quadm (p42, negative)

Percentage Accurate: 52.7% → 87.2%

Time: 13.8s

Alternatives: 7

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: 52.7% 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: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{-102}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{\left(c \cdot a\right) \cdot 4}{b - t_0}}{a}\\ \mathbf{elif}\;b \leq 10^{+100}:\\ \;\;\;\;-0.5 \cdot \frac{b + t_0}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -1.2e+17)
     (* -0.5 (/ 1.0 (+ (* 0.5 (/ b c)) (* -0.5 (/ a b)))))
     (if (<= b -2.55e-102)
       (* -0.5 (/ (/ (* (* c a) 4.0) (- b t_0)) a))
       (if (<= b 1e+100) (* -0.5 (/ (+ b t_0) a)) (/ (- b) a))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp;
	if (b <= -1.2e+17) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= -2.55e-102) {
		tmp = -0.5 * ((((c * a) * 4.0) / (b - t_0)) / a);
	} else if (b <= 1e+100) {
		tmp = -0.5 * ((b + t_0) / a);
	} else {
		tmp = -b / 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) - (c * (a * 4.0d0))))
    if (b <= (-1.2d+17)) then
        tmp = (-0.5d0) * (1.0d0 / ((0.5d0 * (b / c)) + ((-0.5d0) * (a / b))))
    else if (b <= (-2.55d-102)) then
        tmp = (-0.5d0) * ((((c * a) * 4.0d0) / (b - t_0)) / a)
    else if (b <= 1d+100) then
        tmp = (-0.5d0) * ((b + t_0) / a)
    else
        tmp = -b / 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) - (c * (a * 4.0))));
	double tmp;
	if (b <= -1.2e+17) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= -2.55e-102) {
		tmp = -0.5 * ((((c * a) * 4.0) / (b - t_0)) / a);
	} else if (b <= 1e+100) {
		tmp = -0.5 * ((b + t_0) / a);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = math.sqrt(((b * b) - (c * (a * 4.0))))
	tmp = 0
	if b <= -1.2e+17:
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))))
	elif b <= -2.55e-102:
		tmp = -0.5 * ((((c * a) * 4.0) / (b - t_0)) / a)
	elif b <= 1e+100:
		tmp = -0.5 * ((b + t_0) / a)
	else:
		tmp = -b / a
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp = 0.0
	if (b <= -1.2e+17)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(0.5 * Float64(b / c)) + Float64(-0.5 * Float64(a / b)))));
	elseif (b <= -2.55e-102)
		tmp = Float64(-0.5 * Float64(Float64(Float64(Float64(c * a) * 4.0) / Float64(b - t_0)) / a));
	elseif (b <= 1e+100)
		tmp = Float64(-0.5 * Float64(Float64(b + t_0) / a));
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	tmp = 0.0;
	if (b <= -1.2e+17)
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	elseif (b <= -2.55e-102)
		tmp = -0.5 * ((((c * a) * 4.0) / (b - t_0)) / a);
	elseif (b <= 1e+100)
		tmp = -0.5 * ((b + t_0) / a);
	else
		tmp = -b / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -1.2e+17], N[(-0.5 * N[(1.0 / N[(N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.55e-102], N[(-0.5 * N[(N[(N[(N[(c * a), $MachinePrecision] * 4.0), $MachinePrecision] / N[(b - t$95$0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+100], N[(-0.5 * N[(N[(b + t$95$0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[((-b) / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.2e17

