Cubic critical

Percentage Accurate: 53.1% → 85.3%

Time: 16.2s

Alternatives: 13

Speedup: 11.6×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * 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) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 53.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * 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) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{b \cdot -2}{a}}{3}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b + a \cdot \left(-3 \cdot c\right)} - b}{3}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -6e+153)
   (/ (/ (* b -2.0) a) 3.0)
   (if (<= b 4.2e-57)
     (/ (/ (- (sqrt (+ (* b b) (* a (* -3.0 c)))) b) 3.0) a)
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e+153) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else if (b <= 4.2e-57) {
		tmp = ((sqrt(((b * b) + (a * (-3.0 * c)))) - b) / 3.0) / a;
	} else {
		tmp = (c * -0.5) / 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 <= (-6d+153)) then
        tmp = ((b * (-2.0d0)) / a) / 3.0d0
    else if (b <= 4.2d-57) then
        tmp = ((sqrt(((b * b) + (a * ((-3.0d0) * c)))) - b) / 3.0d0) / a
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -6e+153) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else if (b <= 4.2e-57) {
		tmp = ((Math.sqrt(((b * b) + (a * (-3.0 * c)))) - b) / 3.0) / a;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -6e+153:
		tmp = ((b * -2.0) / a) / 3.0
	elif b <= 4.2e-57:
		tmp = ((math.sqrt(((b * b) + (a * (-3.0 * c)))) - b) / 3.0) / a
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -6e+153)
		tmp = Float64(Float64(Float64(b * -2.0) / a) / 3.0);
	elseif (b <= 4.2e-57)
		tmp = Float64(Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(a * Float64(-3.0 * c)))) - b) / 3.0) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -6e+153)
		tmp = ((b * -2.0) / a) / 3.0;
	elseif (b <= 4.2e-57)
		tmp = ((sqrt(((b * b) + (a * (-3.0 * c)))) - b) / 3.0) / a;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -6e+153], N[(N[(N[(b * -2.0), $MachinePrecision] / a), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[b, 4.2e-57], N[(N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(a * N[(-3.0 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / 3.0), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.00000000000000037e153

   1. Initial program 46.5%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.00000000000000037e153 < b < 4.1999999999999999e-57

   1. Initial program 86.1%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   8. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.1999999999999999e-57 < b

   1. Initial program 8.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{b \cdot -2}{a}}{3}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{\sqrt{b \cdot b + -3 \cdot \left(a \cdot c\right)} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e+157)
   (/ (/ (* b -2.0) a) 3.0)
   (if (<= b 3.3e-55)
     (/ (- (sqrt (+ (* b b) (* -3.0 (* a c)))) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e+157) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else if (b <= 3.3e-55) {
		tmp = (sqrt(((b * b) + (-3.0 * (a * c)))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / 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+157)) then
        tmp = ((b * (-2.0d0)) / a) / 3.0d0
    else if (b <= 3.3d-55) then
        tmp = (sqrt(((b * b) + ((-3.0d0) * (a * c)))) - b) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e+157) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else if (b <= 3.3e-55) {
		tmp = (Math.sqrt(((b * b) + (-3.0 * (a * c)))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e+157:
		tmp = ((b * -2.0) / a) / 3.0
	elif b <= 3.3e-55:
		tmp = (math.sqrt(((b * b) + (-3.0 * (a * c)))) - b) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e+157)
		tmp = Float64(Float64(Float64(b * -2.0) / a) / 3.0);
	elseif (b <= 3.3e-55)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(-3.0 * Float64(a * c)))) - b) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e+157)
		tmp = ((b * -2.0) / a) / 3.0;
	elseif (b <= 3.3e-55)
		tmp = (sqrt(((b * b) + (-3.0 * (a * c)))) - b) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e+157], N[(N[(N[(b * -2.0), $MachinePrecision] / a), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[b, 3.3e-55], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(-3.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.99999999999999976e157

   1. Initial program 46.5%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.99999999999999976e157 < b < 3.2999999999999999e-55

   1. Initial program 86.1%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   8. Applied egg-rr 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if 3.2999999999999999e-55 < b

