		tmp = Float64(Float64(-0.5 / a) * Float64(b - sqrt(Float64(a * Float64(c * -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 <= -1.8e-54)
		tmp = -b / a;
	elseif (b <= 9.5e-75)
		tmp = (-0.5 / a) * (b - sqrt((a * (c * -4.0))));
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.8e-54], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 9.5e-75], N[(N[(-0.5 / a), $MachinePrecision] * N[(b - N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.79999999999999988e-54

   1. Initial program 65.2%

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

      1. neg-sub0 65.2%

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

      2. associate-+l- 65.2%

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

      3. sub0-neg 65.2%

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

      4. neg-mul-1 65.2%

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

      5. *-commutative 65.2%

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

      6. associate-*r/ 65.0%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in b around -inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. mul-1-neg 92.0%

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

   6. Simplified 92.0%

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

   if -1.79999999999999988e-54 < b < 9.4999999999999991e-75

   1. Initial program 73.7%

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

      1. neg-sub0 73.7%

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

      2. associate-+l- 73.7%

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

      3. sub0-neg 73.7%

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

      4. neg-mul-1 73.7%

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

      5. *-commutative 73.7%

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

      6. associate-*r/ 73.5%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in a around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   6. Simplified 66.6%

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

   if 9.4999999999999991e-75 < b

   1. Initial program 10.0%

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

      1. neg-sub0 10.0%

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

      2. associate-+l- 10.0%

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

      3. sub0-neg 10.0%

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

      4. neg-mul-1 10.0%

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

      5. *-commutative 10.0%

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

      6. associate-*r/ 9.9%

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

   3. Simplified 9.9%

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

   4. Taylor expanded in b around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-54}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{-0.5}{a} \cdot \left(b - \sqrt{a \cdot \left(c \cdot -4\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 5: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-74}:\\ \;\;\;\;\frac{-0.5 \cdot \left(b - \sqrt{a \cdot \left(c \cdot -4\right)}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.55e-55)
   (/ (- b) a)
   (if (<= b 1.25e-74)
     (/ (* -0.5 (- b (sqrt (* a (* c -4.0))))) a)
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.55e-55) {
		tmp = -b / a;
	} else if (b <= 1.25e-74) {
		tmp = (-0.5 * (b - sqrt((a * (c * -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 <= (-1.55d-55)) then
        tmp = -b / a
    else if (b <= 1.25d-74) then
        tmp = ((-0.5d0) * (b - sqrt((a * (c * (-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 <= -1.55e-55) {
		tmp = -b / a;
	} else if (b <= 1.25e-74) {
		tmp = (-0.5 * (b - Math.sqrt((a * (c * -4.0))))) / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.55e-55:
		tmp = -b / a
	elif b <= 1.25e-74:
		tmp = (-0.5 * (b - math.sqrt((a * (c * -4.0))))) / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.55e-55)
		tmp = Float64(Float64(-b) / a);
	elseif (b <= 1.25e-74)
		tmp = Float64(Float64(-0.5 * Float64(b - sqrt(Float64(a * Float64(c * -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 <= -1.55e-55)
		tmp = -b / a;
	elseif (b <= 1.25e-74)
		tmp = (-0.5 * (b - sqrt((a * (c * -4.0))))) / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.55e-55], N[((-b) / a), $MachinePrecision], If[LessEqual[b, 1.25e-74], N[(N[(-0.5 * N[(b - N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.54999999999999998e-55

   1. Initial program 65.2%

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

      1. neg-sub0 65.2%

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

      2. associate-+l- 65.2%

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

      3. sub0-neg 65.2%

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

      4. neg-mul-1 65.2%

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

      5. *-commutative 65.2%

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

      6. associate-*r/ 65.0%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in b around -inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. mul-1-neg 92.0%

