Cubic critical, medium range

Percentage Accurate: 31.3% → 99.2%

Time: 27.2s

Alternatives: 8

Speedup: 23.2×

Specification

\[\left(\left(1.1102230246251565 \cdot 10^{-16} < a \land a < 9007199254740992\right) \land \left(1.1102230246251565 \cdot 10^{-16} < b \land b < 9007199254740992\right)\right) \land \left(1.1102230246251565 \cdot 10^{-16} < c \land c < 9007199254740992\right)\]

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: 31.3% 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: 99.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{c \cdot -0.3333333333333333}{a}}{\frac{\frac{\sqrt{b \cdot b + c \cdot \frac{a}{-0.3333333333333333}}}{3} - b \cdot -0.3333333333333333}{a}} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/
  (/ (* c -0.3333333333333333) a)
  (/
   (-
    (/ (sqrt (+ (* b b) (* c (/ a -0.3333333333333333)))) 3.0)
    (* b -0.3333333333333333))
   a)))

C

double code(double a, double b, double c) {
	return ((c * -0.3333333333333333) / a) / (((sqrt(((b * b) + (c * (a / -0.3333333333333333)))) / 3.0) - (b * -0.3333333333333333)) / 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 = ((c * (-0.3333333333333333d0)) / a) / (((sqrt(((b * b) + (c * (a / (-0.3333333333333333d0))))) / 3.0d0) - (b * (-0.3333333333333333d0))) / a)
end function

Java

public static double code(double a, double b, double c) {
	return ((c * -0.3333333333333333) / a) / (((Math.sqrt(((b * b) + (c * (a / -0.3333333333333333)))) / 3.0) - (b * -0.3333333333333333)) / a);
}

Python

def code(a, b, c):
	return ((c * -0.3333333333333333) / a) / (((math.sqrt(((b * b) + (c * (a / -0.3333333333333333)))) / 3.0) - (b * -0.3333333333333333)) / a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(c * -0.3333333333333333) / a) / Float64(Float64(Float64(sqrt(Float64(Float64(b * b) + Float64(c * Float64(a / -0.3333333333333333)))) / 3.0) - Float64(b * -0.3333333333333333)) / a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = ((c * -0.3333333333333333) / a) / (((sqrt(((b * b) + (c * (a / -0.3333333333333333)))) / 3.0) - (b * -0.3333333333333333)) / a);
end

Wolfram

code[a_, b_, c_] := N[(N[(N[(c * -0.3333333333333333), $MachinePrecision] / a), $MachinePrecision] / N[(N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(c * N[(a / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision] - N[(b * -0.3333333333333333), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.5%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

6. Applied egg-rr 0

   \[\leadsto expr\]

7. Taylor expanded in b around 0 0

   \[\leadsto expr\]

9. Simplified 0

   \[\leadsto expr\]
10. Add Preprocessing

Alternative 2: 95.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := b \cdot \left(b \cdot b\right)\\ -0.5 \cdot \frac{c}{b} + \left(\frac{\left(c \cdot c\right) \cdot -0.375}{t\_0} + a \cdot \left(\frac{-0.16666666666666666}{\frac{b}{\frac{6.328125 \cdot a}{\frac{\left(b \cdot b\right) \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot b\right)\right)}{\left(c \cdot c\right) \cdot \left(c \cdot c\right)}}}} + \frac{c \cdot \left(\left(c \cdot c\right) \cdot -0.5625\right)}{\left(b \cdot b\right) \cdot t\_0}\right)\right) \cdot a \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* b (* b b))))
   (+
    (* -0.5 (/ c b))
    (*
     (+
      (/ (* (* c c) -0.375) t_0)
      (*
       a
       (+
        (/
         -0.16666666666666666
         (/
          b
          (/
           (* 6.328125 a)
           (/ (* (* b b) (* (* b b) (* b b))) (* (* c c) (* c c))))))
        (/ (* c (* (* c c) -0.5625)) (* (* b b) t_0)))))
     a))))

