jeff quadratic root 2

Percentage Accurate: 72.2% → 89.9%

Time: 15.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (if (>= b 0.0) (/ (* 2.0 c) (- (- b) t_0)) (/ (+ (- 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 = (2.0 * c) / (-b - t_0);
	} 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 = (2.0d0 * c) / (-b - t_0)
    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 = (2.0 * c) / (-b - t_0);
	} 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 = (2.0 * c) / (-b - t_0)
	else:
		tmp = (-b + t_0) / (2.0 * a)
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(2.0 * c) / Float64(Float64(-b) - t_0));
	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 = (2.0 * c) / (-b - t_0);
	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[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[GreaterEqual[b, 0.0], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[((-b) + t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Initial Program: 72.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* (* 4.0 a) c)))))
   (if (>= b 0.0) (/ (* 2.0 c) (- (- b) t_0)) (/ (+ (- 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 = (2.0 * c) / (-b - t_0);
	} 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 = (2.0d0 * c) / (-b - t_0)
    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 = (2.0 * c) / (-b - t_0);
	} 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 = (2.0 * c) / (-b - t_0)
	else:
		tmp = (-b + t_0) / (2.0 * a)
	return tmp

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(2.0 * c) / Float64(Float64(-b) - t_0));
	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 = (2.0 * c) / (-b - t_0);
	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[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[GreaterEqual[b, 0.0], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[((-b) + t$95$0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 89.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-c}{b}\\ t_1 := c \cdot \left(a \cdot -4\right)\\ t_2 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(\frac{b \cdot b - \mathsf{fma}\left(b, b, t_1\right)}{b + \mathsf{hypot}\left(b, \sqrt{t_1}\right)} \cdot \frac{1}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- c) b))
        (t_1 (* c (* a -4.0)))
        (t_2 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -7.4e+161)
     (if (>= b 0.0) t_0 (* (+ (* -2.0 (/ c b)) (* 2.0 (/ b a))) -0.5))
     (if (<= b 2.2e+109)
       (if (>= b 0.0) (/ (* c 2.0) (- (- b) t_2)) (/ (- t_2 b) (* 2.0 a)))
       (if (>= b 0.0)
         t_0
         (*
          -0.5
          (*
           (/ (- (* b b) (fma b b t_1)) (+ b (hypot b (sqrt t_1))))
           (/ 1.0 a))))))))

C

double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = c * (a * -4.0);
	double t_2 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -7.4e+161) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = ((-2.0 * (c / b)) + (2.0 * (b / a))) * -0.5;
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.2e+109) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_2);
		} else {
			tmp_3 = (t_2 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = -0.5 * ((((b * b) - fma(b, b, t_1)) / (b + hypot(b, sqrt(t_1)))) * (1.0 / a));
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = Float64(Float64(-c) / b)
	t_1 = Float64(c * Float64(a * -4.0))
	t_2 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -7.4e+161)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))) * -0.5);
		end
		tmp_1 = tmp_2;
	elseif (b <= 2.2e+109)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - t_2));
		else
			tmp_3 = Float64(Float64(t_2 - b) / Float64(2.0 * a));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(-0.5 * Float64(Float64(Float64(Float64(b * b) - fma(b, b, t_1)) / Float64(b + hypot(b, sqrt(t_1)))) * Float64(1.0 / a)));
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$1 = N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -7.4e+161], If[GreaterEqual[b, 0.0], t$95$0, N[(N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], If[LessEqual[b, 2.2e+109], If[GreaterEqual[b, 0.0], N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(N[(N[(b * b), $MachinePrecision] - N[(b * b + t$95$1), $MachinePrecision]), $MachinePrecision] / N[(b + N[Sqrt[b ^ 2 + N[Sqrt[t$95$1], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.39999999999999958e161

   1. Initial program 43.6%

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

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   7. Taylor expanded in b around -inf 99.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

   if -7.39999999999999958e161 < b < 2.1999999999999999e109

   1. Initial program 91.3%

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

   if 2.1999999999999999e109 < b

   1. Initial program 47.2%

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

   3. Simplified 47.1%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   7. Step-by-step derivation

      1. div-inv 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}\right) \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      2. fma-udef 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - \sqrt{b \cdot b + c \cdot \left(a \cdot -4\right)}\right) \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      3. add-sqr-sqrt 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - \sqrt{b \cdot b + \sqrt{c \cdot \left(a \cdot -4\right)} \cdot \sqrt{c \cdot \left(a \cdot -4\right)}}\right) \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      4. hypot-udef 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)\right) \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

