quadp (p42, positive)

Percentage Accurate: 51.5% → 85.7%

Time: 14.2s

Alternatives: 8

Speedup: 19.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 51.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -4.2e+108)
   (- (/ c b) (/ b a))
   (if (<= b 4.8e-51)
     (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) (* a 2.0))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -4.2e+108) {
		tmp = (c / b) - (b / a);
	} else if (b <= 4.8e-51) {
		tmp = (sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4.2d+108)) then
        tmp = (c / b) - (b / a)
    else if (b <= 4.8d-51) then
        tmp = (sqrt(((b * b) - (4.0d0 * (c * a)))) - b) / (a * 2.0d0)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -4.2e+108) {
		tmp = (c / b) - (b / a);
	} else if (b <= 4.8e-51) {
		tmp = (Math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -4.2e+108:
		tmp = (c / b) - (b / a)
	elif b <= 4.8e-51:
		tmp = (math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -4.2e+108)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 4.8e-51)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a)))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -4.2e+108)
		tmp = (c / b) - (b / a);
	elseif (b <= 4.8e-51)
		tmp = (sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -4.2e+108], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e-51], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.20000000000000019e108

   1. Initial program 53.5%

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

      1. neg-sub0 53.5%

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

      2. associate-+l- 53.5%

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

      3. sub0-neg 53.5%

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

      4. neg-mul-1 53.5%

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

      5. *-commutative 53.5%

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

      6. associate-*r/ 53.5%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in b around -inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. unsub-neg 96.7%

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

   6. Simplified 96.7%

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

   if -4.20000000000000019e108 < b < 4.8e-51

   1. Initial program 78.3%

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

   if 4.8e-51 < b

   1. Initial program 11.0%

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

      1. neg-sub0 11.0%

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

      2. associate-+l- 11.0%

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

      3. sub0-neg 11.0%

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

      4. neg-mul-1 11.0%

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

      5. *-commutative 11.0%

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

      6. associate-*r/ 11.0%

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

   3. Simplified 11.0%

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

   4. Taylor expanded in b around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   6. Simplified 86.8%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 2: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+108}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-51}:\\ \;\;\;\;\left(\sqrt{b \cdot b + a \cdot \left(c \cdot -4\right)} - b\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.65e+108)
   (- (/ c b) (/ b a))
   (if (<= b 4.7e-51)
     (* (- (sqrt (+ (* b b) (* a (* c -4.0)))) b) (/ 0.5 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.65e+108) {
		tmp = (c / b) - (b / a);
	} else if (b <= 4.7e-51) {
		tmp = (sqrt(((b * b) + (a * (c * -4.0)))) - b) * (0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.65d+108)) then
        tmp = (c / b) - (b / a)
    else if (b <= 4.7d-51) then
        tmp = (sqrt(((b * b) + (a * (c * (-4.0d0))))) - b) * (0.5d0 / a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.65e+108) {
		tmp = (c / b) - (b / a);
	} else if (b <= 4.7e-51) {
		tmp = (Math.sqrt(((b * b) + (a * (c * -4.0)))) - b) * (0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.65e+108:
		tmp = (c / b) - (b / a)
	elif b <= 4.7e-51:
		tmp = (math.sqrt(((b * b) + (a * (c * -4.0)))) - b) * (0.5 / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.65e+108)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 4.7e-51)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(a * Float64(c * -4.0)))) - b) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.65e+108)
		tmp = (c / b) - (b / a);
	elseif (b <= 4.7e-51)
		tmp = (sqrt(((b * b) + (a * (c * -4.0)))) - b) * (0.5 / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.65e+108], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e-51], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6500000000000001e108

   1. Initial program 53.5%

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

      1. neg-sub0 53.5%

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

      2. associate-+l- 53.5%

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

      3. sub0-neg 53.5%

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

      4. neg-mul-1 53.5%

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

      5. *-commutative 53.5%

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

      6. associate-*r/ 53.5%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in b around -inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. unsub-neg 96.7%

