quadp (p42, positive)

Percentage Accurate: 52.4% → 85.0%

Time: 12.4s

Alternatives: 9

Speedup: 19.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 52.4% 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: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+113}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-12}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -4e+113)
   (- (/ c b) (/ b a))
   (if (<= b 9e-12)
     (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) (* a 2.0))
     (pow (- (/ a b) (/ b c)) -1.0))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -4e+113) {
		tmp = (c / b) - (b / a);
	} else if (b <= 9e-12) {
		tmp = (sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	} else {
		tmp = pow(((a / b) - (b / c)), -1.0);
	}
	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 <= (-4d+113)) then
        tmp = (c / b) - (b / a)
    else if (b <= 9d-12) then
        tmp = (sqrt(((b * b) - (4.0d0 * (c * a)))) - b) / (a * 2.0d0)
    else
        tmp = ((a / b) - (b / c)) ** (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -4e+113) {
		tmp = (c / b) - (b / a);
	} else if (b <= 9e-12) {
		tmp = (Math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	} else {
		tmp = Math.pow(((a / b) - (b / c)), -1.0);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -4e+113:
		tmp = (c / b) - (b / a)
	elif b <= 9e-12:
		tmp = (math.sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0)
	else:
		tmp = math.pow(((a / b) - (b / c)), -1.0)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -4e+113)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	elseif (b <= 9e-12)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a)))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(a / b) - Float64(b / c)) ^ -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -4e+113)
		tmp = (c / b) - (b / a);
	elseif (b <= 9e-12)
		tmp = (sqrt(((b * b) - (4.0 * (c * a)))) - b) / (a * 2.0);
	else
		tmp = ((a / b) - (b / c)) ^ -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -4e+113], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-12], 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[Power[N[(N[(a / b), $MachinePrecision] - N[(b / c), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e113

   1. Initial program 52.6%

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

   2. Taylor expanded in b around -inf 90.7%

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

      1. +-commutative 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

   4. Simplified 90.7%

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

   if -4e113 < b < 8.99999999999999962e-12

   1. Initial program 86.9%

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

   if 8.99999999999999962e-12 < b

   1. Initial program 14.6%

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

      1. clear-num 14.6%

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

      2. inv-pow 14.6%

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

      3. *-commutative 14.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 7.1%

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

      6. sqr-neg 7.1%

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

      7. sqrt-prod 7.1%

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

      8. add-sqr-sqrt 7.1%

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

      9. fma-neg 7.1%

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

      10. distribute-lft-neg-in 7.1%

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

      11. *-commutative 7.1%

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

      12. associate-*r* 7.1%

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

      13. metadata-eval 7.1%

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

   3. Applied egg-rr 7.1%

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

   4. Taylor expanded in b around -inf 25.6%

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

      1. +-commutative 25.6%

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

      2. mul-1-neg 25.6%

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

      3. unsub-neg 25.6%

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

   6. Simplified 25.6%

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

      1. sub-neg 25.6%

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

      2. neg-mul-1 25.6%

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

      3. metadata-eval 25.6%

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

      4. add-sqr-sqrt 10.8%

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

      5. sqrt-unprod 21.5%

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

      6. sqr-neg 21.5%

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

      7. sqrt-unprod 15.1%

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

      8. add-sqr-sqrt 26.2%

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

      9. times-frac 26.2%

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

      10. *-un-lft-identity 26.2%

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

      11. neg-mul-1 26.2%

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

      12. frac-2neg 26.2%

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

      13. frac-2neg 26.2%

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

      14. clear-num 26.2%

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

      15. frac-add 18.1%

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

      16. add-sqr-sqrt 0.0%

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

      17. sqrt-unprod 31.6%

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

      18. sqr-neg 31.6%

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

      19. sqrt-unprod 43.9%

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

      20. add-sqr-sqrt 44.1%

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

   8. Applied egg-rr 44.1%

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

   9. Taylor expanded in b around 0 91.0%

      \[\leadsto {\color{blue}{\left(-1 \cdot \frac{b}{c} + \frac{a}{b}\right)}}^{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+113}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-12}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \]

Alternative 2: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c}{b} - \frac{b}{a}\\ t_1 := \frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a \cdot 2}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (- (/ c b) (/ b a)))
        (t_1 (/ (+ b (sqrt (* a (* c -4.0)))) (* a 2.0))))
   (if (<= b -1.4e-17)
     t_0
     (if (<= b -5e-66)
       t_1
       (if (<= b -4.5e-133)
         t_0
         (if (<= b 1.5e-11) t_1 (pow (- (/ a b) (/ b c)) -1.0)))))))

