quadm (p42, negative)

Percentage Accurate: 51.8% → 85.4%

Time: 15.0s

Alternatives: 7

Speedup: 19.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 51.8% 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: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-96}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.7e-96)
   (/ (- c) b)
   (if (<= b 5.4e+73)
     (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))) (* a 2.0))
     (- (/ c b) (/ b a)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.7e-96) {
		tmp = -c / b;
	} else if (b <= 5.4e+73) {
		tmp = (-b - sqrt(((b * b) - (4.0 * (c * a))))) / (a * 2.0);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.7d-96)) then
        tmp = -c / b
    else if (b <= 5.4d+73) then
        tmp = (-b - sqrt(((b * b) - (4.0d0 * (c * a))))) / (a * 2.0d0)
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.7e-96) {
		tmp = -c / b;
	} else if (b <= 5.4e+73) {
		tmp = (-b - Math.sqrt(((b * b) - (4.0 * (c * a))))) / (a * 2.0);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.7e-96:
		tmp = -c / b
	elif b <= 5.4e+73:
		tmp = (-b - math.sqrt(((b * b) - (4.0 * (c * a))))) / (a * 2.0)
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.7e-96)
		tmp = Float64(Float64(-c) / b);
	elseif (b <= 5.4e+73)
		tmp = Float64(Float64(Float64(-b) - sqrt(Float64(Float64(b * b) - Float64(4.0 * Float64(c * a))))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.7e-96)
		tmp = -c / b;
	elseif (b <= 5.4e+73)
		tmp = (-b - sqrt(((b * b) - (4.0 * (c * a))))) / (a * 2.0);
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.7e-96], N[((-c) / b), $MachinePrecision], If[LessEqual[b, 5.4e+73], N[(N[((-b) - N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(4.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7e-96

   1. Initial program 14.1%

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

   3. Simplified 14.1%

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

   4. Taylor expanded in b around -inf 85.9%

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

      1. associate-*r/ 85.9%

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

      2. neg-mul-1 85.9%

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

   6. Simplified 85.9%

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

   if -1.7e-96 < b < 5.3999999999999998e73

   1. Initial program 82.3%

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

   if 5.3999999999999998e73 < b

   1. Initial program 64.6%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in b around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-96}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \]

Alternative 2: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-52}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{c \cdot \left(a \cdot -4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2.4e-97)
   (/ (- c) b)
   (if (<= b 6.8e-52)
     (* -0.5 (/ (+ b (sqrt (* c (* a -4.0)))) a))
     (- (/ c b) (/ b a)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.4e-97) {
		tmp = -c / b;
	} else if (b <= 6.8e-52) {
		tmp = -0.5 * ((b + sqrt((c * (a * -4.0)))) / a);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.4d-97)) then
        tmp = -c / b
    else if (b <= 6.8d-52) then
        tmp = (-0.5d0) * ((b + sqrt((c * (a * (-4.0d0))))) / a)
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2.4e-97) {
		tmp = -c / b;
	} else if (b <= 6.8e-52) {
		tmp = -0.5 * ((b + Math.sqrt((c * (a * -4.0)))) / a);
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2.4e-97:
		tmp = -c / b
	elif b <= 6.8e-52:
		tmp = -0.5 * ((b + math.sqrt((c * (a * -4.0)))) / a)
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2.4e-97)
		tmp = Float64(Float64(-c) / b);
	elseif (b <= 6.8e-52)
		tmp = Float64(-0.5 * Float64(Float64(b + sqrt(Float64(c * Float64(a * -4.0)))) / a));
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2.4e-97)
		tmp = -c / b;
	elseif (b <= 6.8e-52)
		tmp = -0.5 * ((b + sqrt((c * (a * -4.0)))) / a);
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2.4e-97], N[((-c) / b), $MachinePrecision], If[LessEqual[b, 6.8e-52], N[(-0.5 * N[(N[(b + N[Sqrt[N[(c * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4e-97

   1. Initial program 14.1%

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

   3. Simplified 14.1%

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

   4. Taylor expanded in b around -inf 85.9%

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

      1. associate-*r/ 85.9%

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

      2. neg-mul-1 85.9%

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

   6. Simplified 85.9%

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

   if -2.4e-97 < b < 6.80000000000000035e-52

   1. Initial program 77.9%

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

   3. Simplified 77.9%

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

      1. pow1/2 77.9%

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

      2. pow-to-exp 72.7%

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

   5. Applied egg-rr 72.7%

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

   6. Taylor expanded in a around inf 36.3%

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

      1. +-commutative 36.3%

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

      2. mul-1-neg 36.3%

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

      3. log-rec 36.3%

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

      4. remove-double-neg 36.3%

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

      5. log-prod 70.1%

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

      6. associate-*r* 70.1%

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

      7. *-commutative 70.1%

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

      8. *-commutative 70.1%

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

      9. associate-*r* 70.1%

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

   8. Simplified 70.1%

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

      1. expm1-log1p-u 48.5%

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

      2. expm1-udef 21.0%

         \[\leadsto -0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{b + e^{\log \left(a \cdot \left(c \cdot -4\right)\right) \cdot 0.5}}{a}\right)} - 1\right)} \]

      3. exp-to-pow 21.2%

         \[\leadsto -0.5 \cdot \left(e^{\mathsf{log1p}\left(\frac{b + \color{blue}{{\left(a \cdot \left(c \cdot -4\right)\right)}^{0.5}}}{a}\right)} - 1\right) \]

