jeff quadratic root 2

Percentage Accurate: 72.1% → 91.3%

Time: 22.1s

Alternatives: 4

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: 72.1% 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: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+122}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+127}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\mathsf{fma}\left(-2, c \cdot \frac{a}{b}, b \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + b}{a} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -5.8e+122)
     (if (>= b 0.0) (/ 2.0 (/ (* b -2.0) c)) (- (/ c b) (/ b a)))
     (if (<= b 1.45e+127)
       (if (>= b 0.0) (/ (* 2.0 c) (- (- b) t_0)) (/ (- t_0 b) (* 2.0 a)))
       (if (>= b 0.0)
         (* c (/ -2.0 (fma -2.0 (* c (/ a b)) (* b 2.0))))
         (* (/ (+ b b) a) -0.5))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -5.8e+122) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = 2.0 / ((b * -2.0) / c);
		} else {
			tmp_2 = (c / b) - (b / a);
		}
		tmp_1 = tmp_2;
	} else if (b <= 1.45e+127) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = (2.0 * c) / (-b - t_0);
		} else {
			tmp_3 = (t_0 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = c * (-2.0 / fma(-2.0, (c * (a / b)), (b * 2.0)));
	} else {
		tmp_1 = ((b + b) / a) * -0.5;
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -5.8e+122)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(2.0 / Float64(Float64(b * -2.0) / c));
		else
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		end
		tmp_1 = tmp_2;
	elseif (b <= 1.45e+127)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(Float64(2.0 * c) / Float64(Float64(-b) - t_0));
		else
			tmp_3 = Float64(Float64(t_0 - b) / Float64(2.0 * a));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(c * Float64(-2.0 / fma(-2.0, Float64(c * Float64(a / b)), Float64(b * 2.0))));
	else
		tmp_1 = Float64(Float64(Float64(b + b) / a) * -0.5);
	end
	return tmp_1
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, -5.8e+122], If[GreaterEqual[b, 0.0], N[(2.0 / N[(N[(b * -2.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 1.45e+127], If[GreaterEqual[b, 0.0], N[(N[(2.0 * c), $MachinePrecision] / N[((-b) - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(-2.0 * N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(b * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision] * -0.5), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8000000000000002e122

   1. Initial program 41.4%

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

   3. Simplified 41.4%

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

   4. Taylor expanded in b around inf 41.4%

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

      1. *-commutative 41.4%

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

   6. Simplified 41.4%

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

   7. Taylor expanded in b around -inf 97.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a} + \frac{c}{b}\\ \end{array} \]

   if -5.8000000000000002e122 < b < 1.4500000000000001e127

   1. Initial program 83.8%

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

   if 1.4500000000000001e127 < b

   1. Initial program 55.3%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in b around -inf 55.4%

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

   5. Taylor expanded in b around inf 95.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\color{blue}{-2 \cdot \frac{a \cdot c}{b} + 2 \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - -1 \cdot b}{a} \cdot -0.5\\ \end{array} \]
   6. Step-by-step derivation

      1. fma-def 95.4%

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

      2. associate-/l* 99.8%

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

      3. associate-/r/ 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\color{blue}{\mathsf{fma}\left(-2, \frac{a}{b} \cdot c, b \cdot 2\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - -1 \cdot b}{a} \cdot -0.5\\ \end{array} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+122}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+127}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\mathsf{fma}\left(-2, c \cdot \frac{a}{b}, b \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + b}{a} \cdot -0.5\\ \end{array} \]

Alternative 2: 91.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}\\ \mathbf{if}\;b \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+119}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{\left(-b\right) - t_0}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\mathsf{fma}\left(-2, c \cdot \frac{a}{b}, b \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + b}{a} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (sqrt (- (* b b) (* c (* a 4.0))))))
   (if (<= b -5e+123)
     (if (>= b 0.0) (/ 2.0 (/ (* b -2.0) c)) (- (/ c b) (/ b a)))
     (if (<= b 2e+119)
       (if (>= b 0.0) (/ 2.0 (/ (- (- b) t_0) c)) (/ (- t_0 b) (* 2.0 a)))
       (if (>= b 0.0)
         (* c (/ -2.0 (fma -2.0 (* c (/ a b)) (* b 2.0))))
         (* (/ (+ b b) a) -0.5))))))