C

double code(double a, double b, double c) {
	double t_0 = (c / b) - (b / a);
	double t_1 = (b + sqrt((a * (c * -4.0)))) / (a * 2.0);
	double tmp;
	if (b <= -1.4e-17) {
		tmp = t_0;
	} else if (b <= -5e-66) {
		tmp = t_1;
	} else if (b <= -4.5e-133) {
		tmp = t_0;
	} else if (b <= 1.5e-11) {
		tmp = t_1;
	} else {
		tmp = pow(((a / b) - (b / c)), -1.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (c / b) - (b / a)
    t_1 = (b + sqrt((a * (c * (-4.0d0))))) / (a * 2.0d0)
    if (b <= (-1.4d-17)) then
        tmp = t_0
    else if (b <= (-5d-66)) then
        tmp = t_1
    else if (b <= (-4.5d-133)) then
        tmp = t_0
    else if (b <= 1.5d-11) then
        tmp = t_1
    else
        tmp = ((a / b) - (b / c)) ** (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = (c / b) - (b / a);
	double t_1 = (b + Math.sqrt((a * (c * -4.0)))) / (a * 2.0);
	double tmp;
	if (b <= -1.4e-17) {
		tmp = t_0;
	} else if (b <= -5e-66) {
		tmp = t_1;
	} else if (b <= -4.5e-133) {
		tmp = t_0;
	} else if (b <= 1.5e-11) {
		tmp = t_1;
	} else {
		tmp = Math.pow(((a / b) - (b / c)), -1.0);
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = (c / b) - (b / a)
	t_1 = (b + math.sqrt((a * (c * -4.0)))) / (a * 2.0)
	tmp = 0
	if b <= -1.4e-17:
		tmp = t_0
	elif b <= -5e-66:
		tmp = t_1
	elif b <= -4.5e-133:
		tmp = t_0
	elif b <= 1.5e-11:
		tmp = t_1
	else:
		tmp = math.pow(((a / b) - (b / c)), -1.0)
	return tmp

Julia

function code(a, b, c)
	t_0 = Float64(Float64(c / b) - Float64(b / a))
	t_1 = Float64(Float64(b + sqrt(Float64(a * Float64(c * -4.0)))) / Float64(a * 2.0))
	tmp = 0.0
	if (b <= -1.4e-17)
		tmp = t_0;
	elseif (b <= -5e-66)
		tmp = t_1;
	elseif (b <= -4.5e-133)
		tmp = t_0;
	elseif (b <= 1.5e-11)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / b) - Float64(b / c)) ^ -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = (c / b) - (b / a);
	t_1 = (b + sqrt((a * (c * -4.0)))) / (a * 2.0);
	tmp = 0.0;
	if (b <= -1.4e-17)
		tmp = t_0;
	elseif (b <= -5e-66)
		tmp = t_1;
	elseif (b <= -4.5e-133)
		tmp = t_0;
	elseif (b <= 1.5e-11)
		tmp = t_1;
	else
		tmp = ((a / b) - (b / c)) ^ -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e-17], t$95$0, If[LessEqual[b, -5e-66], t$95$1, If[LessEqual[b, -4.5e-133], t$95$0, If[LessEqual[b, 1.5e-11], t$95$1, N[Power[N[(N[(a / b), $MachinePrecision] - N[(b / c), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3999999999999999e-17 or -4.99999999999999962e-66 < b < -4.50000000000000009e-133

   1. Initial program 73.4%

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

   2. Taylor expanded in b around -inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

   if -1.3999999999999999e-17 < b < -4.99999999999999962e-66 or -4.50000000000000009e-133 < b < 1.5e-11

   1. Initial program 81.6%

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

      1. add-cube-cbrt 80.7%

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

      2. pow3 80.7%

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

      3. fma-neg 80.7%

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

      4. distribute-lft-neg-in 80.7%

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

      5. *-commutative 80.7%

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

      6. associate-*r* 80.7%

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

      7. metadata-eval 80.7%

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

   3. Applied egg-rr 80.7%

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

   4. Taylor expanded in b around 0 78.0%

      \[\leadsto \frac{\left(-b\right) + \sqrt{{\left(\sqrt[3]{\color{blue}{-4 \cdot \left(a \cdot c\right)}}\right)}^{3}}}{2 \cdot a} \]
   5. Step-by-step derivation