      4. pow1/2 21.2%

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

   10. Applied egg-rr 21.2%

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

       1. expm1-def 51.0%

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

       2. expm1-log1p 75.0%

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

       3. *-lft-identity 75.0%

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

       4. *-lft-identity 75.0%

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

       5. associate-*r* 75.0%

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

       6. *-commutative 75.0%

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

       7. rem-square-sqrt 0.0%

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

       8. unpow2 0.0%

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

       9. associate-*r* 0.0%

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

       10. unpow2 0.0%

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

       11. rem-square-sqrt 75.0%

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

   12. Simplified 75.0%

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

   if 6.80000000000000035e-52 < b

   1. Initial program 71.8%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in b around inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. unsub-neg 90.6%

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

   6. Simplified 90.6%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-52}:\\ \;\;\;\;-0.5 \cdot \frac{b + \sqrt{c \cdot \left(a \cdot -4\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \]

Alternative 3: 67.1% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-311) (/ (- c) b) (- (/ c b) (/ b a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-311) {
		tmp = -c / b;
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5d-311)) then
        tmp = -c / b
    else
        tmp = (c / b) - (b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-311) {
		tmp = -c / b;
	} else {
		tmp = (c / b) - (b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-311:
		tmp = -c / b
	else:
		tmp = (c / b) - (b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-311)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(Float64(c / b) - Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-311)
		tmp = -c / b;
	else
		tmp = (c / b) - (b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-311], N[((-c) / b), $MachinePrecision], N[(N[(c / b), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.00000000000023e-311

   1. Initial program 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in b around -inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. neg-mul-1 70.9%

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

   6. Simplified 70.9%

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

   if -5.00000000000023e-311 < b

   1. Initial program 73.8%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in b around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array} \]

Alternative 4: 42.5% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{c}{b}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b -7.5e-10) (/ c b) (- (/ b a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-10) {
		tmp = c / b;
	} else {
		tmp = -(b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-7.5d-10)) then
        tmp = c / b
    else
        tmp = -(b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-10) {
		tmp = c / b;
	} else {
		tmp = -(b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -7.5e-10:
		tmp = c / b
	else:
		tmp = -(b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -7.5e-10)
		tmp = Float64(c / b);
	else
		tmp = Float64(-Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -7.5e-10)
		tmp = c / b;
	else
		tmp = -(b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -7.5e-10], N[(c / b), $MachinePrecision], (-N[(b / a), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if b < -7.49999999999999995e-10

   1. Initial program 8.5%

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

      1. clear-num 8.5%

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

      2. associate-/r/ 8.5%

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

      3. associate-/r* 8.5%

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

      4. metadata-eval 8.5%

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

      5. add-sqr-sqrt 6.1%

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

      6. sqrt-unprod 7.5%

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

      7. sqr-neg 7.5%

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

      8. sqrt-prod 0.0%

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

      9. add-sqr-sqrt 5.4%

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

      10. fma-neg 5.4%

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

      11. *-commutative 5.4%

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

      12. distribute-rgt-neg-in 5.4%

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

      13. metadata-eval 5.4%

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

      14. associate-*r* 5.4%

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

   3. Applied egg-rr 5.4%

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

   4. Taylor expanded in a around 0 27.0%

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

   if -7.49999999999999995e-10 < b

   1. Initial program 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in b around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. mul-1-neg 55.2%

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

   6. Simplified 55.2%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{c}{b}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array} \]

Alternative 5: 66.9% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-307}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -1.45e-307) (/ (- c) b) (- (/ b a))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.45e-307) {
		tmp = -c / b;
	} else {
		tmp = -(b / a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.45d-307)) then
        tmp = -c / b
    else
        tmp = -(b / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -1.45e-307) {
		tmp = -c / b;
	} else {
		tmp = -(b / a);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -1.45e-307:
		tmp = -c / b
	else:
		tmp = -(b / a)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -1.45e-307)
		tmp = Float64(Float64(-c) / b);
	else
		tmp = Float64(-Float64(b / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -1.45e-307)
		tmp = -c / b;
	else
		tmp = -(b / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -1.45e-307], N[((-c) / b), $MachinePrecision], (-N[(b / a), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if b < -1.45e-307

   1. Initial program 26.4%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in b around -inf 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

   6. Simplified 71.4%

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

   if -1.45e-307 < b

   1. Initial program 74.0%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in b around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. mul-1-neg 74.3%

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

   6. Simplified 74.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-307}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{else}:\\ \;\;\;\;-\frac{b}{a}\\ \end{array} \]

Alternative 6: 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 49.5%

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

3. Simplified 49.5%

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

   1. clear-num 49.5%

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

   2. un-div-inv 49.5%

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

5. Applied egg-rr 49.5%

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

6. Taylor expanded in b around -inf 37.7%

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

7. Taylor expanded in b around 0 2.5%

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

8. Final simplification 2.5%

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

Alternative 7: 11.2% 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 49.5%

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

   1. clear-num 49.4%

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

   2. associate-/r/ 49.4%

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

   3. associate-/r* 49.4%

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

   4. metadata-eval 49.4%

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

   5. add-sqr-sqrt 13.2%

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

   6. sqrt-unprod 24.7%

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

   7. sqr-neg 24.7%

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

   8. sqrt-prod 19.6%

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

   9. add-sqr-sqrt 30.5%

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

   10. fma-neg 30.5%

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

   11. *-commutative 30.5%

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

   12. distribute-rgt-neg-in 30.5%

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

   13. metadata-eval 30.5%

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

   14. associate-*r* 30.5%

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

3. Applied egg-rr 30.5%

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

4. Taylor expanded in a around 0 11.2%

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

5. Final simplification 11.2%

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

Developer target: 70.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023194 
(FPCore (a b c)
  :name "quadm (p42, negative)"
  :precision binary64

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

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