   8. Applied egg-rr 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)\right) \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]
   9. Step-by-step derivation

      1. flip-- 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right) \cdot \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      2. hypot-udef 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \sqrt{b \cdot b + \sqrt{c \cdot \left(a \cdot -4\right)} \cdot \sqrt{c \cdot \left(a \cdot -4\right)}} \cdot \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      3. hypot-udef 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \sqrt{b \cdot b + \sqrt{c \cdot \left(a \cdot -4\right)} \cdot \sqrt{c \cdot \left(a \cdot -4\right)}} \cdot \sqrt{b \cdot b + \sqrt{c \cdot \left(a \cdot -4\right)} \cdot \sqrt{c \cdot \left(a \cdot -4\right)}}}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      4. add-sqr-sqrt 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \left(b \cdot b + \sqrt{c \cdot \left(a \cdot -4\right)} \cdot \sqrt{c \cdot \left(a \cdot -4\right)}\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      5. add-sqr-sqrt 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \left(b \cdot b + c \cdot \left(a \cdot -4\right)\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

      6. fma-def 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]

   10. Applied egg-rr 98.3%

       \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b \cdot b - \mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right) \cdot -0.5\\ \end{array} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(\frac{b \cdot b - \mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}{b + \mathsf{hypot}\left(b, \sqrt{c \cdot \left(a \cdot -4\right)}\right)} \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternative 2: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-c}{b}\\ t_1 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- c) b)) (t_1 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -7.4e+161)
     (if (>= b 0.0) t_0 (* (+ (* -2.0 (/ c b)) (* 2.0 (/ b a))) -0.5))
     (if (<= b 2e+109)
       (if (>= b 0.0) (/ (* c 2.0) (- (- b) t_1)) (/ (- t_1 b) (* 2.0 a)))
       (if (>= b 0.0)
         t_0
         (* -0.5 (/ (- b (sqrt (fma b b (* c (* a -4.0))))) a)))))))

C

double code(double a, double b, double c) {
	double t_0 = -c / b;
	double t_1 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -7.4e+161) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = ((-2.0 * (c / b)) + (2.0 * (b / a))) * -0.5;
		}
		tmp_1 = tmp_2;
	} else if (b <= 2e+109) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_1);
		} else {
			tmp_3 = (t_1 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = -0.5 * ((b - sqrt(fma(b, b, (c * (a * -4.0))))) / a);
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = Float64(Float64(-c) / b)
	t_1 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -7.4e+161)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))) * -0.5);
		end
		tmp_1 = tmp_2;
	elseif (b <= 2e+109)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - t_1));
		else
			tmp_3 = Float64(Float64(t_1 - b) / Float64(2.0 * a));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(-0.5 * Float64(Float64(b - sqrt(fma(b, b, Float64(c * Float64(a * -4.0))))) / a));
	end
	return tmp_1
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -7.4e+161], If[GreaterEqual[b, 0.0], t$95$0, N[(N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], If[LessEqual[b, 2e+109], If[GreaterEqual[b, 0.0], N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(-0.5 * N[(N[(b - N[Sqrt[N[(b * b + N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.39999999999999958e161

   1. Initial program 43.6%

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

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   7. Taylor expanded in b around -inf 99.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

   if -7.39999999999999958e161 < b < 1.99999999999999996e109

   1. Initial program 91.3%

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

   if 1.99999999999999996e109 < b

   1. Initial program 47.2%

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

   3. Simplified 47.1%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a}\\ \end{array} \]

Alternative 3: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \frac{b}{a}\\ t_1 := \frac{-c}{b}\\ t_2 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + t_0\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{2}{\left(-b\right) - t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* 2.0 (/ b a)))
        (t_1 (/ (- c) b))
        (t_2 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -7.4e+161)
     (if (>= b 0.0) t_1 (* (+ (* -2.0 (/ c b)) t_0) -0.5))
     (if (<= b 1.45e+109)
       (if (>= b 0.0) (* c (/ 2.0 (- (- b) t_2))) (/ (- t_2 b) (* 2.0 a)))
       (if (>= b 0.0) t_1 (* t_0 -0.5))))))