      1. cbrt-prod 78.0%

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

      2. unpow-prod-down 77.9%

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

      3. pow3 78.0%

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

      4. add-cube-cbrt 78.4%

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

      5. *-commutative 78.4%

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

   6. Applied egg-rr 78.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{\color{blue}{{\left(\sqrt[3]{-4}\right)}^{3} \cdot \left(c \cdot a\right)}}}{2 \cdot a} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 52.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(-b\right) + \sqrt{{\left(\sqrt[3]{-4}\right)}^{3} \cdot \left(c \cdot a\right)}}{2 \cdot a}\right)\right)} \]

      2. expm1-udef 19.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(-b\right) + \sqrt{{\left(\sqrt[3]{-4}\right)}^{3} \cdot \left(c \cdot a\right)}}{2 \cdot a}\right)} - 1} \]

   8. Applied egg-rr 19.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(0.5 \cdot \frac{b + \sqrt{\left(a \cdot -4\right) \cdot c}}{a}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 52.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{b + \sqrt{\left(a \cdot -4\right) \cdot c}}{a}\right)\right)} \]

      2. expm1-log1p 77.8%

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

      3. *-commutative 77.8%

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

      4. metadata-eval 77.8%

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

      5. times-frac 77.8%

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

      6. *-rgt-identity 77.8%

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

      7. associate-*l* 77.8%

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

      8. *-commutative 77.8%

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

   10. Simplified 77.8%

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

   if 1.5e-11 < b

   1. Initial program 14.6%

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

      1. clear-num 14.6%

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

      2. inv-pow 14.6%

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

      3. *-commutative 14.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 7.1%

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

      6. sqr-neg 7.1%

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

      7. sqrt-prod 7.1%

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

      8. add-sqr-sqrt 7.1%

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

      9. fma-neg 7.1%

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

      10. distribute-lft-neg-in 7.1%

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

      11. *-commutative 7.1%

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

      12. associate-*r* 7.1%

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

      13. metadata-eval 7.1%

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

   3. Applied egg-rr 7.1%

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

   4. Taylor expanded in b around -inf 25.6%

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

      1. +-commutative 25.6%

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

      2. mul-1-neg 25.6%

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

      3. unsub-neg 25.6%

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

   6. Simplified 25.6%

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

      1. sub-neg 25.6%

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

      2. neg-mul-1 25.6%

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

      3. metadata-eval 25.6%

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

      4. add-sqr-sqrt 10.8%

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

      5. sqrt-unprod 21.5%

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

      6. sqr-neg 21.5%

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

      7. sqrt-unprod 15.1%

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

      8. add-sqr-sqrt 26.2%

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

      9. times-frac 26.2%

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

      10. *-un-lft-identity 26.2%

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

      11. neg-mul-1 26.2%

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

      12. frac-2neg 26.2%

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

      13. frac-2neg 26.2%

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

      14. clear-num 26.2%

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

      15. frac-add 18.1%

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

      16. add-sqr-sqrt 0.0%

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

      17. sqrt-unprod 31.6%

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

      18. sqr-neg 31.6%

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

      19. sqrt-unprod 43.9%

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

      20. add-sqr-sqrt 44.1%

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

   8. Applied egg-rr 44.1%

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

   9. Taylor expanded in b around 0 91.0%

      \[\leadsto {\color{blue}{\left(-1 \cdot \frac{b}{c} + \frac{a}{b}\right)}}^{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-66}:\\ \;\;\;\;\frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a \cdot 2}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \]

Alternative 3: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c}{b} - \frac{b}{a}\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-66}:\\ \;\;\;\;\frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a \cdot 2}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (- (/ c b) (/ b a))))
   (if (<= b -8.8e-16)
     t_0
     (if (<= b -8.4e-66)
       (/ (+ b (sqrt (* a (* c -4.0)))) (* a 2.0))
       (if (<= b -4.5e-133)
         t_0
         (if (<= b 3e-12)
           (/ (- (sqrt (* c (* a -4.0))) b) (* a 2.0))
           (pow (- (/ a b) (/ b c)) -1.0)))))))

