Quadratic roots, full range

Percentage Accurate: 51.5% → 84.4%

Time: 14.6s

Alternatives: 6

Speedup: 12.9×

Specification

Math

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

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(Float64(4.0 * 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[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 51.5% accurate, 1.0× speedup

Math

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

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(Float64(4.0 * 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[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{b}{-a}\\ \mathbf{elif}\;b \leq 0.053:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -7.2e+64)
   (/ b (- a))
   (if (<= b 0.053)
     (/ (- (sqrt (- (* b b) (* (* a 4.0) c))) b) (* a 2.0))
     (/ c (- b)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.2e+64) {
		tmp = b / -a;
	} else if (b <= 0.053) {
		tmp = (sqrt(((b * b) - ((a * 4.0) * c))) - b) / (a * 2.0);
	} else {
		tmp = c / -b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-7.2d+64)) then
        tmp = b / -a
    else if (b <= 0.053d0) then
        tmp = (sqrt(((b * b) - ((a * 4.0d0) * c))) - b) / (a * 2.0d0)
    else
        tmp = c / -b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.2e+64) {
		tmp = b / -a;
	} else if (b <= 0.053) {
		tmp = (Math.sqrt(((b * b) - ((a * 4.0) * c))) - b) / (a * 2.0);
	} else {
		tmp = c / -b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -7.2e+64:
		tmp = b / -a
	elif b <= 0.053:
		tmp = (math.sqrt(((b * b) - ((a * 4.0) * c))) - b) / (a * 2.0)
	else:
		tmp = c / -b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -7.2e+64)
		tmp = Float64(b / Float64(-a));
	elseif (b <= 0.053)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 4.0) * c))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(c / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -7.2e+64)
		tmp = b / -a;
	elseif (b <= 0.053)
		tmp = (sqrt(((b * b) - ((a * 4.0) * c))) - b) / (a * 2.0);
	else
		tmp = c / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -7.2e+64], N[(b / (-a)), $MachinePrecision], If[LessEqual[b, 0.053], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(c / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.20000000000000027e64

   1. Initial program 59.7%

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

      1. *-commutative 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in b around -inf 95.6%

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

      1. associate-*r/ 95.6%

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

      2. mul-1-neg 95.6%

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

   7. Simplified 95.6%

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

   if -7.20000000000000027e64 < b < 0.0529999999999999985

   1. Initial program 80.6%

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

   if 0.0529999999999999985 < b

   1. Initial program 11.3%

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

      1. *-commutative 11.3%

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

   3. Simplified 11.3%

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

   5. Taylor expanded in b around inf 93.4%

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

      1. associate-*r/ 93.4%

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

      2. mul-1-neg 93.4%

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

   7. Simplified 93.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{b}{-a}\\ \mathbf{elif}\;b \leq 0.053:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 4\right) \cdot c} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{-a}\\ \mathbf{elif}\;b \leq 0.08:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6.8e-12)
   (/ b (- a))
   (if (<= b 0.08) (/ (- (sqrt (* a (* c -4.0))) b) (* a 2.0)) (/ c (- b)))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.8e-12) {
		tmp = b / -a;
	} else if (b <= 0.08) {
		tmp = (sqrt((a * (c * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = c / -b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-6.8d-12)) then
        tmp = b / -a
    else if (b <= 0.08d0) then
        tmp = (sqrt((a * (c * (-4.0d0)))) - b) / (a * 2.0d0)
    else
        tmp = c / -b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6.8e-12) {
		tmp = b / -a;
	} else if (b <= 0.08) {
		tmp = (Math.sqrt((a * (c * -4.0))) - b) / (a * 2.0);
	} else {
		tmp = c / -b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6.8e-12:
		tmp = b / -a
	elif b <= 0.08:
		tmp = (math.sqrt((a * (c * -4.0))) - b) / (a * 2.0)
	else:
		tmp = c / -b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6.8e-12)
		tmp = Float64(b / Float64(-a));
	elseif (b <= 0.08)
		tmp = Float64(Float64(sqrt(Float64(a * Float64(c * -4.0))) - b) / Float64(a * 2.0));
	else
		tmp = Float64(c / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6.8e-12)
		tmp = b / -a;
	elseif (b <= 0.08)
		tmp = (sqrt((a * (c * -4.0))) - b) / (a * 2.0);
	else
		tmp = c / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6.8e-12], N[(b / (-a)), $MachinePrecision], If[LessEqual[b, 0.08], N[(N[(N[Sqrt[N[(a * N[(c * -4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(c / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8000000000000001e-12

   1. Initial program 68.6%

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

      1. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in b around -inf 93.2%

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

      1. associate-*r/ 93.2%

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

      2. mul-1-neg 93.2%

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

   7. Simplified 93.2%

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

   if -6.8000000000000001e-12 < b < 0.0800000000000000017

   1. Initial program 77.1%

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

      1. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in b around 0 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-*r* 69.1%