   1. Initial program 10.4%

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

      1. sub-neg 10.4%

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

      2. distribute-neg-out 10.4%

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

      3. neg-mul-1 10.4%

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

      4. times-frac 10.4%

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

      5. metadata-eval 10.4%

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

      6. fma-neg 10.4%

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

      7. distribute-lft-neg-in 10.4%

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

      8. *-commutative 10.4%

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

      9. associate-*l* 10.4%

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

      10. metadata-eval 10.4%

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

   3. Simplified 10.4%

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

      1. associate-*r* 10.4%

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

      2. metadata-eval 10.4%

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

      3. distribute-rgt-neg-in 10.4%

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

      4. *-commutative 10.4%

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

      5. fma-neg 10.4%

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

      6. *-commutative 10.4%

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

      7. *-commutative 10.4%

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

      8. associate-*l* 10.4%

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

   5. Applied egg-rr 10.4%

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

      1. clear-num 10.4%

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

      2. inv-pow 10.4%

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

   7. Applied egg-rr 10.4%

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

      1. unpow-1 10.4%

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

      2. sub-neg 10.4%

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

      3. +-commutative 10.4%

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

      4. distribute-rgt-neg-in 10.4%

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

      5. fma-def 10.4%

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

      6. distribute-rgt-neg-in 10.4%

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

      7. metadata-eval 10.4%

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

   9. Simplified 10.4%

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

   10. Taylor expanded in b around -inf 95.8%

       \[\leadsto -0.5 \cdot \frac{1}{\color{blue}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}} \]

   if -1.2e17 < b < -2.55e-102

   1. Initial program 58.6%

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

      1. sub-neg 58.6%

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

      2. distribute-neg-out 58.6%

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

      3. neg-mul-1 58.6%

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

      4. times-frac 58.6%

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

      5. metadata-eval 58.6%

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

      6. fma-neg 58.6%

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

      7. distribute-lft-neg-in 58.6%

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

      8. *-commutative 58.6%

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

      9. associate-*l* 58.6%

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

      10. metadata-eval 58.6%

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

   3. Simplified 58.6%

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

      1. associate-*r* 58.6%

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

      2. metadata-eval 58.6%

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

      3. distribute-rgt-neg-in 58.6%

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

      4. *-commutative 58.6%

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

      5. fma-neg 58.6%

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

      6. *-commutative 58.6%

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

      7. *-commutative 58.6%

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

      8. associate-*l* 58.6%

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

   5. Applied egg-rr 58.6%

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

      1. flip-+ 58.4%

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

      2. add-sqr-sqrt 58.5%

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

   7. Applied egg-rr 58.5%

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

   8. Taylor expanded in b around 0 88.7%

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

      1. *-commutative 88.7%

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

   10. Simplified 88.7%

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

   if -2.55e-102 < b < 1.00000000000000002e100

   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. sub-neg 83.6%

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

      2. distribute-neg-out 83.6%

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

      3. neg-mul-1 83.6%

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

      4. times-frac 83.6%

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

      5. metadata-eval 83.6%

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

      6. fma-neg 83.6%

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

      7. distribute-lft-neg-in 83.6%

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

      8. *-commutative 83.6%

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

      9. associate-*l* 83.7%

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

      10. metadata-eval 83.7%

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

   3. Simplified 83.7%

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

      1. associate-*r* 83.6%

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

      2. metadata-eval 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

      4. *-commutative 83.6%

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

      5. fma-neg 83.6%

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

      6. *-commutative 83.6%

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

      7. *-commutative 83.6%

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

      8. associate-*l* 83.7%

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

   5. Applied egg-rr 83.7%

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

   if 1.00000000000000002e100 < b

   1. Initial program 65.8%

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

   2. Taylor expanded in b around inf 95.4%

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

      1. associate-*r/ 95.4%

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

      2. mul-1-neg 95.4%

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

   4. Simplified 95.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{-102}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{\left(c \cdot a\right) \cdot 4}{b - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}}{a}\\ \mathbf{elif}\;b \leq 10^{+100}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