C

double code(double a, double b, double c) {
	double t_0 = (c / b) - (b / a);
	double tmp;
	if (b <= -8.8e-16) {
		tmp = t_0;
	} else if (b <= -8.4e-66) {
		tmp = (b + sqrt((a * (c * -4.0)))) / (a * 2.0);
	} else if (b <= -4.5e-133) {
		tmp = t_0;
	} else if (b <= 3e-12) {
		tmp = (sqrt((c * (a * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = pow(((a / b) - (b / c)), -1.0);
	}
	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 = (c / b) - (b / a)
    if (b <= (-8.8d-16)) then
        tmp = t_0
    else if (b <= (-8.4d-66)) then
        tmp = (b + sqrt((a * (c * (-4.0d0))))) / (a * 2.0d0)
    else if (b <= (-4.5d-133)) then
        tmp = t_0
    else if (b <= 3d-12) then
        tmp = (sqrt((c * (a * (-4.0d0)))) - b) / (a * 2.0d0)
    else
        tmp = ((a / b) - (b / c)) ** (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = (c / b) - (b / a);
	double tmp;
	if (b <= -8.8e-16) {
		tmp = t_0;
	} else if (b <= -8.4e-66) {
		tmp = (b + Math.sqrt((a * (c * -4.0)))) / (a * 2.0);
	} else if (b <= -4.5e-133) {
		tmp = t_0;
	} else if (b <= 3e-12) {
		tmp = (Math.sqrt((c * (a * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = Math.pow(((a / b) - (b / c)), -1.0);
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = (c / b) - (b / a)
	tmp = 0
	if b <= -8.8e-16:
		tmp = t_0
	elif b <= -8.4e-66:
		tmp = (b + math.sqrt((a * (c * -4.0)))) / (a * 2.0)
	elif b <= -4.5e-133:
		tmp = t_0
	elif b <= 3e-12:
		tmp = (math.sqrt((c * (a * -4.0))) - b) / (a * 2.0)
	else:
		tmp = math.pow(((a / b) - (b / c)), -1.0)
	return tmp

Julia

function code(a, b, c)
	t_0 = Float64(Float64(c / b) - Float64(b / a))
	tmp = 0.0
	if (b <= -8.8e-16)
		tmp = t_0;
	elseif (b <= -8.4e-66)
		tmp = Float64(Float64(b + sqrt(Float64(a * Float64(c * -4.0)))) / Float64(a * 2.0));
	elseif (b <= -4.5e-133)
		tmp = t_0;
	elseif (b <= 3e-12)
		tmp = Float64(Float64(sqrt(Float64(c * Float64(a * -4.0))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(a / b) - Float64(b / c)) ^ -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = (c / b) - (b / a);
	tmp = 0.0;
	if (b <= -8.8e-16)
		tmp = t_0;
	elseif (b <= -8.4e-66)
		tmp = (b + sqrt((a * (c * -4.0)))) / (a * 2.0);
	elseif (b <= -4.5e-133)
		tmp = t_0;
	elseif (b <= 3e-12)
		tmp = (sqrt((c * (a * -4.0))) - b) / (a * 2.0);
	else
		tmp = ((a / b) - (b / c)) ^ -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-16], t$95$0, If[LessEqual[b, -8.4e-66], N[(N[(b + N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-133], t$95$0, If[LessEqual[b, 3e-12], N[(N[(N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(a / b), $MachinePrecision] - N[(b / c), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.80000000000000001e-16 or -8.4000000000000001e-66 < b < -4.50000000000000009e-133

   1. Initial program 73.4%

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

   2. Taylor expanded in b around -inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

   if -8.80000000000000001e-16 < b < -8.4000000000000001e-66

   1. Initial program 99.7%

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

      1. add-cube-cbrt 99.1%

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

      2. pow3 99.1%

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

      3. fma-neg 99.1%

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

      4. distribute-lft-neg-in 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-*r* 99.1%

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

      7. metadata-eval 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in b around 0 99.1%

      \[\leadsto \frac{\left(-b\right) + \sqrt{{\left(\sqrt[3]{\color{blue}{-4 \cdot \left(a \cdot c\right)}}\right)}^{3}}}{2 \cdot a} \]
   5. Step-by-step derivation

      1. cbrt-prod 98.4%

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

      2. unpow-prod-down 98.4%

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

      3. pow3 98.4%

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

      4. add-cube-cbrt 99.1%

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

      5. *-commutative 99.1%

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

   6. Applied egg-rr 99.1%

      \[\leadsto \frac{\left(-b\right) + \sqrt{\color{blue}{{\left(\sqrt[3]{-4}\right)}^{3} \cdot \left(c \cdot a\right)}}}{2 \cdot a} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 75.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(-b\right) + \sqrt{{\left(\sqrt[3]{-4}\right)}^{3} \cdot \left(c \cdot a\right)}}{2 \cdot a}\right)\right)} \]

      2. expm1-udef 37.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(-b\right) + \sqrt{{\left(\sqrt[3]{-4}\right)}^{3} \cdot \left(c \cdot a\right)}}{2 \cdot a}\right)} - 1} \]

   8. Applied egg-rr 37.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(0.5 \cdot \frac{b + \sqrt{\left(a \cdot -4\right) \cdot c}}{a}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 75.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{b + \sqrt{\left(a \cdot -4\right) \cdot c}}{a}\right)\right)} \]