C

double code(double a, double b, double c) {
	double t_0 = sqrt(((b * b) - (c * (a * 4.0))));
	double tmp_1;
	if (b <= -5e+123) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = 2.0 / ((b * -2.0) / c);
		} else {
			tmp_2 = (c / b) - (b / a);
		}
		tmp_1 = tmp_2;
	} else if (b <= 2e+119) {
		double tmp_3;
		if (b >= 0.0) {
			tmp_3 = 2.0 / ((-b - t_0) / c);
		} else {
			tmp_3 = (t_0 - b) / (2.0 * a);
		}
		tmp_1 = tmp_3;
	} else if (b >= 0.0) {
		tmp_1 = c * (-2.0 / fma(-2.0, (c * (a / b)), (b * 2.0)));
	} else {
		tmp_1 = ((b + b) / a) * -0.5;
	}
	return tmp_1;
}

Julia

function code(a, b, c)
	t_0 = sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0))))
	tmp_1 = 0.0
	if (b <= -5e+123)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = Float64(2.0 / Float64(Float64(b * -2.0) / c));
		else
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		end
		tmp_1 = tmp_2;
	elseif (b <= 2e+119)
		tmp_3 = 0.0
		if (b >= 0.0)
			tmp_3 = Float64(2.0 / Float64(Float64(Float64(-b) - t_0) / c));
		else
			tmp_3 = Float64(Float64(t_0 - b) / Float64(2.0 * a));
		end
		tmp_1 = tmp_3;
	elseif (b >= 0.0)
		tmp_1 = Float64(c * Float64(-2.0 / fma(-2.0, Float64(c * Float64(a / b)), Float64(b * 2.0))));
	else
		tmp_1 = Float64(Float64(Float64(b + b) / a) * -0.5);
	end
	return tmp_1
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, -5e+123], If[GreaterEqual[b, 0.0], N[(2.0 / N[(N[(b * -2.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]], If[LessEqual[b, 2e+119], If[GreaterEqual[b, 0.0], N[(2.0 / N[(N[((-b) - t$95$0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], N[(c * N[(-2.0 / N[(-2.0 * N[(c * N[(a / b), $MachinePrecision]), $MachinePrecision] + N[(b * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + b), $MachinePrecision] / a), $MachinePrecision] * -0.5), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.99999999999999974e123

   1. Initial program 41.4%

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

   3. Simplified 41.4%

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

   4. Taylor expanded in b around inf 41.4%

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

      1. *-commutative 41.4%

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

   6. Simplified 41.4%

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

   7. Taylor expanded in b around -inf 97.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a} + \frac{c}{b}\\ \end{array} \]

   if -4.99999999999999974e123 < b < 1.99999999999999989e119

   1. Initial program 83.5%

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

   3. Simplified 83.5%

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

   if 1.99999999999999989e119 < b

   1. Initial program 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in b around -inf 57.3%

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

   5. Taylor expanded in b around inf 95.6%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\color{blue}{-2 \cdot \frac{a \cdot c}{b} + 2 \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - -1 \cdot b}{a} \cdot -0.5\\ \end{array} \]
   6. Step-by-step derivation

      1. fma-def 95.6%

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

      2. associate-/l* 99.8%

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

      3. associate-/r/ 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\color{blue}{\mathsf{fma}\left(-2, \frac{a}{b} \cdot c, b \cdot 2\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - -1 \cdot b}{a} \cdot -0.5\\ \end{array} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+119}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{\left(-b\right) - \sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)}}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;c \cdot \frac{-2}{\mathsf{fma}\left(-2, c \cdot \frac{a}{b}, b \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + b}{a} \cdot -0.5\\ \end{array} \]

Alternative 3: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+133}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ 2.0 (/ (* b -2.0) c))))
   (if (<= b -1e+133)
     (if (>= b 0.0) t_0 (- (/ c b) (/ b a)))
     (if (>= b 0.0)
       t_0
       (/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) (* 2.0 a))))))