Alternative 2: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-145}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq 10^{+100}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6e-145)
   (* -0.5 (/ 1.0 (+ (* 0.5 (/ b c)) (* -0.5 (/ a b)))))
   (if (<= b 1e+100)
     (* -0.5 (/ (+ b (sqrt (- (* b b) (* c (* a 4.0))))) a))
     (/ (- b) a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e-145) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= 1e+100) {
		tmp = -0.5 * ((b + sqrt(((b * b) - (c * (a * 4.0))))) / a);
	} else {
		tmp = -b / 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) :: tmp
    if (b <= (-6d-145)) then
        tmp = (-0.5d0) * (1.0d0 / ((0.5d0 * (b / c)) + ((-0.5d0) * (a / b))))
    else if (b <= 1d+100) then
        tmp = (-0.5d0) * ((b + sqrt(((b * b) - (c * (a * 4.0d0))))) / a)
    else
        tmp = -b / a
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e-145) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= 1e+100) {
		tmp = -0.5 * ((b + Math.sqrt(((b * b) - (c * (a * 4.0))))) / a);
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6e-145:
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))))
	elif b <= 1e+100:
		tmp = -0.5 * ((b + math.sqrt(((b * b) - (c * (a * 4.0))))) / a)
	else:
		tmp = -b / a
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6e-145)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(0.5 * Float64(b / c)) + Float64(-0.5 * Float64(a / b)))));
	elseif (b <= 1e+100)
		tmp = Float64(-0.5 * Float64(Float64(b + sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))) / a));
	else
		tmp = Float64(Float64(-b) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6e-145)
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	elseif (b <= 1e+100)
		tmp = -0.5 * ((b + sqrt(((b * b) - (c * (a * 4.0))))) / a);
	else
		tmp = -b / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6e-145], N[(-0.5 * N[(1.0 / N[(N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+100], N[(-0.5 * N[(N[(b + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[((-b) / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999985e-145

   1. Initial program 21.8%

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

      1. sub-neg 21.8%

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

      2. distribute-neg-out 21.8%

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

      3. neg-mul-1 21.8%

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

      4. times-frac 21.8%

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

      5. metadata-eval 21.8%

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

      6. fma-neg 21.8%

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

      7. distribute-lft-neg-in 21.8%

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

      8. *-commutative 21.8%

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

      9. associate-*l* 21.8%

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

      10. metadata-eval 21.8%

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

   3. Simplified 21.8%

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

      1. associate-*r* 21.8%

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

      2. metadata-eval 21.8%

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

      3. distribute-rgt-neg-in 21.8%

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

      4. *-commutative 21.8%

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

      5. fma-neg 21.8%

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

      6. *-commutative 21.8%

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

      7. *-commutative 21.8%

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

      8. associate-*l* 21.8%

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

   5. Applied egg-rr 21.8%

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

      1. clear-num 21.7%

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

      2. inv-pow 21.7%

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

   7. Applied egg-rr 21.7%

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

      1. unpow-1 21.7%

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

      2. sub-neg 21.7%

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

      3. +-commutative 21.7%

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

      4. distribute-rgt-neg-in 21.7%

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

      5. fma-def 21.8%

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

      6. distribute-rgt-neg-in 21.8%

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

      7. metadata-eval 21.8%

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

   9. Simplified 21.8%

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

   10. Taylor expanded in b around -inf 82.8%

       \[\leadsto -0.5 \cdot \frac{1}{\color{blue}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}} \]

   if -5.99999999999999985e-145 < b < 1.00000000000000002e100

   1. Initial program 88.9%

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

      1. sub-neg 88.9%

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

      2. distribute-neg-out 88.9%

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

      3. neg-mul-1 88.9%

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

      4. times-frac 88.9%

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

      5. metadata-eval 88.9%

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

      6. fma-neg 88.9%

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

      7. distribute-lft-neg-in 88.9%

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

      8. *-commutative 88.9%

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

      9. associate-*l* 88.9%

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

      10. metadata-eval 88.9%

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

   3. Simplified 88.9%

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

      1. associate-*r* 88.9%

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

      2. metadata-eval 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

      4. *-commutative 88.9%

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

      5. fma-neg 88.9%

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

      6. *-commutative 88.9%

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

      7. *-commutative 88.9%

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

      8. associate-*l* 88.9%

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

   5. Applied egg-rr 88.9%

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

   if 1.00000000000000002e100 < b

   1. Initial program 65.8%

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

   2. Taylor expanded in b around inf 95.4%

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

      1. associate-*r/ 95.4%

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

      2. mul-1-neg 95.4%

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

   4. Simplified 95.4%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-145}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq 10^{+100}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