      2. expm1-log1p 99.7%

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

      3. *-commutative 99.7%

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

      4. metadata-eval 99.7%

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

      5. times-frac 99.7%

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

      6. *-rgt-identity 99.7%

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

      7. associate-*l* 99.7%

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

      8. *-commutative 99.7%

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

   10. Simplified 99.7%

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

   if -4.50000000000000009e-133 < b < 3.0000000000000001e-12

   1. Initial program 80.3%

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

   2. Taylor expanded in b around 0 77.4%

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

      1. associate-*r* 77.4%

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

   4. Simplified 77.4%

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

   if 3.0000000000000001e-12 < b

   1. Initial program 14.6%

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

      1. clear-num 14.6%

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

      2. inv-pow 14.6%

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

      3. *-commutative 14.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 7.1%

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

      6. sqr-neg 7.1%

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

      7. sqrt-prod 7.1%

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

      8. add-sqr-sqrt 7.1%

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

      9. fma-neg 7.1%

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

      10. distribute-lft-neg-in 7.1%

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

      11. *-commutative 7.1%

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

      12. associate-*r* 7.1%

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

      13. metadata-eval 7.1%

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

   3. Applied egg-rr 7.1%

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

   4. Taylor expanded in b around -inf 25.6%

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

      1. +-commutative 25.6%

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

      2. mul-1-neg 25.6%

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

      3. unsub-neg 25.6%

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

   6. Simplified 25.6%

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

      1. sub-neg 25.6%

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

      2. neg-mul-1 25.6%

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

      3. metadata-eval 25.6%

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

      4. add-sqr-sqrt 10.8%

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

      5. sqrt-unprod 21.5%

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

      6. sqr-neg 21.5%

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

      7. sqrt-unprod 15.1%

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

      8. add-sqr-sqrt 26.2%

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

      9. times-frac 26.2%

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

      10. *-un-lft-identity 26.2%

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

      11. neg-mul-1 26.2%

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

      12. frac-2neg 26.2%

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

      13. frac-2neg 26.2%

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

      14. clear-num 26.2%

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

      15. frac-add 18.1%

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

      16. add-sqr-sqrt 0.0%

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

      17. sqrt-unprod 31.6%

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

      18. sqr-neg 31.6%

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

      19. sqrt-unprod 43.9%

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

      20. add-sqr-sqrt 44.1%

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

   8. Applied egg-rr 44.1%

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

   9. Taylor expanded in b around 0 91.0%

      \[\leadsto {\color{blue}{\left(-1 \cdot \frac{b}{c} + \frac{a}{b}\right)}}^{-1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-66}:\\ \;\;\;\;\frac{b + \sqrt{a \cdot \left(c \cdot -4\right)}}{a \cdot 2}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\sqrt{c \cdot \left(a \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \]

Alternative 4: 67.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-268}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e-268) (- (/ c b) (/ b a)) (pow (- (/ a b) (/ b c)) -1.0)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e-268) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = pow(((a / b) - (b / c)), -1.0);
	}
	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-268)) then
        tmp = (c / b) - (b / a)
    else
        tmp = ((a / b) - (b / c)) ** (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e-268) {
		tmp = (c / b) - (b / a);
	} else {
		tmp = Math.pow(((a / b) - (b / c)), -1.0);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.8e-268:
		tmp = (c / b) - (b / a)
	else:
		tmp = math.pow(((a / b) - (b / c)), -1.0)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e-268)
		tmp = Float64(Float64(c / b) - Float64(b / a));
	else
		tmp = Float64(Float64(a / b) - Float64(b / c)) ^ -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.8e-268)
		tmp = (c / b) - (b / a);
	else
		tmp = ((a / b) - (b / c)) ^ -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e-268], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(a / b), $MachinePrecision] - N[(b / c), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8000000000000002e-268