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

   6. Simplified 96.7%

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

   if -1.6500000000000001e108 < b < 4.6999999999999997e-51

   1. Initial program 78.3%

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

      1. /-rgt-identity 78.3%

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

      2. metadata-eval 78.3%

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

      3. associate-/l* 78.3%

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

      4. associate-*r/ 78.1%

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

      5. +-commutative 78.1%

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

      6. unsub-neg 78.1%

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

      7. fma-neg 78.1%

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

      8. *-commutative 78.1%

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

      9. distribute-rgt-neg-in 78.1%

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

      10. associate-*l* 78.2%

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

      11. metadata-eval 78.2%

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

      12. associate-/r* 78.2%

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

      13. metadata-eval 78.2%

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

      14. metadata-eval 78.2%

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

   3. Simplified 78.2%

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

      1. fma-udef 78.2%

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

   5. Applied egg-rr 78.2%

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

   if 4.6999999999999997e-51 < b

   1. Initial program 11.0%

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

      1. neg-sub0 11.0%

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

      2. associate-+l- 11.0%

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

      3. sub0-neg 11.0%

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

      4. neg-mul-1 11.0%

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

      5. *-commutative 11.0%

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

      6. associate-*r/ 11.0%

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

   3. Simplified 11.0%

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

   4. Taylor expanded in b around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   6. Simplified 86.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+108}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-51}:\\ \;\;\;\;\left(\sqrt{b \cdot b + a \cdot \left(c \cdot -4\right)} - b\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 3: 79.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;\left(b - \sqrt{a \cdot \left(c \cdot -4\right)}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e-154)
   (- (/ c b) (/ b a))
   (if (<= b 4.2e-48)
     (* (- b (sqrt (* a (* c -4.0)))) (/ -0.5 a))
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e-154) {
		tmp = (c / b) - (b / a);
	} else if (b <= 4.2e-48) {
		tmp = (b - sqrt((a * (c * -4.0)))) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-3.8d-154)) then
        tmp = (c / b) - (b / a)
    else if (b <= 4.2d-48) then
        tmp = (b - sqrt((a * (c * (-4.0d0))))) * ((-0.5d0) / a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e-154) {
		tmp = (c / b) - (b / a);
	} else if (b <= 4.2e-48) {
		tmp = (b - Math.sqrt((a * (c * -4.0)))) * (-0.5 / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.8e-154:
		tmp = (c / b) - (b / a)
	elif b <= 4.2e-48:
		tmp = (b - math.sqrt((a * (c * -4.0)))) * (-0.5 / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e-154)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 4.2e-48)
		tmp = Float64(Float64(b - sqrt(Float64(a * Float64(c * -4.0)))) * Float64(-0.5 / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.8e-154)
		tmp = (c / b) - (b / a);
	elseif (b <= 4.2e-48)
		tmp = (b - sqrt((a * (c * -4.0)))) * (-0.5 / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e-154], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-48], N[(N[(b - N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.8000000000000001e-154

   1. Initial program 73.8%

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

      1. neg-sub0 73.8%

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

      2. associate-+l- 73.8%

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

      3. sub0-neg 73.8%

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

      4. neg-mul-1 73.8%

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

      5. *-commutative 73.8%

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

      6. associate-*r/ 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in b around -inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. unsub-neg 84.8%

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

   6. Simplified 84.8%

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

   if -3.8000000000000001e-154 < b < 4.19999999999999977e-48

   1. Initial program 62.3%

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

      1. neg-sub0 62.3%

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

      2. associate-+l- 62.3%

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

      3. sub0-neg 62.3%

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

      4. neg-mul-1 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-*r/ 62.3%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in a around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if 4.19999999999999977e-48 < b