Alternative 3: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-145}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;-0.5 \cdot \left(\left(b + \sqrt{c \cdot \left(a \cdot -4\right)}\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6e-145)
   (* -0.5 (/ 1.0 (+ (* 0.5 (/ b c)) (* -0.5 (/ a b)))))
   (if (<= b 1.9e-46)
     (* -0.5 (* (+ b (sqrt (* c (* a -4.0)))) (/ 1.0 a)))
     (- (/ c b) (/ b a)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e-145) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= 1.9e-46) {
		tmp = -0.5 * ((b + sqrt((c * (a * -4.0)))) * (1.0 / a));
	} else {
		tmp = (c / b) - (b / 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) :: tmp
    if (b <= (-6d-145)) then
        tmp = (-0.5d0) * (1.0d0 / ((0.5d0 * (b / c)) + ((-0.5d0) * (a / b))))
    else if (b <= 1.9d-46) then
        tmp = (-0.5d0) * ((b + sqrt((c * (a * (-4.0d0))))) * (1.0d0 / a))
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e-145) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= 1.9e-46) {
		tmp = -0.5 * ((b + Math.sqrt((c * (a * -4.0)))) * (1.0 / a));
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6e-145:
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))))
	elif b <= 1.9e-46:
		tmp = -0.5 * ((b + math.sqrt((c * (a * -4.0)))) * (1.0 / a))
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6e-145)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(0.5 * Float64(b / c)) + Float64(-0.5 * Float64(a / b)))));
	elseif (b <= 1.9e-46)
		tmp = Float64(-0.5 * Float64(Float64(b + sqrt(Float64(c * Float64(a * -4.0)))) * Float64(1.0 / a)));
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6e-145)
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	elseif (b <= 1.9e-46)
		tmp = -0.5 * ((b + sqrt((c * (a * -4.0)))) * (1.0 / a));
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6e-145], N[(-0.5 * N[(1.0 / N[(N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-46], N[(-0.5 * N[(N[(b + N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999985e-145

   1. Initial program 21.8%

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

      1. sub-neg 21.8%

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

      2. distribute-neg-out 21.8%

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

      3. neg-mul-1 21.8%

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

      4. times-frac 21.8%

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

      5. metadata-eval 21.8%

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

      6. fma-neg 21.8%

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

      7. distribute-lft-neg-in 21.8%

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

      8. *-commutative 21.8%

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

      9. associate-*l* 21.8%

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

      10. metadata-eval 21.8%

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

   3. Simplified 21.8%

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

      1. associate-*r* 21.8%

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

      2. metadata-eval 21.8%

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

      3. distribute-rgt-neg-in 21.8%

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

      4. *-commutative 21.8%

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

      5. fma-neg 21.8%

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

      6. *-commutative 21.8%

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

      7. *-commutative 21.8%

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

      8. associate-*l* 21.8%

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

   5. Applied egg-rr 21.8%

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

      1. clear-num 21.7%

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

      2. inv-pow 21.7%

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

   7. Applied egg-rr 21.7%

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

      1. unpow-1 21.7%

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

      2. sub-neg 21.7%

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

      3. +-commutative 21.7%

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

      4. distribute-rgt-neg-in 21.7%

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

      5. fma-def 21.8%

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

      6. distribute-rgt-neg-in 21.8%

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

      7. metadata-eval 21.8%

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

   9. Simplified 21.8%

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

   10. Taylor expanded in b around -inf 82.8%

       \[\leadsto -0.5 \cdot \frac{1}{\color{blue}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}} \]

   if -5.99999999999999985e-145 < b < 1.8999999999999998e-46

   1. Initial program 85.4%

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

      1. sub-neg 85.4%

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

      2. distribute-neg-out 85.4%

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

      3. neg-mul-1 85.4%

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

      4. times-frac 85.4%

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

      5. metadata-eval 85.4%

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

      6. fma-neg 85.4%

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

      7. distribute-lft-neg-in 85.4%

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

      8. *-commutative 85.4%

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

      9. associate-*l* 85.4%

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

      10. metadata-eval 85.4%

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

   3. Simplified 85.4%

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

      1. associate-*r* 85.4%

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

      2. metadata-eval 85.4%

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

      3. distribute-rgt-neg-in 85.4%

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

      4. *-commutative 85.4%

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

      5. fma-neg 85.4%

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

      6. *-commutative 85.4%

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

      7. *-commutative 85.4%

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

      8. associate-*l* 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. div-inv 85.5%