   1. Initial program 76.7%

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

   2. Taylor expanded in b around -inf 71.2%

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

      1. +-commutative 71.2%

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

      2. mul-1-neg 71.2%

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

      3. unsub-neg 71.2%

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

   4. Simplified 71.2%

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

   if -3.8000000000000002e-268 < b

   1. Initial program 41.8%

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

      1. clear-num 41.8%

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

      2. inv-pow 41.8%

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

      3. *-commutative 41.8%

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

      4. add-sqr-sqrt 3.4%

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

      5. sqrt-unprod 37.4%

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

      6. sqr-neg 37.4%

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

      7. sqrt-prod 34.0%

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

      8. add-sqr-sqrt 37.4%

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

      9. fma-neg 37.4%

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

      10. distribute-lft-neg-in 37.4%

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

      11. *-commutative 37.4%

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

      12. associate-*r* 37.4%

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

      13. metadata-eval 37.4%

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

   3. Applied egg-rr 37.4%

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

   4. Taylor expanded in b around -inf 15.8%

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

      1. +-commutative 15.8%

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

      2. mul-1-neg 15.8%

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

      3. unsub-neg 15.8%

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

   6. Simplified 15.8%

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

      1. sub-neg 15.8%

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

      2. neg-mul-1 15.8%

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

      3. metadata-eval 15.8%

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

      4. add-sqr-sqrt 6.7%

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

      5. sqrt-unprod 13.6%

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

      6. sqr-neg 13.6%

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

      7. sqrt-unprod 9.7%

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

      8. add-sqr-sqrt 16.7%

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

      9. times-frac 16.7%

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

      10. *-un-lft-identity 16.7%

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

      11. neg-mul-1 16.7%

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

      12. frac-2neg 16.7%

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

      13. frac-2neg 16.7%

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

      14. clear-num 16.7%

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

      15. frac-add 12.1%

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

      16. add-sqr-sqrt 0.2%

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

      17. sqrt-unprod 24.6%

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

      18. sqr-neg 24.6%

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

      19. sqrt-unprod 31.4%

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

      20. add-sqr-sqrt 31.7%

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

   8. Applied egg-rr 31.7%

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

   9. Taylor expanded in b around 0 59.0%

      \[\leadsto {\color{blue}{\left(-1 \cdot \frac{b}{c} + \frac{a}{b}\right)}}^{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-268}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{b} - \frac{b}{c}\right)}^{-1}\\ \end{array} \]

Alternative 5: 67.5% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if b < -4.999999999999985e-310

   1. Initial program 77.4%

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

   2. Taylor expanded in b around -inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

   4. Simplified 69.3%

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

   if -4.999999999999985e-310 < b

   1. Initial program 39.8%

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

   2. Taylor expanded in b around inf 60.9%

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

      1. associate-*r/ 60.9%

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

      2. neg-mul-1 60.9%

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

   4. Simplified 60.9%

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

4. Final simplification 65.6%

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

Alternative 6: 43.1% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 4e-11) (/ (- b) a) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 4e-11) {
		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 <= 4d-11) 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 <= 4e-11) {
		tmp = -b / a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 4e-11:
		tmp = -b / a
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 4e-11)
		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 <= 4e-11)
		tmp = -b / a;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 4e-11], N[((-b) / a), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.99999999999999976e-11

   1. Initial program 76.8%

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

   2. Taylor expanded in b around -inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. mul-1-neg 52.8%

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

   4. Simplified 52.8%

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

   if 3.99999999999999976e-11 < b

   1. Initial program 14.6%

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

   2. Taylor expanded in b around inf 68.6%

      \[\leadsto \frac{\color{blue}{-2 \cdot \frac{a \cdot c}{b}}}{2 \cdot a} \]
   3. Step-by-step derivation

      1. frac-2neg 68.6%

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

      2. distribute-frac-neg 68.6%

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

      3. associate-*r/ 68.6%

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

      4. frac-2neg 68.6%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 26.2%

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

      7. sqr-neg 26.2%

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

      8. sqrt-unprod 25.8%

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

      9. add-sqr-sqrt 25.8%

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

      10. distribute-neg-frac 25.8%

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

      11. associate-*r/ 25.8%

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

      12. frac-2neg 25.8%

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

      13. times-frac 25.8%

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

      14. metadata-eval 25.8%

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

      15. mul-1-neg 25.8%

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

      16. associate-/l* 25.9%

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

      17. associate-/l/ 25.9%

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

   4. Applied egg-rr 25.9%

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

      1. remove-double-neg 25.9%

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

      2. associate-/r* 25.6%

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

      3. *-inverses 25.6%

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

      4. associate-/r/ 25.6%

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

      5. *-commutative 25.6%

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

      6. associate-*r/ 25.6%

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

      7. *-rgt-identity 25.6%

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

   6. Simplified 25.6%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]

Alternative 7: 67.4% accurate, 19.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if b < -4.999999999999985e-310

   1. Initial program 77.4%

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

   2. Taylor expanded in b around -inf 69.2%

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

      1. associate-*r/ 69.2%

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

      2. mul-1-neg 69.2%

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

   4. Simplified 69.2%

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

   if -4.999999999999985e-310 < b

   1. Initial program 39.8%

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

   2. Taylor expanded in b around inf 60.9%

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

      1. associate-*r/ 60.9%

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

      2. neg-mul-1 60.9%

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

   4. Simplified 60.9%

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

4. Final simplification 65.5%

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

Alternative 8: 2.6% accurate, 38.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.8%