   1. Initial program 11.0%

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

      1. neg-sub0 11.0%

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

      2. associate-+l- 11.0%

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

      3. sub0-neg 11.0%

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

      4. neg-mul-1 11.0%

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

      5. *-commutative 11.0%

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

      6. associate-*r/ 11.0%

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

   3. Simplified 11.0%

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

   4. Taylor expanded in b around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   6. Simplified 86.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;\left(b - \sqrt{a \cdot \left(c \cdot -4\right)}\right) \cdot \frac{-0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 4: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{\left(b - \sqrt{c \cdot \left(a \cdot -4\right)}\right) \cdot -0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.7e-154)
   (- (/ c b) (/ b a))
   (if (<= b 2.2e-51)
     (/ (* (- b (sqrt (* c (* a -4.0)))) -0.5) a)
     (/ (- c) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.7e-154) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.2e-51) {
		tmp = ((b - sqrt((c * (a * -4.0)))) * -0.5) / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-3.7d-154)) then
        tmp = (c / b) - (b / a)
    else if (b <= 2.2d-51) then
        tmp = ((b - sqrt((c * (a * (-4.0d0))))) * (-0.5d0)) / a
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.7e-154) {
		tmp = (c / b) - (b / a);
	} else if (b <= 2.2e-51) {
		tmp = ((b - Math.sqrt((c * (a * -4.0)))) * -0.5) / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.7e-154:
		tmp = (c / b) - (b / a)
	elif b <= 2.2e-51:
		tmp = ((b - math.sqrt((c * (a * -4.0)))) * -0.5) / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.7e-154)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 2.2e-51)
		tmp = Float64(Float64(Float64(b - sqrt(Float64(c * Float64(a * -4.0)))) * -0.5) / a);
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.7e-154)
		tmp = (c / b) - (b / a);
	elseif (b <= 2.2e-51)
		tmp = ((b - sqrt((c * (a * -4.0)))) * -0.5) / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.7e-154], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-51], N[(N[(N[(b - N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision] / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.69999999999999987e-154

   1. Initial program 73.8%

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

      1. neg-sub0 73.8%

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

      2. associate-+l- 73.8%

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

      3. sub0-neg 73.8%

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

      4. neg-mul-1 73.8%

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

      5. *-commutative 73.8%

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

      6. associate-*r/ 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in b around -inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. unsub-neg 84.8%

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

   6. Simplified 84.8%

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

   if -3.69999999999999987e-154 < b < 2.2e-51

   1. Initial program 62.3%

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

      1. neg-sub0 62.3%

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

      2. associate-+l- 62.3%

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

      3. sub0-neg 62.3%

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

      4. neg-mul-1 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-*r/ 62.3%

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

   3. Simplified 62.4%

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

      1. add-cbrt-cube 46.0%

         \[\leadsto \left(b - \color{blue}{\sqrt[3]{\left(\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)} \cdot \sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}\right) \cdot \sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}}\right) \cdot \frac{-0.5}{a} \]

      2. pow3 45.9%

         \[\leadsto \left(b - \sqrt[3]{\color{blue}{{\left(\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}\right)}^{3}}}\right) \cdot \frac{-0.5}{a} \]

      3. pow1/3 42.9%

         \[\leadsto \left(b - \color{blue}{{\left({\left(\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}\right)}^{3}\right)}^{0.3333333333333333}}\right) \cdot \frac{-0.5}{a} \]

      4. sqrt-pow2 42.9%

         \[\leadsto \left(b - {\color{blue}{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{\left(\frac{3}{2}\right)}\right)}}^{0.3333333333333333}\right) \cdot \frac{-0.5}{a} \]

      5. metadata-eval 42.9%

         \[\leadsto \left(b - {\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{\color{blue}{1.5}}\right)}^{0.3333333333333333}\right) \cdot \frac{-0.5}{a} \]

   5. Applied egg-rr 42.9%

      \[\leadsto \left(b - \color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{1.5}\right)}^{0.3333333333333333}}\right) \cdot \frac{-0.5}{a} \]
   6. Step-by-step derivation

      1. unpow1/3 45.9%

         \[\leadsto \left(b - \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{1.5}}}\right) \cdot \frac{-0.5}{a} \]

      2. fma-def 45.9%

         \[\leadsto \left(b - \sqrt[3]{{\color{blue}{\left(a \cdot \left(c \cdot -4\right) + b \cdot b\right)}}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      3. +-commutative 45.9%

         \[\leadsto \left(b - \sqrt[3]{{\color{blue}{\left(b \cdot b + a \cdot \left(c \cdot -4\right)\right)}}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      4. fma-def 45.9%

         \[\leadsto \left(b - \sqrt[3]{{\color{blue}{\left(\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)\right)}}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

   7. Simplified 45.9%

      \[\leadsto \left(b - \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(b, b, a \cdot \left(c \cdot -4\right)\right)\right)}^{1.5}}}\right) \cdot \frac{-0.5}{a} \]