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

   7. Applied egg-rr 85.5%

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

   8. Taylor expanded in b around 0 81.5%

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

      1. metadata-eval 81.5%

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

      2. distribute-lft-neg-in 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-*r* 81.5%

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

      5. distribute-rgt-neg-in 81.5%

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

      6. distribute-rgt-neg-in 81.5%

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

      7. metadata-eval 81.5%

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

   10. Simplified 81.5%

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

   if 1.8999999999999998e-46 < b

   1. Initial program 76.9%

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

   2. Taylor expanded in b around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. unsub-neg 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-145}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;-0.5 \cdot \left(\left(b + \sqrt{c \cdot \left(a \cdot -4\right)}\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \]

Alternative 4: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-145}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{\left(c \cdot a\right) \cdot -4}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6e-145)
   (* -0.5 (/ 1.0 (+ (* 0.5 (/ b c)) (* -0.5 (/ a b)))))
   (if (<= b 8.5e-47)
     (* -0.5 (/ (+ b (sqrt (* (* c a) -4.0))) a))
     (- (/ c b) (/ b a)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e-145) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= 8.5e-47) {
		tmp = -0.5 * ((b + sqrt(((c * a) * -4.0))) / a);
	} else {
		tmp = (c / b) - (b / 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) :: tmp
    if (b <= (-6d-145)) then
        tmp = (-0.5d0) * (1.0d0 / ((0.5d0 * (b / c)) + ((-0.5d0) * (a / b))))
    else if (b <= 8.5d-47) then
        tmp = (-0.5d0) * ((b + sqrt(((c * a) * (-4.0d0)))) / a)
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e-145) {
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	} else if (b <= 8.5e-47) {
		tmp = -0.5 * ((b + Math.sqrt(((c * a) * -4.0))) / a);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6e-145:
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))))
	elif b <= 8.5e-47:
		tmp = -0.5 * ((b + math.sqrt(((c * a) * -4.0))) / a)
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6e-145)
		tmp = Float64(-0.5 * Float64(1.0 / Float64(Float64(0.5 * Float64(b / c)) + Float64(-0.5 * Float64(a / b)))));
	elseif (b <= 8.5e-47)
		tmp = Float64(-0.5 * Float64(Float64(b + sqrt(Float64(Float64(c * a) * -4.0))) / a));
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6e-145)
		tmp = -0.5 * (1.0 / ((0.5 * (b / c)) + (-0.5 * (a / b))));
	elseif (b <= 8.5e-47)
		tmp = -0.5 * ((b + sqrt(((c * a) * -4.0))) / a);
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6e-145], N[(-0.5 * N[(1.0 / N[(N[(0.5 * N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-47], N[(-0.5 * N[(N[(b + N[Sqrt[N[(N[(c * a), $MachinePrecision] * -4.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999985e-145