C

double code(double a, double b, double c) {
	double t_0 = 2.0 * (b / a);
	double t_1 = -c / b;
	double t_2 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -7.4e+161) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_1;
		} else {
			tmp_2 = ((-2.0 * (c / b)) + t_0) * -0.5;
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.45e+109) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = c * (2.0 / (-b - t_2));
		} else {
			tmp_3 = (t_2 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_1;
	} else {
		tmp_1 = t_0 * -0.5;
	}
	return tmp_1;
}

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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    real(8) :: tmp_3
    t_0 = 2.0d0 * (b / a)
    t_1 = -c / b
    t_2 = sqrt(((b * b) - (c * (a * 4.0d0))))
    if (b <= (-7.4d+161)) then
        if (b >= 0.0d0) then
            tmp_2 = t_1
        else
            tmp_2 = (((-2.0d0) * (c / b)) + t_0) * (-0.5d0)
        end if
        tmp_1 = tmp_2
    else if (b <= 1.45d+109) then
        if (b >= 0.0d0) then
            tmp_3 = c * (2.0d0 / (-b - t_2))
        else
            tmp_3 = (t_2 - b) / (2.0d0 * a)
        end if
        tmp_1 = tmp_3
    else if (b >= 0.0d0) then
        tmp_1 = t_1
    else
        tmp_1 = t_0 * (-0.5d0)
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = 2.0 * (b / a);
	double t_1 = -c / b;
	double t_2 = Math.sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -7.4e+161) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_1;
		} else {
			tmp_2 = ((-2.0 * (c / b)) + t_0) * -0.5;
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.45e+109) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = c * (2.0 / (-b - t_2));
		} else {
			tmp_3 = (t_2 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_1;
	} else {
		tmp_1 = t_0 * -0.5;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = 2.0 * (b / a)
	t_1 = -c / b
	t_2 = math.sqrt(((b * b) - (c * (a * 4.0))))
	tmp_1 = 0
	if b <= -7.4e+161:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_1
		else:
			tmp_2 = ((-2.0 * (c / b)) + t_0) * -0.5
		tmp_1 = tmp_2
	elif b <= 1.45e+109:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = c * (2.0 / (-b - t_2))
		else:
			tmp_3 = (t_2 - b) / (2.0 * a)
		tmp_1 = tmp_3
	elif b >= 0.0:
		tmp_1 = t_1
	else:
		tmp_1 = t_0 * -0.5
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(2.0 * Float64(b / a))
	t_1 = Float64(Float64(-c) / b)
	t_2 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -7.4e+161)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_1;
		else
			tmp_2 = Float64(Float64(Float64(-2.0 * Float64(c / b)) + t_0) * -0.5);
		end
		tmp_1 = tmp_2;
	elseif (b <= 1.45e+109)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(c * Float64(2.0 / Float64(Float64(-b) - t_2)));
		else
			tmp_3 = Float64(Float64(t_2 - b) / Float64(2.0 * a));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = t_1;
	else
		tmp_1 = Float64(t_0 * -0.5);
	end
	return tmp_1
end

MATLAB

function tmp_5 = code(a, b, c)
	t_0 = 2.0 * (b / a);
	t_1 = -c / b;
	t_2 = sqrt(((b * b) - (c * (a * 4.0))));
	tmp_2 = 0.0;
	if (b <= -7.4e+161)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_1;
		else
			tmp_3 = ((-2.0 * (c / b)) + t_0) * -0.5;
		end
		tmp_2 = tmp_3;
	elseif (b <= 1.45e+109)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = c * (2.0 / (-b - t_2));
		else
			tmp_4 = (t_2 - b) / (2.0 * a);
		end
		tmp_2 = tmp_4;
	elseif (b >= 0.0)
		tmp_2 = t_1;
	else
		tmp_2 = t_0 * -0.5;
	end
	tmp_5 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -7.4e+161], If[GreaterEqual[b, 0.0], t$95$1, N[(N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] * -0.5), $MachinePrecision]], If[LessEqual[b, 1.45e+109], If[GreaterEqual[b, 0.0], N[(c * N[(2.0 / N[((-b) - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$1, N[(t$95$0 * -0.5), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.39999999999999958e161

   1. Initial program 43.6%

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

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   7. Taylor expanded in b around -inf 99.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

   if -7.39999999999999958e161 < b < 1.45e109

   1. Initial program 91.3%

      \[\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]
   2. Step-by-step derivation

      1. expm1-log1p-u 81.2%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]