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

   6. Simplified 92.0%

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

   if -1.54999999999999998e-55 < b < 1.25e-74

   1. Initial program 73.7%

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

      1. neg-sub0 73.7%

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

      2. associate-+l- 73.7%

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

      3. sub0-neg 73.7%

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

      4. neg-mul-1 73.7%

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

      5. *-commutative 73.7%

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

      6. associate-*r/ 73.5%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in a around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   6. Simplified 66.6%

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

      1. associate-*r/ 66.8%

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

   8. Applied egg-rr 66.8%

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

   if 1.25e-74 < b

   1. Initial program 10.0%

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

      1. neg-sub0 10.0%

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

      2. associate-+l- 10.0%

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

      3. sub0-neg 10.0%

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

      4. neg-mul-1 10.0%

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

      5. *-commutative 10.0%

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

      6. associate-*r/ 9.9%

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

   3. Simplified 9.9%

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

   4. Taylor expanded in b around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-74}:\\ \;\;\;\;\frac{-0.5 \cdot \left(b - \sqrt{a \cdot \left(c \cdot -4\right)}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 6: 68.2% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-310) (- (/ c b) (/ b a)) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5d-310)) then
        tmp = (c / b) - (b / a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-310) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-310:
		tmp = (c / b) - (b / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-310)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-310)
		tmp = (c / b) - (b / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-310], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.999999999999985e-310

   1. Initial program 69.8%

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

      1. neg-sub0 69.8%

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

      2. associate-+l- 69.8%

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

      3. sub0-neg 69.8%

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

      4. neg-mul-1 69.8%

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

      5. *-commutative 69.8%

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

      6. associate-*r/ 69.6%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in b around -inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

   6. Simplified 69.6%

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

   if -4.999999999999985e-310 < b

   1. Initial program 23.2%

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

      1. neg-sub0 23.2%

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

      2. associate-+l- 23.2%

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

      3. sub0-neg 23.2%

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

      4. neg-mul-1 23.2%

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

      5. *-commutative 23.2%

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

      6. associate-*r/ 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in b around inf 71.6%

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

      1. associate-*r/ 71.6%

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

      2. neg-mul-1 71.6%

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

   6. Simplified 71.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 7: 43.6% accurate, 19.1× speedup

Math

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

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 2e+42) (/ (- b) a) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2e+42) {
		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 <= 2d+42) 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 <= 2e+42) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2e+42:
		tmp = -b / a
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2e+42)
		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 <= 2e+42)
		tmp = -b / a;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2e+42], N[((-b) / a), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.00000000000000009e42

   1. Initial program 62.0%

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

      1. neg-sub0 62.0%

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

      2. associate-+l- 62.0%

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

      3. sub0-neg 62.0%

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

      4. neg-mul-1 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-*r/ 61.8%

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

   3. Simplified 61.9%

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

   4. Taylor expanded in b around -inf 49.0%

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

      1. associate-*r/ 49.0%

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

      2. mul-1-neg 49.0%

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

   6. Simplified 49.0%

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

   if 2.00000000000000009e42 < b

   1. Initial program 7.1%

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

      1. neg-sub0 7.1%

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

      2. associate-+l- 7.1%

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

      3. sub0-neg 7.1%

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

      4. neg-mul-1 7.1%

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

      5. *-commutative 7.1%

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

      6. associate-*r/ 7.1%

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

   3. Simplified 7.1%

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

      1. associate-*r/ 7.1%

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

      2. frac-2neg 7.1%

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

   5. Applied egg-rr 7.1%

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

      1. distribute-rgt-neg-in 7.1%

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

      2. metadata-eval 7.1%

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

      3. *-commutative 7.1%

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

      4. associate-/l* 7.1%

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

      5. fma-def 7.1%

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

      6. +-commutative 7.1%

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

      7. fma-def 7.1%

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

   7. Simplified 7.1%

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

   8. Taylor expanded in b around -inf 2.5%

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

      1. fma-def 2.5%

         \[\leadsto \frac{0.5}{\frac{-a}{b - \color{blue}{\mathsf{fma}\left(2, \frac{c \cdot a}{b}, -1 \cdot b\right)}}} \]