   1. Initial program 8.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{b \cdot -2}{a}}{3}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{a}{\sqrt{b \cdot b + a \cdot \left(-3 \cdot c\right)} - b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e+151)
   (/ (/ (* b -2.0) a) 3.0)
   (if (<= b 1.7e-54)
     (/ 0.3333333333333333 (/ a (- (sqrt (+ (* b b) (* a (* -3.0 c)))) b)))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e+151) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else if (b <= 1.7e-54) {
		tmp = 0.3333333333333333 / (a / (sqrt(((b * b) + (a * (-3.0 * c)))) - b));
	} else {
		tmp = (c * -0.5) / 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+151)) then
        tmp = ((b * (-2.0d0)) / a) / 3.0d0
    else if (b <= 1.7d-54) then
        tmp = 0.3333333333333333d0 / (a / (sqrt(((b * b) + (a * ((-3.0d0) * c)))) - b))
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e+151) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else if (b <= 1.7e-54) {
		tmp = 0.3333333333333333 / (a / (Math.sqrt(((b * b) + (a * (-3.0 * c)))) - b));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e+151:
		tmp = ((b * -2.0) / a) / 3.0
	elif b <= 1.7e-54:
		tmp = 0.3333333333333333 / (a / (math.sqrt(((b * b) + (a * (-3.0 * c)))) - b))
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e+151)
		tmp = Float64(Float64(Float64(b * -2.0) / a) / 3.0);
	elseif (b <= 1.7e-54)
		tmp = Float64(0.3333333333333333 / Float64(a / Float64(sqrt(Float64(Float64(b * b) + Float64(a * Float64(-3.0 * c)))) - b)));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e+151)
		tmp = ((b * -2.0) / a) / 3.0;
	elseif (b <= 1.7e-54)
		tmp = 0.3333333333333333 / (a / (sqrt(((b * b) + (a * (-3.0 * c)))) - b));
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e+151], N[(N[(N[(b * -2.0), $MachinePrecision] / a), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[b, 1.7e-54], N[(0.3333333333333333 / N[(a / N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(a * N[(-3.0 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.0000000000000002e151

   1. Initial program 46.5%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -5.0000000000000002e151 < b < 1.69999999999999994e-54

   1. Initial program 86.1%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   8. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.69999999999999994e-54 < b

   1. Initial program 8.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-127}:\\ \;\;\;\;-\left(\frac{b}{\frac{a}{0.6666666666666666}} + \frac{\frac{c}{b}}{-2}\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-57}:\\ \;\;\;\;\frac{\sqrt{\left(a \cdot c\right) \cdot -3} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -7.5e-127)
   (- (+ (/ b (/ a 0.6666666666666666)) (/ (/ c b) -2.0)))
   (if (<= b 1.15e-57)
     (/ (- (sqrt (* (* a c) -3.0)) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-127) {
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0));
	} else if (b <= 1.15e-57) {
		tmp = (sqrt(((a * c) * -3.0)) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / 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 <= (-7.5d-127)) then
        tmp = -((b / (a / 0.6666666666666666d0)) + ((c / b) / (-2.0d0)))
    else if (b <= 1.15d-57) then
        tmp = (sqrt(((a * c) * (-3.0d0))) - b) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-127) {
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0));
	} else if (b <= 1.15e-57) {
		tmp = (Math.sqrt(((a * c) * -3.0)) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -7.5e-127:
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0))
	elif b <= 1.15e-57:
		tmp = (math.sqrt(((a * c) * -3.0)) - b) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -7.5e-127)
		tmp = Float64(-Float64(Float64(b / Float64(a / 0.6666666666666666)) + Float64(Float64(c / b) / -2.0)));
	elseif (b <= 1.15e-57)
		tmp = Float64(Float64(sqrt(Float64(Float64(a * c) * -3.0)) - b) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -7.5e-127)
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0));
	elseif (b <= 1.15e-57)
		tmp = (sqrt(((a * c) * -3.0)) - b) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -7.5e-127], (-N[(N[(b / N[(a / 0.6666666666666666), $MachinePrecision]), $MachinePrecision] + N[(N[(c / b), $MachinePrecision] / -2.0), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, 1.15e-57], N[(N[(N[Sqrt[N[(N[(a * c), $MachinePrecision] * -3.0), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5000000000000004e-127

   1. Initial program 80.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -7.5000000000000004e-127 < b < 1.15e-57

   1. Initial program 75.5%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   8. Applied egg-rr 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   11. Taylor expanded in b around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 1.15e-57 < b