      2. expm1-udef 65.2%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{e^{\mathsf{log1p}\left(\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\right)} - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]

      3. associate-/l* 65.2%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;e^{\mathsf{log1p}\left(\color{blue}{\frac{2}{\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{c}}}\right)} - 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]

      4. *-commutative 65.2%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;e^{\mathsf{log1p}\left(\frac{2}{\frac{\left(-b\right) - \sqrt{b \cdot b - \color{blue}{c \cdot \left(4 \cdot a\right)}}}{c}}\right)} - 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]

      5. *-commutative 65.2%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;e^{\mathsf{log1p}\left(\frac{2}{\frac{\left(-b\right) - \sqrt{b \cdot b - c \cdot \color{blue}{\left(a \cdot 4\right)}}}{c}}\right)} - 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]

   3. Applied egg-rr 65.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{e^{\mathsf{log1p}\left(\frac{2}{\frac{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{c}}\right)} - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]
   4. Step-by-step derivation

      1. expm1-def 80.9%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2}{\frac{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{c}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array} \]

      2. expm1-log1p 90.9%

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

      3. associate-/r/ 91.2%

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

   5. Simplified 91.2%

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

   if 1.45e109 < b

   1. Initial program 47.2%

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

   3. Simplified 47.1%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   7. Taylor expanded in b around -inf 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]
   8. Step-by-step derivation

      1. *-commutative 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{a} \cdot 2\right) \cdot -0.5\\ \end{array} \]

   9. Simplified 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{a} \cdot 2\right) \cdot -0.5\\ \end{array} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

Alternative 4: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \frac{b}{a}\\ t_1 := \frac{-c}{b}\\ t_2 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + t_0\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* 2.0 (/ b a)))
        (t_1 (/ (- c) b))
        (t_2 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -7.4e+161)
     (if (>= b 0.0) t_1 (* (+ (* -2.0 (/ c b)) t_0) -0.5))
     (if (<= b 2.4e+109)
       (if (>= b 0.0) (/ (* c 2.0) (- (- b) t_2)) (/ (- t_2 b) (* 2.0 a)))
       (if (>= b 0.0) t_1 (* t_0 -0.5))))))

C

double code(double a, double b, double c) {
	double t_0 = 2.0 * (b / a);
	double t_1 = -c / b;
	double t_2 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -7.4e+161) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_1;
		} else {
			tmp_2 = ((-2.0 * (c / b)) + t_0) * -0.5;
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.4e+109) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_2);
		} else {
			tmp_3 = (t_2 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_1;
	} else {
		tmp_1 = t_0 * -0.5;
	}
	return tmp_1;
}

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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    real(8) :: tmp_3
    t_0 = 2.0d0 * (b / a)
    t_1 = -c / b
    t_2 = sqrt(((b * b) - (c * (a * 4.0d0))))
    if (b <= (-7.4d+161)) then
        if (b >= 0.0d0) then
            tmp_2 = t_1
        else
            tmp_2 = (((-2.0d0) * (c / b)) + t_0) * (-0.5d0)
        end if
        tmp_1 = tmp_2
    else if (b <= 2.4d+109) then
        if (b >= 0.0d0) then
            tmp_3 = (c * 2.0d0) / (-b - t_2)
        else
            tmp_3 = (t_2 - b) / (2.0d0 * a)
        end if
        tmp_1 = tmp_3
    else if (b >= 0.0d0) then
        tmp_1 = t_1
    else
        tmp_1 = t_0 * (-0.5d0)
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = 2.0 * (b / a);
	double t_1 = -c / b;
	double t_2 = Math.sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -7.4e+161) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_1;
		} else {
			tmp_2 = ((-2.0 * (c / b)) + t_0) * -0.5;
		}
		tmp_1 = tmp_2;
	} else if (b <= 2.4e+109) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (c * 2.0) / (-b - t_2);
		} else {
			tmp_3 = (t_2 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = t_1;
	} else {
		tmp_1 = t_0 * -0.5;
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = 2.0 * (b / a)
	t_1 = -c / b
	t_2 = math.sqrt(((b * b) - (c * (a * 4.0))))
	tmp_1 = 0
	if b <= -7.4e+161:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_1
		else:
			tmp_2 = ((-2.0 * (c / b)) + t_0) * -0.5
		tmp_1 = tmp_2
	elif b <= 2.4e+109:
		tmp_3 = 0
		if b >= 0.0:
			tmp_3 = (c * 2.0) / (-b - t_2)
		else:
			tmp_3 = (t_2 - b) / (2.0 * a)
		tmp_1 = tmp_3
	elif b >= 0.0:
		tmp_1 = t_1
	else:
		tmp_1 = t_0 * -0.5
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(2.0 * Float64(b / a))
	t_1 = Float64(Float64(-c) / b)
	t_2 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -7.4e+161)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_1;
		else
			tmp_2 = Float64(Float64(Float64(-2.0 * Float64(c / b)) + t_0) * -0.5);
		end
		tmp_1 = tmp_2;
	elseif (b <= 2.4e+109)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(c * 2.0) / Float64(Float64(-b) - t_2));
		else
			tmp_3 = Float64(Float64(t_2 - b) / Float64(2.0 * a));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = t_1;
	else
		tmp_1 = Float64(t_0 * -0.5);
	end
	return tmp_1
end