   8. Taylor expanded in a around inf 22.0%

      \[\leadsto \left(b - \sqrt[3]{\color{blue}{e^{1.5 \cdot \left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right)}}}\right) \cdot \frac{-0.5}{a} \]
   9. Step-by-step derivation

      1. *-commutative 22.0%

         \[\leadsto \left(b - \sqrt[3]{e^{\color{blue}{\left(-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)\right) \cdot 1.5}}}\right) \cdot \frac{-0.5}{a} \]

      2. exp-prod 22.1%

         \[\leadsto \left(b - \sqrt[3]{\color{blue}{{\left(e^{-1 \cdot \log \left(\frac{1}{a}\right) + \log \left(-4 \cdot c\right)}\right)}^{1.5}}}\right) \cdot \frac{-0.5}{a} \]

      3. mul-1-neg 22.1%

         \[\leadsto \left(b - \sqrt[3]{{\left(e^{\color{blue}{\left(-\log \left(\frac{1}{a}\right)\right)} + \log \left(-4 \cdot c\right)}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      4. log-rec 22.1%

         \[\leadsto \left(b - \sqrt[3]{{\left(e^{\left(-\color{blue}{\left(-\log a\right)}\right) + \log \left(-4 \cdot c\right)}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      5. remove-double-neg 22.1%

         \[\leadsto \left(b - \sqrt[3]{{\left(e^{\color{blue}{\log a} + \log \left(-4 \cdot c\right)}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      6. *-commutative 22.1%

         \[\leadsto \left(b - \sqrt[3]{{\left(e^{\log a + \log \color{blue}{\left(c \cdot -4\right)}}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      7. log-prod 43.5%

         \[\leadsto \left(b - \sqrt[3]{{\left(e^{\color{blue}{\log \left(a \cdot \left(c \cdot -4\right)\right)}}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      8. rem-exp-log 45.9%

         \[\leadsto \left(b - \sqrt[3]{{\color{blue}{\left(a \cdot \left(c \cdot -4\right)\right)}}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      9. associate-*r* 45.9%

         \[\leadsto \left(b - \sqrt[3]{{\color{blue}{\left(\left(a \cdot c\right) \cdot -4\right)}}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      10. *-commutative 45.9%

          \[\leadsto \left(b - \sqrt[3]{{\left(\color{blue}{\left(c \cdot a\right)} \cdot -4\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      11. rem-square-sqrt 0.0%

          \[\leadsto \left(b - \sqrt[3]{{\left(\left(c \cdot a\right) \cdot \color{blue}{\left(\sqrt{-4} \cdot \sqrt{-4}\right)}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      12. unpow2 0.0%

          \[\leadsto \left(b - \sqrt[3]{{\left(\left(c \cdot a\right) \cdot \color{blue}{{\left(\sqrt{-4}\right)}^{2}}\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      13. associate-*r* 0.0%

          \[\leadsto \left(b - \sqrt[3]{{\color{blue}{\left(c \cdot \left(a \cdot {\left(\sqrt{-4}\right)}^{2}\right)\right)}}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      14. unpow2 0.0%

          \[\leadsto \left(b - \sqrt[3]{{\left(c \cdot \left(a \cdot \color{blue}{\left(\sqrt{-4} \cdot \sqrt{-4}\right)}\right)\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

      15. rem-square-sqrt 45.9%

          \[\leadsto \left(b - \sqrt[3]{{\left(c \cdot \left(a \cdot \color{blue}{-4}\right)\right)}^{1.5}}\right) \cdot \frac{-0.5}{a} \]

   10. Simplified 45.9%

       \[\leadsto \left(b - \sqrt[3]{\color{blue}{{\left(c \cdot \left(a \cdot -4\right)\right)}^{1.5}}}\right) \cdot \frac{-0.5}{a} \]
   11. Step-by-step derivation

       1. associate-*r/ 45.9%

          \[\leadsto \color{blue}{\frac{\left(b - \sqrt[3]{{\left(c \cdot \left(a \cdot -4\right)\right)}^{1.5}}\right) \cdot -0.5}{a}} \]

       2. pow1/3 42.9%

          \[\leadsto \frac{\left(b - \color{blue}{{\left({\left(c \cdot \left(a \cdot -4\right)\right)}^{1.5}\right)}^{0.3333333333333333}}\right) \cdot -0.5}{a} \]