   1. Initial program 21.8%

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

      1. sub-neg 21.8%

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

      2. distribute-neg-out 21.8%

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

      3. neg-mul-1 21.8%

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

      4. times-frac 21.8%

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

      5. metadata-eval 21.8%

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

      6. fma-neg 21.8%

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

      7. distribute-lft-neg-in 21.8%

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

      8. *-commutative 21.8%

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

      9. associate-*l* 21.8%

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

      10. metadata-eval 21.8%

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

   3. Simplified 21.8%

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

      1. associate-*r* 21.8%

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

      2. metadata-eval 21.8%

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

      3. distribute-rgt-neg-in 21.8%

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

      4. *-commutative 21.8%

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

      5. fma-neg 21.8%

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

      6. *-commutative 21.8%

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

      7. *-commutative 21.8%

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

      8. associate-*l* 21.8%

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

   5. Applied egg-rr 21.8%

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

      1. clear-num 21.7%

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

      2. inv-pow 21.7%

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

   7. Applied egg-rr 21.7%

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

      1. unpow-1 21.7%

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

      2. sub-neg 21.7%

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

      3. +-commutative 21.7%

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

      4. distribute-rgt-neg-in 21.7%

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

      5. fma-def 21.8%

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

      6. distribute-rgt-neg-in 21.8%

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

      7. metadata-eval 21.8%

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

   9. Simplified 21.8%

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

   10. Taylor expanded in b around -inf 82.8%

       \[\leadsto -0.5 \cdot \frac{1}{\color{blue}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}} \]

   if -5.99999999999999985e-145 < b < 8.4999999999999999e-47

   1. Initial program 85.4%

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

      1. sub-neg 85.4%

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

      2. distribute-neg-out 85.4%

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

      3. neg-mul-1 85.4%

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

      4. times-frac 85.4%

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

      5. metadata-eval 85.4%

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

      6. fma-neg 85.4%

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

      7. distribute-lft-neg-in 85.4%

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

      8. *-commutative 85.4%

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

      9. associate-*l* 85.4%

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

      10. metadata-eval 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in b around 0 81.5%

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

      1. *-commutative 81.5%

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

   6. Simplified 81.5%

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

   if 8.4999999999999999e-47 < b

   1. Initial program 76.9%

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

   2. Taylor expanded in b around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. unsub-neg 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-145}:\\ \;\;\;\;-0.5 \cdot \frac{1}{0.5 \cdot \frac{b}{c} + -0.5 \cdot \frac{a}{b}}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{\left(c \cdot a\right) \cdot -4}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \]

Alternative 5: 68.5% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if b < -4.999999999999985e-310

   1. Initial program 31.6%

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

   2. Taylor expanded in b around -inf 69.7%

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

      1. associate-*r/ 69.7%

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

      2. neg-mul-1 69.7%

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

   4. Simplified 69.7%

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

   if -4.999999999999985e-310 < b

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

   4. Simplified 66.4%

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

4. Final simplification 68.0%

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

Alternative 6: 68.3% accurate, 19.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if b < -4.999999999999985e-310

   1. Initial program 31.6%

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

   2. Taylor expanded in b around -inf 69.7%

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

      1. associate-*r/ 69.7%

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

      2. neg-mul-1 69.7%

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

   4. Simplified 69.7%

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

   if -4.999999999999985e-310 < b

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf 66.2%

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

      1. associate-*r/ 66.2%

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

      2. mul-1-neg 66.2%

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

   4. Simplified 66.2%

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

4. Final simplification 67.9%

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

Alternative 7: 36.0% accurate, 29.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c) {
	return -b / 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 / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.3%

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

2. Taylor expanded in b around inf 35.5%

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

   1. associate-*r/ 35.5%

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

   2. mul-1-neg 35.5%

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

4. Simplified 35.5%

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

5. Final simplification 35.5%

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

Developer target: 71.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* 4.0 (* a c))))))
   (if (< b 0.0)
     (/ c (* a (/ (+ (- b) t_0) (* 2.0 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 = c / (a * ((-b + t_0) / (2.0 * a)));
	} else {
		tmp = (-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 = c / (a * ((-b + t_0) / (2.0d0 * a)))
    else
        tmp = (-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 = c / (a * ((-b + t_0) / (2.0 * a)));
	} else {
		tmp = (-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 = c / (a * ((-b + t_0) / (2.0 * a)))
	else:
		tmp = (-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(c / Float64(a * Float64(Float64(Float64(-b) + t_0) / Float64(2.0 * a))));
	else
		tmp = 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 = c / (a * ((-b + t_0) / (2.0 * a)));
	else
		tmp = (-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[(c / N[(a * N[(N[((-b) + t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-b) - t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023272 
(FPCore (a b c)
  :name "quadm (p42, negative)"
  :precision binary64

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

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