      2. associate-*l/ 2.5%

         \[\leadsto \frac{0.5}{\frac{-a}{b - \mathsf{fma}\left(2, \color{blue}{\frac{c}{b} \cdot a}, -1 \cdot b\right)}} \]

      3. mul-1-neg 2.5%

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

      4. fma-neg 2.5%

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

      5. *-commutative 2.5%

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

      6. associate-/r/ 2.5%

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

      7. associate-/r/ 2.5%

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

      8. associate-/l/ 2.5%

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

      9. *-commutative 2.5%

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

   10. Simplified 2.5%

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

   11. Taylor expanded in a around inf 30.2%

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

4. Final simplification 43.7%

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

Alternative 8: 68.0% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-254}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.3e-254) (/ (- b) a) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.3e-254) {
		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 <= 2.3d-254) 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 <= 2.3e-254) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.3e-254:
		tmp = -b / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.3e-254)
		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 <= 2.3e-254)
		tmp = -b / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.3e-254], N[((-b) / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.2999999999999999e-254

   1. Initial program 70.7%

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

      1. neg-sub0 70.7%

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

      2. associate-+l- 70.7%

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

      3. sub0-neg 70.7%

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

      4. neg-mul-1 70.7%

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

      5. *-commutative 70.7%

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

      6. associate-*r/ 70.4%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in b around -inf 65.8%

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

      1. associate-*r/ 65.8%

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

      2. mul-1-neg 65.8%

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

   6. Simplified 65.8%

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

   if 2.2999999999999999e-254 < b

   1. Initial program 19.6%

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

      1. neg-sub0 19.6%

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

      2. associate-+l- 19.6%

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

      3. sub0-neg 19.6%

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

      4. neg-mul-1 19.6%

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

      5. *-commutative 19.6%

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

      6. associate-*r/ 19.6%

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

   3. Simplified 19.6%

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

   4. Taylor expanded in b around inf 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-254}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 9: 10.8% 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 46.3%

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

   1. neg-sub0 46.3%

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

   2. associate-+l- 46.3%

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

   3. sub0-neg 46.3%

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

   4. neg-mul-1 46.3%

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

   5. *-commutative 46.3%

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

   6. associate-*r/ 46.2%

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

3. Simplified 46.2%

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

   1. associate-*r/ 46.4%

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

   2. frac-2neg 46.4%

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

5. Applied egg-rr 46.4%

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

   1. distribute-rgt-neg-in 46.4%

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

   2. metadata-eval 46.4%

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

   3. *-commutative 46.4%

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

   4. associate-/l* 46.3%

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

   5. fma-def 46.2%

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

   6. +-commutative 46.2%

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

   7. fma-def 46.2%

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

7. Simplified 46.2%

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

8. Taylor expanded in b around -inf 34.0%

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

   1. fma-def 34.0%

      \[\leadsto \frac{0.5}{\frac{-a}{b - \color{blue}{\mathsf{fma}\left(2, \frac{c \cdot a}{b}, -1 \cdot b\right)}}} \]

   2. associate-*l/ 35.6%

      \[\leadsto \frac{0.5}{\frac{-a}{b - \mathsf{fma}\left(2, \color{blue}{\frac{c}{b} \cdot a}, -1 \cdot b\right)}} \]

   3. mul-1-neg 35.6%

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

   4. fma-neg 35.6%

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

   5. *-commutative 35.6%

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

   6. associate-/r/ 35.6%

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

   7. associate-/r/ 35.6%

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

   8. associate-/l/ 35.6%

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

   9. *-commutative 35.6%

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

10. Simplified 35.6%

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

11. Taylor expanded in a around inf 10.8%

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

12. Final simplification 10.8%

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

Developer target: 70.0% 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 2023215 
(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)))