       3. pow-pow 62.4%

          \[\leadsto \frac{\left(b - \color{blue}{{\left(c \cdot \left(a \cdot -4\right)\right)}^{\left(1.5 \cdot 0.3333333333333333\right)}}\right) \cdot -0.5}{a} \]

       4. metadata-eval 62.4%

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

       5. pow1/2 62.4%

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

   12. Applied egg-rr 62.4%

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

   if 2.2e-51 < b

   1. Initial program 11.0%

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

      1. neg-sub0 11.0%

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

      2. associate-+l- 11.0%

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

      3. sub0-neg 11.0%

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

      4. neg-mul-1 11.0%

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

      5. *-commutative 11.0%

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

      6. associate-*r/ 11.0%

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

   3. Simplified 11.0%

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

   4. Taylor expanded in b around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   6. Simplified 86.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{\left(b - \sqrt{c \cdot \left(a \cdot -4\right)}\right) \cdot -0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 5: 68.5% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1e-310) (- (/ c b) (/ b a)) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1e-310) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1d-310)) then
        tmp = (c / b) - (b / a)
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1e-310) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1e-310:
		tmp = (c / b) - (b / a)
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1e-310)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1e-310)
		tmp = (c / b) - (b / a);
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1e-310], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.999999999999969e-311

   1. Initial program 73.9%

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

      1. neg-sub0 73.9%

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

      2. associate-+l- 73.9%

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

      3. sub0-neg 73.9%

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

      4. neg-mul-1 73.9%

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

      5. *-commutative 73.9%

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

      6. associate-*r/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in b around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   6. Simplified 73.4%

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

   if -9.999999999999969e-311 < b

   1. Initial program 22.9%

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

      1. neg-sub0 22.9%

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

      2. associate-+l- 22.9%

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

      3. sub0-neg 22.9%

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

      4. neg-mul-1 22.9%

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

      5. *-commutative 22.9%

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

      6. associate-*r/ 22.8%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in b around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. neg-mul-1 69.9%

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

   6. Simplified 69.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 6: 43.5% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.02 \cdot 10^{+24}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 1.02e+24) (/ (- b) a) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.02e+24) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.02d+24) then
        tmp = -b / a
    else
        tmp = c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.02e+24) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.02e+24:
		tmp = -b / a
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.02e+24)
		tmp = Float64(Float64(-b) / a);
	else
		tmp = Float64(c / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.02e+24)
		tmp = -b / a;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.02e+24], N[((-b) / a), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.02000000000000004e24

   1. Initial program 65.5%

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

      1. neg-sub0 65.5%

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

      2. associate-+l- 65.5%

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

      3. sub0-neg 65.5%

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

      4. neg-mul-1 65.5%

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

      5. *-commutative 65.5%

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

      6. associate-*r/ 65.4%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in b around -inf 54.2%

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

      1. associate-*r/ 54.2%

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

      2. mul-1-neg 54.2%

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

   6. Simplified 54.2%

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

   if 1.02000000000000004e24 < b

   1. Initial program 9.8%

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

      1. neg-sub0 9.8%

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

      2. associate-+l- 9.8%

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

      3. sub0-neg 9.8%

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

      4. neg-mul-1 9.8%

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

      5. *-commutative 9.8%

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

      6. associate-*r/ 9.9%

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

   3. Simplified 9.9%

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

   4. Taylor expanded in b around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l* 68.0%

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

   6. Simplified 68.0%

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

      1. associate-*l/ 68.0%

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

      2. frac-2neg 68.0%

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

      3. metadata-eval 68.0%

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

      4. frac-times 74.3%

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

   8. Applied egg-rr 74.3%

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

      1. associate-/r* 68.1%

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

      2. associate-*l* 68.1%

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

      3. metadata-eval 68.1%

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

      4. associate-*r/ 68.0%

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

      5. associate-/r/ 68.0%

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

   10. Simplified 68.0%

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

       1. expm1-log1p-u 59.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{c \cdot \left(\frac{1}{b} \cdot a\right)}{-a}\right)\right)} \]