C

double code(double a, double b, double c) {
	double t_0 = b * (b * b);
	return (-0.5 * (c / b)) + (((((c * c) * -0.375) / t_0) + (a * ((-0.16666666666666666 / (b / ((6.328125 * a) / (((b * b) * ((b * b) * (b * b))) / ((c * c) * (c * c)))))) + ((c * ((c * c) * -0.5625)) / ((b * b) * t_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
    real(8) :: t_0
    t_0 = b * (b * b)
    code = ((-0.5d0) * (c / b)) + (((((c * c) * (-0.375d0)) / t_0) + (a * (((-0.16666666666666666d0) / (b / ((6.328125d0 * a) / (((b * b) * ((b * b) * (b * b))) / ((c * c) * (c * c)))))) + ((c * ((c * c) * (-0.5625d0))) / ((b * b) * t_0))))) * a)
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = b * (b * b);
	return (-0.5 * (c / b)) + (((((c * c) * -0.375) / t_0) + (a * ((-0.16666666666666666 / (b / ((6.328125 * a) / (((b * b) * ((b * b) * (b * b))) / ((c * c) * (c * c)))))) + ((c * ((c * c) * -0.5625)) / ((b * b) * t_0))))) * a);
}

Python

def code(a, b, c):
	t_0 = b * (b * b)
	return (-0.5 * (c / b)) + (((((c * c) * -0.375) / t_0) + (a * ((-0.16666666666666666 / (b / ((6.328125 * a) / (((b * b) * ((b * b) * (b * b))) / ((c * c) * (c * c)))))) + ((c * ((c * c) * -0.5625)) / ((b * b) * t_0))))) * a)

Julia

function code(a, b, c)
	t_0 = Float64(b * Float64(b * b))
	return Float64(Float64(-0.5 * Float64(c / b)) + Float64(Float64(Float64(Float64(Float64(c * c) * -0.375) / t_0) + Float64(a * Float64(Float64(-0.16666666666666666 / Float64(b / Float64(Float64(6.328125 * a) / Float64(Float64(Float64(b * b) * Float64(Float64(b * b) * Float64(b * b))) / Float64(Float64(c * c) * Float64(c * c)))))) + Float64(Float64(c * Float64(Float64(c * c) * -0.5625)) / Float64(Float64(b * b) * t_0))))) * a))
end

MATLAB

function tmp = code(a, b, c)
	t_0 = b * (b * b);
	tmp = (-0.5 * (c / b)) + (((((c * c) * -0.375) / t_0) + (a * ((-0.16666666666666666 / (b / ((6.328125 * a) / (((b * b) * ((b * b) * (b * b))) / ((c * c) * (c * c)))))) + ((c * ((c * c) * -0.5625)) / ((b * b) * t_0))))) * a);
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]}, N[(N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(c * c), $MachinePrecision] * -0.375), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(a * N[(N[(-0.16666666666666666 / N[(b / N[(N[(6.328125 * a), $MachinePrecision] / N[(N[(N[(b * b), $MachinePrecision] * N[(N[(b * b), $MachinePrecision] * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(c * c), $MachinePrecision] * -0.5625), $MachinePrecision]), $MachinePrecision] / N[(N[(b * b), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 32.5%

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

3. Taylor expanded in a around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 3: 93.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot \frac{c}{b} + a \cdot \frac{\frac{a \cdot \left(c \cdot \left(c \cdot c\right)\right)}{b} \cdot \frac{-0.5625}{b} + \left(c \cdot c\right) \cdot -0.375}{b \cdot \left(b \cdot b\right)} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (+
  (* -0.5 (/ c b))
  (*
   a
   (/
    (+ (* (/ (* a (* c (* c c))) b) (/ -0.5625 b)) (* (* c c) -0.375))
    (* b (* b b))))))