MATLAB

function tmp_5 = code(a, b, c)
	t_0 = 2.0 * (b / a);
	t_1 = -c / b;
	t_2 = sqrt(((b * b) - (c * (a * 4.0))));
	tmp_2 = 0.0;
	if (b <= -7.4e+161)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_1;
		else
			tmp_3 = ((-2.0 * (c / b)) + t_0) * -0.5;
		end
		tmp_2 = tmp_3;
	elseif (b <= 2.4e+109)
		tmp_4 = 0.0;
		if (b >= 0.0)
			tmp_4 = (c * 2.0) / (-b - t_2);
		else
			tmp_4 = (t_2 - b) / (2.0 * a);
		end
		tmp_2 = tmp_4;
	elseif (b >= 0.0)
		tmp_2 = t_1;
	else
		tmp_2 = t_0 * -0.5;
	end
	tmp_5 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-c) / b), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -7.4e+161], If[GreaterEqual[b, 0.0], t$95$1, N[(N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] * -0.5), $MachinePrecision]], If[LessEqual[b, 2.4e+109], If[GreaterEqual[b, 0.0], N[(N[(c * 2.0), $MachinePrecision] / N[((-b) - t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$1, N[(t$95$0 * -0.5), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.39999999999999958e161

   1. Initial program 43.6%

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

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 43.6%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 43.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   7. Taylor expanded in b around -inf 99.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

   if -7.39999999999999958e161 < b < 2.39999999999999987e109

   1. Initial program 91.3%

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

   if 2.39999999999999987e109 < b

   1. Initial program 47.2%

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

   3. Simplified 47.1%

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

   4. Taylor expanded in c around 0 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
   5. Step-by-step derivation

      1. mul-1-neg 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

      2. distribute-neg-frac 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   6. Simplified 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   7. Taylor expanded in b around -inf 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]
   8. Step-by-step derivation

      1. *-commutative 98.3%

         \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{a} \cdot 2\right) \cdot -0.5\\ \end{array} \]

   9. Simplified 98.3%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{a} \cdot 2\right) \cdot -0.5\\ \end{array} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+161}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+109}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{c \cdot 2}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

Alternative 5: 67.4% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0) (/ (- c) b) (* (+ (* -2.0 (/ c b)) (* 2.0 (/ b a))) -0.5)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = ((-2.0 * (c / b)) + (2.0 * (b / a))) * -0.5;
	}
	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 >= 0.0d0) then
        tmp = -c / b
    else
        tmp = (((-2.0d0) * (c / b)) + (2.0d0 * (b / a))) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = ((-2.0 * (c / b)) + (2.0 * (b / a))) * -0.5;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = -c / b
	else:
		tmp = ((-2.0 * (c / b)) + (2.0 * (b / a))) * -0.5
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(Float64(Float64(-2.0 * Float64(c / b)) + Float64(2.0 * Float64(b / a))) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = -c / b;
	else
		tmp = ((-2.0 * (c / b)) + (2.0 * (b / a))) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[(N[(N[(-2.0 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]]

Derivation

1. Initial program 73.8%

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

3. Simplified 73.8%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

4. Taylor expanded in c around 0 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
5. Step-by-step derivation

   1. mul-1-neg 75.0%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   2. distribute-neg-frac 75.0%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

6. Simplified 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

7. Taylor expanded in b around -inf 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

8. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b} + 2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