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

   7. Simplified 69.1%

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

      1. +-commutative 69.1%

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

      2. unsub-neg 69.1%

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

   9. Applied egg-rr 69.1%

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

   if 0.0800000000000000017 < b

   1. Initial program 11.3%

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

      1. *-commutative 11.3%

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

   3. Simplified 11.3%

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

   5. Taylor expanded in b around inf 93.4%

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

      1. associate-*r/ 93.4%

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

      2. mul-1-neg 93.4%

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

   7. Simplified 93.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{-a}\\ \mathbf{elif}\;b \leq 0.08:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(c \cdot -4\right)} - b}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.8% accurate, 12.9× 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(b / Float64(-a));
	else
		tmp = Float64(c / Float64(-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 74.9%

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

      1. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in b around -inf 69.0%

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

      1. associate-*r/ 69.0%

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

      2. mul-1-neg 69.0%

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

   7. Simplified 69.0%

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

   if -4.999999999999985e-310 < b

   1. Initial program 35.4%

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

      1. *-commutative 35.4%

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

   3. Simplified 35.4%

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

   5. Taylor expanded in b around inf 64.9%

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

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

   7. Simplified 64.9%

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

4. Final simplification 66.9%

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

Alternative 4: 42.3% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{b}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (if (<= b 5.8e+94) (/ b (- a)) (/ c b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 5.8e+94) {
		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 <= 5.8d+94) 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 <= 5.8e+94) {
		tmp = b / -a;
	} else {
		tmp = c / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 5.8e+94:
		tmp = b / -a
	else:
		tmp = c / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 5.8e+94)
		tmp = Float64(b / Float64(-a));
	else
		tmp = Float64(c / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 5.8e+94)
		tmp = b / -a;
	else
		tmp = c / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 5.8e+94], N[(b / (-a)), $MachinePrecision], N[(c / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.7999999999999997e94

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in b around -inf 44.4%

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

      1. associate-*r/ 44.4%

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

      2. mul-1-neg 44.4%

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

   7. Simplified 44.4%

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

   if 5.7999999999999997e94 < b

   1. Initial program 5.8%

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

      1. *-commutative 5.8%

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

   3. Simplified 5.8%

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

      1. *-un-lft-identity 5.8%

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

      2. times-frac 5.8%

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

   6. Applied egg-rr 1.5%

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

   7. Taylor expanded in b around -inf 0.0%

      \[\leadsto \frac{1}{a} \cdot \frac{\color{blue}{-0.5 \cdot \frac{a \cdot \left(c \cdot {\left(\sqrt{-4}\right)}^{2}\right)}{b}}}{2} \]
   8. Step-by-step derivation

      1. associate-/l* 0.0%

         \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \color{blue}{\left(a \cdot \frac{c \cdot {\left(\sqrt{-4}\right)}^{2}}{b}\right)}}{2} \]

      2. associate-/l* 0.0%

         \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{{\left(\sqrt{-4}\right)}^{2}}{b}\right)}\right)}{2} \]

      3. unpow2 0.0%

         \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{\color{blue}{\sqrt{-4} \cdot \sqrt{-4}}}{b}\right)\right)}{2} \]

      4. rem-square-sqrt 31.2%

         \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{\color{blue}{-4}}{b}\right)\right)}{2} \]

   9. Simplified 31.2%

      \[\leadsto \frac{1}{a} \cdot \frac{\color{blue}{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{-4}{b}\right)\right)}}{2} \]

   10. Taylor expanded in a around 0 31.1%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{b}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 11.3% accurate, 38.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 54.8%

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

   1. *-commutative 54.8%

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

3. Simplified 54.8%

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

   1. *-un-lft-identity 54.8%

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

   2. times-frac 54.7%

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

6. Applied egg-rr 29.2%

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

7. Taylor expanded in b around -inf 0.0%

   \[\leadsto \frac{1}{a} \cdot \frac{\color{blue}{-0.5 \cdot \frac{a \cdot \left(c \cdot {\left(\sqrt{-4}\right)}^{2}\right)}{b}}}{2} \]
8. Step-by-step derivation

   1. associate-/l* 0.0%

      \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \color{blue}{\left(a \cdot \frac{c \cdot {\left(\sqrt{-4}\right)}^{2}}{b}\right)}}{2} \]

   2. associate-/l* 0.0%

      \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{{\left(\sqrt{-4}\right)}^{2}}{b}\right)}\right)}{2} \]

   3. unpow2 0.0%

      \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{\color{blue}{\sqrt{-4} \cdot \sqrt{-4}}}{b}\right)\right)}{2} \]

   4. rem-square-sqrt 9.0%

      \[\leadsto \frac{1}{a} \cdot \frac{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{\color{blue}{-4}}{b}\right)\right)}{2} \]

9. Simplified 9.0%

   \[\leadsto \frac{1}{a} \cdot \frac{\color{blue}{-0.5 \cdot \left(a \cdot \left(c \cdot \frac{-4}{b}\right)\right)}}{2} \]

10. Taylor expanded in a around 0 9.0%

    \[\leadsto \color{blue}{\frac{c}{b}} \]
11. Add Preprocessing

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 54.8%

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

   1. *-commutative 54.8%

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

3. Simplified 54.8%

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

   1. *-un-lft-identity 54.8%

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

   2. times-frac 54.7%

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

6. Applied egg-rr 29.2%

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

7. Taylor expanded in a around 0 2.6%

   \[\leadsto \color{blue}{\frac{b}{a}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024101 
(FPCore (a b c)
  :name "Quadratic roots, full range"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))