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

   1. clear-num 60.7%

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

   2. inv-pow 60.7%

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

   3. *-commutative 60.7%

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

   4. add-sqr-sqrt 43.1%

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

   5. sqrt-unprod 58.6%

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

   6. sqr-neg 58.6%

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

   7. sqrt-prod 15.5%

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

   8. add-sqr-sqrt 37.8%

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

   9. fma-neg 37.8%

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

   10. distribute-lft-neg-in 37.8%

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

   11. *-commutative 37.8%

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

   12. associate-*r* 37.8%

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

   13. metadata-eval 37.8%

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

3. Applied egg-rr 37.8%

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

4. Taylor expanded in b around -inf 9.1%

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

   1. +-commutative 9.1%

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

   2. mul-1-neg 9.1%

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

   3. unsub-neg 9.1%

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

6. Simplified 9.1%

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

   1. expm1-log1p-u 8.8%

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

   2. expm1-udef 9.0%

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

   3. unpow-1 9.0%

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

   4. sub-neg 9.0%

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

   5. neg-mul-1 9.0%

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

   6. metadata-eval 9.0%

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

   7. add-sqr-sqrt 4.0%

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

   8. sqrt-unprod 7.7%

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

   9. sqr-neg 7.7%

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

   10. sqrt-unprod 5.0%

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

   11. add-sqr-sqrt 8.9%

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

   12. times-frac 8.9%

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

   13. *-un-lft-identity 8.9%

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

   14. neg-mul-1 8.9%

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

   15. frac-2neg 8.9%

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

8. Applied egg-rr 8.9%

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

   1. expm1-def 8.7%

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

   2. expm1-log1p 8.9%

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

10. Simplified 8.9%

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

11. Taylor expanded in b around 0 2.4%

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

12. Final simplification 2.4%

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

Alternative 9: 10.9% 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 60.8%

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

2. Taylor expanded in b around inf 21.3%

   \[\leadsto \frac{\color{blue}{-2 \cdot \frac{a \cdot c}{b}}}{2 \cdot a} \]
3. Step-by-step derivation

   1. frac-2neg 21.3%

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

   2. distribute-frac-neg 21.3%

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

   3. associate-*r/ 21.3%

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

   4. frac-2neg 21.3%

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

   5. add-sqr-sqrt 1.2%

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

   6. sqrt-unprod 8.1%

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

   7. sqr-neg 8.1%

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

   8. sqrt-unprod 6.9%

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

   9. add-sqr-sqrt 8.7%

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

   10. distribute-neg-frac 8.7%

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

   11. associate-*r/ 8.7%

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

   12. frac-2neg 8.7%

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

   13. times-frac 8.7%

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

   14. metadata-eval 8.7%

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

   15. mul-1-neg 8.7%

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

   16. associate-/l* 8.9%

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

   17. associate-/l/ 9.5%

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

4. Applied egg-rr 9.5%

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

   1. remove-double-neg 9.5%

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

   2. associate-/r* 8.8%

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

   3. *-inverses 8.8%

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

   4. associate-/r/ 8.8%

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

   5. *-commutative 8.8%

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

   6. associate-*r/ 8.8%

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

   7. *-rgt-identity 8.8%

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

6. Simplified 8.8%

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

7. Final simplification 8.8%

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

Developer target: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{b}{2}\right|\\ t_1 := \sqrt{\left|a\right|} \cdot \sqrt{\left|c\right|}\\ t_2 := \begin{array}{l} \mathbf{if}\;\mathsf{copysign}\left(a, c\right) = a:\\ \;\;\;\;\sqrt{t_0 - t_1} \cdot \sqrt{t_0 + t_1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{hypot}\left(\frac{b}{2}, t_1\right)\\ \end{array}\\ \mathbf{if}\;b < 0:\\ \;\;\;\;\frac{t_2 - \frac{b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-c}{\frac{b}{2} + t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (fabs (/ b 2.0)))
        (t_1 (* (sqrt (fabs a)) (sqrt (fabs c))))
        (t_2
         (if (== (copysign a c) a)
           (* (sqrt (- t_0 t_1)) (sqrt (+ t_0 t_1)))
           (hypot (/ b 2.0) t_1))))
   (if (< b 0.0) (/ (- t_2 (/ b 2.0)) a) (/ (- c) (+ (/ b 2.0) t_2)))))