Alternative 6: 35.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + b}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{-2}{\frac{b}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0) (* c (/ -2.0 (+ b b))) (* -0.5 (/ -2.0 (/ b c)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = c * (-2.0 / (b + b));
	} else {
		tmp = -0.5 * (-2.0 / (b / c));
	}
	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 >= 0.0d0) then
        tmp = c * ((-2.0d0) / (b + b))
    else
        tmp = (-0.5d0) * ((-2.0d0) / (b / c))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = c * (-2.0 / (b + b));
	} else {
		tmp = -0.5 * (-2.0 / (b / c));
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = c * (-2.0 / (b + b))
	else:
		tmp = -0.5 * (-2.0 / (b / c))
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(c * Float64(-2.0 / Float64(b + b)));
	else
		tmp = Float64(-0.5 * Float64(-2.0 / Float64(b / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = c * (-2.0 / (b + b));
	else
		tmp = -0.5 * (-2.0 / (b / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(b + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(-2.0 / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 73.8%

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

3. Simplified 73.8%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

4. Taylor expanded in b around -inf 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(-1 \cdot b + 2 \cdot \frac{a \cdot c}{b}\right)}{a} \cdot -0.5\\ \end{array} \]
5. Step-by-step derivation

   1. fma-def 69.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \mathsf{fma}\left(-1, b, 2 \cdot \frac{a \cdot c}{b}\right)}{a} \cdot -0.5\\ \end{array} \]

   2. associate-/l* 71.5%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \mathsf{fma}\left(-1, b, 2 \cdot \frac{a}{\frac{b}{c}}\right)}{a} \cdot -0.5\\ \end{array} \]

6. Simplified 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \mathsf{fma}\left(-1, b, 2 \cdot \frac{a}{\frac{b}{c}}\right)}{a} \cdot -0.5\\ \end{array} \]

7. Taylor expanded in b around inf 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \color{blue}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \mathsf{fma}\left(-1, b, 2 \cdot \frac{a}{\frac{b}{c}}\right)}{a} \cdot -0.5\\ \end{array} \]

8. Taylor expanded in b around 0 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + b}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot \frac{c}{b}\right) \cdot -0.5\\ \end{array} \]
9. Step-by-step derivation

   1. associate-*r/ 36.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot c}{b} \cdot -0.5\\ \end{array} \]

   2. associate-/l* 36.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{\frac{b}{c}} \cdot -0.5\\ \end{array} \]

10. Simplified 36.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{\frac{b}{c}} \cdot -0.5\\ \end{array} \]

11. Final simplification 36.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + b}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{-2}{\frac{b}{c}}\\ \end{array} \]

Alternative 7: 67.3% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (>= b 0.0) (/ (- c) b) (* (* 2.0 (/ b a)) -0.5)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = (2.0 * (b / a)) * -0.5;
	}
	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 >= 0.0d0) then
        tmp = -c / b
    else
        tmp = (2.0d0 * (b / a)) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = (2.0 * (b / a)) * -0.5;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b >= 0.0:
		tmp = -c / b
	else:
		tmp = (2.0 * (b / a)) * -0.5
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b >= 0.0)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(Float64(2.0 * Float64(b / a)) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b >= 0.0)
		tmp = -c / b;
	else
		tmp = (2.0 * (b / a)) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[GreaterEqual[b, 0.0], N[((-c) / b), $MachinePrecision], N[(N[(2.0 * N[(b / a), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]]

Derivation

1. Initial program 73.8%

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

3. Simplified 73.8%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{b + \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ } \end{array}} \]

4. Taylor expanded in c around 0 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]
5. Step-by-step derivation

   1. mul-1-neg 75.0%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

   2. distribute-neg-frac 75.0%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

6. Simplified 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \sqrt{\mathsf{fma}\left(b, b, c \cdot \left(a \cdot -4\right)\right)}}{a} \cdot -0.5\\ \end{array} \]

7. Taylor expanded in b around -inf 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]
8. Step-by-step derivation

   1. *-commutative 72.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{a} \cdot 2\right) \cdot -0.5\\ \end{array} \]

9. Simplified 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{a} \cdot 2\right) \cdot -0.5\\ \end{array} \]

10. Final simplification 72.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{b}{a}\right) \cdot -0.5\\ \end{array} \]

Reproduce

herbie shell --seed 2023290 
(FPCore (a b c)
  :name "jeff quadratic root 2"
  :precision binary64
  (if (>= b 0.0) (/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))