   1. Initial program 8.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 67.4% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-310}:\\ \;\;\;\;-\left(\frac{b}{\frac{a}{0.6666666666666666}} + \frac{\frac{c}{b}}{-2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-310)
   (- (+ (/ b (/ a 0.6666666666666666)) (/ (/ c b) -2.0)))
   (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0));
	} else {
		tmp = (c * -0.5) / 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 <= (-2d-310)) then
        tmp = -((b / (a / 0.6666666666666666d0)) + ((c / b) / (-2.0d0)))
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0));
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-310:
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0))
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-310)
		tmp = Float64(-Float64(Float64(b / Float64(a / 0.6666666666666666)) + Float64(Float64(c / b) / -2.0)));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2e-310)
		tmp = -((b / (a / 0.6666666666666666)) + ((c / b) / -2.0));
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-310], (-N[(N[(b / N[(a / 0.6666666666666666), $MachinePrecision]), $MachinePrecision] + N[(N[(c / b), $MachinePrecision] / -2.0), $MachinePrecision]), $MachinePrecision]), N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.999999999999994e-310

   1. Initial program 79.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.999999999999994e-310 < b

   1. Initial program 29.1%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 67.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{b \cdot -0.6666666666666666}{a} + \frac{c \cdot 0.5}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-310)
   (+ (/ (* b -0.6666666666666666) a) (/ (* c 0.5) b))
   (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = ((b * -0.6666666666666666) / a) + ((c * 0.5) / b);
	} else {
		tmp = (c * -0.5) / 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 <= (-2d-310)) then
        tmp = ((b * (-0.6666666666666666d0)) / a) + ((c * 0.5d0) / b)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = ((b * -0.6666666666666666) / a) + ((c * 0.5) / b);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-310:
		tmp = ((b * -0.6666666666666666) / a) + ((c * 0.5) / b)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-310)
		tmp = Float64(Float64(Float64(b * -0.6666666666666666) / a) + Float64(Float64(c * 0.5) / b));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2e-310)
		tmp = ((b * -0.6666666666666666) / a) + ((c * 0.5) / b);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-310], N[(N[(N[(b * -0.6666666666666666), $MachinePrecision] / a), $MachinePrecision] + N[(N[(c * 0.5), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.999999999999994e-310

   1. Initial program 79.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.999999999999994e-310 < b

   1. Initial program 29.1%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 67.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{b}{a} \cdot -0.6666666666666666 + \frac{c \cdot 0.5}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -2e-310)
   (+ (* (/ b a) -0.6666666666666666) (/ (* c 0.5) b))
   (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = ((b / a) * -0.6666666666666666) + ((c * 0.5) / b);
	} else {
		tmp = (c * -0.5) / 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 <= (-2d-310)) then
        tmp = ((b / a) * (-0.6666666666666666d0)) + ((c * 0.5d0) / b)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -2e-310) {
		tmp = ((b / a) * -0.6666666666666666) + ((c * 0.5) / b);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -2e-310:
		tmp = ((b / a) * -0.6666666666666666) + ((c * 0.5) / b)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -2e-310)
		tmp = Float64(Float64(Float64(b / a) * -0.6666666666666666) + Float64(Float64(c * 0.5) / b));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -2e-310)
		tmp = ((b / a) * -0.6666666666666666) + ((c * 0.5) / b);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -2e-310], N[(N[(N[(b / a), $MachinePrecision] * -0.6666666666666666), $MachinePrecision] + N[(N[(c * 0.5), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.999999999999994e-310

   1. Initial program 79.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.999999999999994e-310 < b

   1. Initial program 29.1%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 67.3% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{b \cdot -2}{a}}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1.85e-290) (/ (/ (* b -2.0) a) 3.0) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.85d-290) then
        tmp = ((b * (-2.0d0)) / a) / 3.0d0
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = ((b * -2.0) / a) / 3.0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.85e-290:
		tmp = ((b * -2.0) / a) / 3.0
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.85e-290)
		tmp = Float64(Float64(Float64(b * -2.0) / a) / 3.0);
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.85e-290)
		tmp = ((b * -2.0) / a) / 3.0;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.85e-290], N[(N[(N[(b * -2.0), $MachinePrecision] / a), $MachinePrecision] / 3.0), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.84999999999999989e-290

   1. Initial program 79.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1.84999999999999989e-290 < b

   1. Initial program 27.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 67.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;\frac{b}{\frac{a}{-0.6666666666666666}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1.85e-290) (/ b (/ a -0.6666666666666666)) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.85d-290) then
        tmp = b / (a / (-0.6666666666666666d0))
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.85e-290:
		tmp = b / (a / -0.6666666666666666)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.85e-290)
		tmp = Float64(b / Float64(a / -0.6666666666666666));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.85e-290)
		tmp = b / (a / -0.6666666666666666);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.85e-290], N[(b / N[(a / -0.6666666666666666), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.84999999999999989e-290