C

double code(double a, double b, double c) {
	double t_0 = 2.0 / ((b * -2.0) / c);
	double tmp_1;
	if (b <= -1e+133) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = (c / b) - (b / a);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = (sqrt(((b * b) - (c * (a * 4.0)))) - b) / (2.0 * a);
	}
	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) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_0 = 2.0d0 / ((b * (-2.0d0)) / c)
    if (b <= (-1d+133)) then
        if (b >= 0.0d0) then
            tmp_2 = t_0
        else
            tmp_2 = (c / b) - (b / a)
        end if
        tmp_1 = tmp_2
    else if (b >= 0.0d0) then
        tmp_1 = t_0
    else
        tmp_1 = (sqrt(((b * b) - (c * (a * 4.0d0)))) - b) / (2.0d0 * a)
    end if
    code = tmp_1
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = 2.0 / ((b * -2.0) / c);
	double tmp_1;
	if (b <= -1e+133) {
		double tmp_2;
		if (b >= 0.0) {
			tmp_2 = t_0;
		} else {
			tmp_2 = (c / b) - (b / a);
		}
		tmp_1 = tmp_2;
	} else if (b >= 0.0) {
		tmp_1 = t_0;
	} else {
		tmp_1 = (Math.sqrt(((b * b) - (c * (a * 4.0)))) - b) / (2.0 * a);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = 2.0 / ((b * -2.0) / c)
	tmp_1 = 0
	if b <= -1e+133:
		tmp_2 = 0
		if b >= 0.0:
			tmp_2 = t_0
		else:
			tmp_2 = (c / b) - (b / a)
		tmp_1 = tmp_2
	elif b >= 0.0:
		tmp_1 = t_0
	else:
		tmp_1 = (math.sqrt(((b * b) - (c * (a * 4.0)))) - b) / (2.0 * a)
	return tmp_1

Julia

function code(a, b, c)
	t_0 = Float64(2.0 / Float64(Float64(b * -2.0) / c))
	tmp_1 = 0.0
	if (b <= -1e+133)
		tmp_2 = 0.0
		if (b >= 0.0)
			tmp_2 = t_0;
		else
			tmp_2 = Float64(Float64(c / b) - Float64(b / a));
		end
		tmp_1 = tmp_2;
	elseif (b >= 0.0)
		tmp_1 = t_0;
	else
		tmp_1 = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(c * Float64(a * 4.0)))) - b) / Float64(2.0 * a));
	end
	return tmp_1
end

MATLAB

function tmp_4 = code(a, b, c)
	t_0 = 2.0 / ((b * -2.0) / c);
	tmp_2 = 0.0;
	if (b <= -1e+133)
		tmp_3 = 0.0;
		if (b >= 0.0)
			tmp_3 = t_0;
		else
			tmp_3 = (c / b) - (b / a);
		end
		tmp_2 = tmp_3;
	elseif (b >= 0.0)
		tmp_2 = t_0;
	else
		tmp_2 = (sqrt(((b * b) - (c * (a * 4.0)))) - b) / (2.0 * a);
	end
	tmp_4 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(2.0 / N[(N[(b * -2.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+133], If[GreaterEqual[b, 0.0], t$95$0, N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]], If[GreaterEqual[b, 0.0], t$95$0, N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(c * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if b < -1e133

   1. Initial program 41.4%

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

   3. Simplified 41.4%

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

   4. Taylor expanded in b around inf 41.4%

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

      1. *-commutative 41.4%

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

   6. Simplified 41.4%

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

   7. Taylor expanded in b around -inf 97.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a} + \frac{c}{b}\\ \end{array} \]

   if -1e133 < b

   1. Initial program 77.5%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in b around inf 74.4%

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

      1. *-commutative 74.4%

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

   6. Simplified 74.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+133}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\\ \mathbf{elif}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - c \cdot \left(a \cdot 4\right)} - b}{2 \cdot a}\\ \end{array} \]

Alternative 4: 68.0% accurate, 19.5× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c) {
	double tmp;
	if (b >= 0.0) {
		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 >= 0.0d0) 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 >= 0.0) {
		tmp = -c / b;
	} else {
		tmp = -b / a;
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 69.4%

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

3. Simplified 69.3%

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

4. Taylor expanded in b around inf 67.1%

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

   1. *-commutative 67.1%

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

6. Simplified 67.1%

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

7. Taylor expanded in b around -inf 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array} \]
8. Step-by-step derivation

   1. associate-*r/ 68.2%

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{2}{\frac{b \cdot -2}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 \cdot b}{a}\\ \end{array} \]

   2. mul-1-neg 68.2%

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

9. Simplified 68.2%

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

    1. associate-/r/ 68.4%

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

    2. *-commutative 68.4%

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

    3. associate-/r* 68.4%

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

    4. metadata-eval 68.4%

       \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\frac{\color{blue}{-1}}{b} \cdot c\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

11. Applied egg-rr 68.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-1}{b} \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

12. Taylor expanded in b around 0 68.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-1 \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]
13. Step-by-step derivation

    1. mul-1-neg 68.5%

       \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{-\frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

    2. distribute-frac-neg 68.5%

       \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

14. Simplified 68.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \geq 0:\\ \;\;\;\;\color{blue}{\frac{-c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a}\\ \end{array} \]

15. Final simplification 68.5%

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

Reproduce

herbie shell --seed 2023301 
(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))))