       2. expm1-udef 35.8%

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

       3. associate-/l* 36.0%

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

       4. *-un-lft-identity 36.0%

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

       5. times-frac 39.3%

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

       6. clear-num 39.3%

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

       7. /-rgt-identity 39.3%

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

       8. add-sqr-sqrt 17.1%

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

       9. sqrt-unprod 22.4%

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

       10. sqr-neg 22.4%

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

       11. sqrt-unprod 17.2%

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

       12. add-sqr-sqrt 32.2%

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

   12. Applied egg-rr 32.2%

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

       1. expm1-def 31.5%

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

       2. expm1-log1p 31.6%

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

       3. *-inverses 31.6%

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

       4. associate-/r* 31.6%

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

       5. /-rgt-identity 31.6%

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

   14. Simplified 31.6%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.02 \cdot 10^{+24}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 7: 68.4% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1e-310) (/ (- b) a) (/ (- c) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1e-310) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1d-310)) then
        tmp = -b / a
    else
        tmp = -c / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1e-310) {
		tmp = -b / a;
	} else {
		tmp = -c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1e-310:
		tmp = -b / a
	else:
		tmp = -c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1e-310)
		tmp = Float64(Float64(-b) / a);
	else
		tmp = Float64(Float64(-c) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1e-310)
		tmp = -b / a;
	else
		tmp = -c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1e-310], N[((-b) / a), $MachinePrecision], N[((-c) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.999999999999969e-311

   1. Initial program 73.9%

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

      1. neg-sub0 73.9%

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

      2. associate-+l- 73.9%

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

      3. sub0-neg 73.9%

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

      4. neg-mul-1 73.9%

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

      5. *-commutative 73.9%

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

      6. associate-*r/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in b around -inf 73.3%

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

      1. associate-*r/ 73.3%

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

      2. mul-1-neg 73.3%

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

   6. Simplified 73.3%

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

   if -9.999999999999969e-311 < b

   1. Initial program 22.9%

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

      1. neg-sub0 22.9%

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

      2. associate-+l- 22.9%

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

      3. sub0-neg 22.9%

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

      4. neg-mul-1 22.9%

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

      5. *-commutative 22.9%

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

      6. associate-*r/ 22.8%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in b around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. neg-mul-1 69.9%

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

   6. Simplified 69.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{b}\\ \end{array} \]

Alternative 8: 11.3% accurate, 38.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 48.8%

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

   1. neg-sub0 48.8%

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

   2. associate-+l- 48.8%

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

   3. sub0-neg 48.8%

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

   4. neg-mul-1 48.8%

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

   5. *-commutative 48.8%

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

   6. associate-*r/ 48.7%

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

3. Simplified 48.8%

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

4. Taylor expanded in b around inf 27.2%

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

   1. *-commutative 27.2%

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

   2. associate-/l* 27.6%

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

6. Simplified 27.6%

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

   1. associate-*l/ 27.6%

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

   2. frac-2neg 27.6%

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

   3. metadata-eval 27.6%

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

   4. frac-times 30.6%

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

8. Applied egg-rr 30.6%

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

   1. associate-/r* 27.6%

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

   2. associate-*l* 27.6%

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

   3. metadata-eval 27.6%

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

   4. associate-*r/ 27.6%

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

   5. associate-/r/ 27.6%

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

10. Simplified 27.6%

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

    1. expm1-log1p-u 23.8%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{c \cdot \left(\frac{1}{b} \cdot a\right)}{-a}\right)\right)} \]

    2. expm1-udef 12.9%

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

    3. associate-/l* 13.0%

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

    4. *-un-lft-identity 13.0%

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

    5. times-frac 14.0%

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

    6. clear-num 14.0%

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

    7. /-rgt-identity 14.0%

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

    8. add-sqr-sqrt 6.2%

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

    9. sqrt-unprod 9.3%

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

    10. sqr-neg 9.3%

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

    11. sqrt-unprod 6.2%

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

    12. add-sqr-sqrt 11.3%

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

12. Applied egg-rr 11.3%

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

    1. expm1-def 11.2%

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

    2. expm1-log1p 11.8%

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

    3. *-inverses 11.8%

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

    4. associate-/r* 11.8%

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

    5. /-rgt-identity 11.8%

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

14. Simplified 11.8%

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

15. Final simplification 11.8%

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

Developer target: 70.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023207 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64

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

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