   1. Initial program 79.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.84999999999999989e-290 < b

   1. Initial program 27.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.1% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;\frac{b}{\frac{a}{-0.6666666666666666}}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{-0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1.85e-290) (/ b (/ a -0.6666666666666666)) (* c (/ -0.5 b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = c * (-0.5 / b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.85d-290) then
        tmp = b / (a / (-0.6666666666666666d0))
    else
        tmp = c * ((-0.5d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = b / (a / -0.6666666666666666);
	} else {
		tmp = c * (-0.5 / b);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.85e-290:
		tmp = b / (a / -0.6666666666666666)
	else:
		tmp = c * (-0.5 / b)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.85e-290)
		tmp = Float64(b / Float64(a / -0.6666666666666666));
	else
		tmp = Float64(c * Float64(-0.5 / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.85e-290)
		tmp = b / (a / -0.6666666666666666);
	else
		tmp = c * (-0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.85e-290], N[(b / N[(a / -0.6666666666666666), $MachinePrecision]), $MachinePrecision], N[(c * N[(-0.5 / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.84999999999999989e-290

   1. Initial program 79.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.84999999999999989e-290 < b

   1. Initial program 27.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 67.1% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;\frac{b}{a} \cdot -0.6666666666666666\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{-0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1.85e-290) (* (/ b a) -0.6666666666666666) (* c (/ -0.5 b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = (b / a) * -0.6666666666666666;
	} else {
		tmp = c * (-0.5 / b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.85d-290) then
        tmp = (b / a) * (-0.6666666666666666d0)
    else
        tmp = c * ((-0.5d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = (b / a) * -0.6666666666666666;
	} else {
		tmp = c * (-0.5 / b);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.85e-290:
		tmp = (b / a) * -0.6666666666666666
	else:
		tmp = c * (-0.5 / b)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.85e-290)
		tmp = Float64(Float64(b / a) * -0.6666666666666666);
	else
		tmp = Float64(c * Float64(-0.5 / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.85e-290)
		tmp = (b / a) * -0.6666666666666666;
	else
		tmp = c * (-0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.85e-290], N[(N[(b / a), $MachinePrecision] * -0.6666666666666666), $MachinePrecision], N[(c * N[(-0.5 / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.84999999999999989e-290

   1. Initial program 79.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.84999999999999989e-290 < b

   1. Initial program 27.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 67.1% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \frac{-0.6666666666666666}{a}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{-0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 1.85e-290) (* b (/ -0.6666666666666666 a)) (* c (/ -0.5 b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = b * (-0.6666666666666666 / a);
	} else {
		tmp = c * (-0.5 / b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.85d-290) then
        tmp = b * ((-0.6666666666666666d0) / a)
    else
        tmp = c * ((-0.5d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 1.85e-290) {
		tmp = b * (-0.6666666666666666 / a);
	} else {
		tmp = c * (-0.5 / b);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 1.85e-290:
		tmp = b * (-0.6666666666666666 / a)
	else:
		tmp = c * (-0.5 / b)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 1.85e-290)
		tmp = Float64(b * Float64(-0.6666666666666666 / a));
	else
		tmp = Float64(c * Float64(-0.5 / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 1.85e-290)
		tmp = b * (-0.6666666666666666 / a);
	else
		tmp = c * (-0.5 / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 1.85e-290], N[(b * N[(-0.6666666666666666 / a), $MachinePrecision]), $MachinePrecision], N[(c * N[(-0.5 / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.84999999999999989e-290

   1. Initial program 79.7%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.84999999999999989e-290 < b

   1. Initial program 27.0%

      \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 35.7% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ b \cdot \frac{-0.6666666666666666}{a} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* b (/ -0.6666666666666666 a)))

C

double code(double a, double b, double c) {
	return b * (-0.6666666666666666 / 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 * ((-0.6666666666666666d0) / a)
end function

Java

public static double code(double a, double b, double c) {
	return b * (-0.6666666666666666 / a);
}

Python

def code(a, b, c):
	return b * (-0.6666666666666666 / a)

Julia

function code(a, b, c)
	return Float64(b * Float64(-0.6666666666666666 / a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = b * (-0.6666666666666666 / a);
end

Wolfram

code[a_, b_, c_] := N[(b * N[(-0.6666666666666666 / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.1%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]
2. Add Preprocessing

3. Taylor expanded in b around -inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (a b c)
  :name "Cubic critical"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))