C

double code(double a, double b, double c) {
	double t_0 = fabs((b / 2.0));
	double t_1 = sqrt(fabs(a)) * sqrt(fabs(c));
	double tmp;
	if (copysign(a, c) == a) {
		tmp = sqrt((t_0 - t_1)) * sqrt((t_0 + t_1));
	} else {
		tmp = hypot((b / 2.0), t_1);
	}
	double t_2 = tmp;
	double tmp_1;
	if (b < 0.0) {
		tmp_1 = (t_2 - (b / 2.0)) / a;
	} else {
		tmp_1 = -c / ((b / 2.0) + t_2);
	}
	return tmp_1;
}

Java

public static double code(double a, double b, double c) {
	double t_0 = Math.abs((b / 2.0));
	double t_1 = Math.sqrt(Math.abs(a)) * Math.sqrt(Math.abs(c));
	double tmp;
	if (Math.copySign(a, c) == a) {
		tmp = Math.sqrt((t_0 - t_1)) * Math.sqrt((t_0 + t_1));
	} else {
		tmp = Math.hypot((b / 2.0), t_1);
	}
	double t_2 = tmp;
	double tmp_1;
	if (b < 0.0) {
		tmp_1 = (t_2 - (b / 2.0)) / a;
	} else {
		tmp_1 = -c / ((b / 2.0) + t_2);
	}
	return tmp_1;
}

Python

def code(a, b, c):
	t_0 = math.fabs((b / 2.0))
	t_1 = math.sqrt(math.fabs(a)) * math.sqrt(math.fabs(c))
	tmp = 0
	if math.copysign(a, c) == a:
		tmp = math.sqrt((t_0 - t_1)) * math.sqrt((t_0 + t_1))
	else:
		tmp = math.hypot((b / 2.0), t_1)
	t_2 = tmp
	tmp_1 = 0
	if b < 0.0:
		tmp_1 = (t_2 - (b / 2.0)) / a
	else:
		tmp_1 = -c / ((b / 2.0) + t_2)
	return tmp_1

Julia

function code(a, b, c)
	t_0 = abs(Float64(b / 2.0))
	t_1 = Float64(sqrt(abs(a)) * sqrt(abs(c)))
	tmp = 0.0
	if (copysign(a, c) == a)
		tmp = Float64(sqrt(Float64(t_0 - t_1)) * sqrt(Float64(t_0 + t_1)));
	else
		tmp = hypot(Float64(b / 2.0), t_1);
	end
	t_2 = tmp
	tmp_1 = 0.0
	if (b < 0.0)
		tmp_1 = Float64(Float64(t_2 - Float64(b / 2.0)) / a);
	else
		tmp_1 = Float64(Float64(-c) / Float64(Float64(b / 2.0) + t_2));
	end
	return tmp_1
end

MATLAB

function tmp_3 = code(a, b, c)
	t_0 = abs((b / 2.0));
	t_1 = sqrt(abs(a)) * sqrt(abs(c));
	tmp = 0.0;
	if ((sign(c) * abs(a)) == a)
		tmp = sqrt((t_0 - t_1)) * sqrt((t_0 + t_1));
	else
		tmp = hypot((b / 2.0), t_1);
	end
	t_2 = tmp;
	tmp_2 = 0.0;
	if (b < 0.0)
		tmp_2 = (t_2 - (b / 2.0)) / a;
	else
		tmp_2 = -c / ((b / 2.0) + t_2);
	end
	tmp_3 = tmp_2;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[Abs[N[(b / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[N[Abs[a], $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[Abs[c], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = If[Equal[N[With[{TMP1 = Abs[a], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], a], N[(N[Sqrt[N[(t$95$0 - t$95$1), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(t$95$0 + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(b / 2.0), $MachinePrecision] ^ 2 + t$95$1 ^ 2], $MachinePrecision]]}, If[Less[b, 0.0], N[(N[(t$95$2 - N[(b / 2.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-c) / N[(N[(b / 2.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2023305 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64
  :herbie-expected 10

  :herbie-target
  (if (< b 0.0) (/ (- (if (== (copysign a c) a) (* (sqrt (- (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot (/ b 2.0) (* (sqrt (fabs a)) (sqrt (fabs c))))) (/ b 2.0)) a) (/ (- c) (+ (/ b 2.0) (if (== (copysign a c) a) (* (sqrt (- (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c))))) (sqrt (+ (fabs (/ b 2.0)) (* (sqrt (fabs a)) (sqrt (fabs c)))))) (hypot (/ b 2.0) (* (sqrt (fabs a)) (sqrt (fabs c))))))))

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