C

double code(double a, double b, double c) {
	return (-0.5 * (c / b)) + (a * (((((a * (c * (c * c))) / b) * (-0.5625 / b)) + ((c * c) * -0.375)) / (b * (b * 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 = ((-0.5d0) * (c / b)) + (a * (((((a * (c * (c * c))) / b) * ((-0.5625d0) / b)) + ((c * c) * (-0.375d0))) / (b * (b * b))))
end function

Java

public static double code(double a, double b, double c) {
	return (-0.5 * (c / b)) + (a * (((((a * (c * (c * c))) / b) * (-0.5625 / b)) + ((c * c) * -0.375)) / (b * (b * b))));
}

Python

def code(a, b, c):
	return (-0.5 * (c / b)) + (a * (((((a * (c * (c * c))) / b) * (-0.5625 / b)) + ((c * c) * -0.375)) / (b * (b * b))))

Julia

function code(a, b, c)
	return Float64(Float64(-0.5 * Float64(c / b)) + Float64(a * Float64(Float64(Float64(Float64(Float64(a * Float64(c * Float64(c * c))) / b) * Float64(-0.5625 / b)) + Float64(Float64(c * c) * -0.375)) / Float64(b * Float64(b * b)))))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-0.5 * (c / b)) + (a * (((((a * (c * (c * c))) / b) * (-0.5625 / b)) + ((c * c) * -0.375)) / (b * (b * b))));
end

Wolfram

code[a_, b_, c_] := N[(N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(N[(N[(N[(a * N[(c * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] * N[(-0.5625 / b), $MachinePrecision]), $MachinePrecision] + N[(N[(c * c), $MachinePrecision] * -0.375), $MachinePrecision]), $MachinePrecision] / N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.5%

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

3. Taylor expanded in a around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in b around inf 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 4: 90.6% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot \frac{c}{b} + \frac{-0.375 \cdot \left(a \cdot \left(\frac{c}{b} \cdot \frac{c}{b}\right)\right)}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (+ (* -0.5 (/ c b)) (/ (* -0.375 (* a (* (/ c b) (/ c b)))) b)))

C

double code(double a, double b, double c) {
	return (-0.5 * (c / b)) + ((-0.375 * (a * ((c / b) * (c / b)))) / 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 = ((-0.5d0) * (c / b)) + (((-0.375d0) * (a * ((c / b) * (c / b)))) / b)
end function

Java

public static double code(double a, double b, double c) {
	return (-0.5 * (c / b)) + ((-0.375 * (a * ((c / b) * (c / b)))) / b);
}

Python

def code(a, b, c):
	return (-0.5 * (c / b)) + ((-0.375 * (a * ((c / b) * (c / b)))) / b)

Julia

function code(a, b, c)
	return Float64(Float64(-0.5 * Float64(c / b)) + Float64(Float64(-0.375 * Float64(a * Float64(Float64(c / b) * Float64(c / b)))) / b))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-0.5 * (c / b)) + ((-0.375 * (a * ((c / b) * (c / b)))) / b);
end

Wolfram

code[a_, b_, c_] := N[(N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.375 * N[(a * N[(N[(c / b), $MachinePrecision] * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.5%

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

3. Taylor expanded in a around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 5: 90.6% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \frac{c \cdot -0.5 + -0.375 \cdot \left(a \cdot \left(\frac{c}{b} \cdot \frac{c}{b}\right)\right)}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (* c -0.5) (* -0.375 (* a (* (/ c b) (/ c b))))) b))

C

double code(double a, double b, double c) {
	return ((c * -0.5) + (-0.375 * (a * ((c / b) * (c / b))))) / 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 * (-0.5d0)) + ((-0.375d0) * (a * ((c / b) * (c / b))))) / b
end function

Java

public static double code(double a, double b, double c) {
	return ((c * -0.5) + (-0.375 * (a * ((c / b) * (c / b))))) / b;
}

Python

def code(a, b, c):
	return ((c * -0.5) + (-0.375 * (a * ((c / b) * (c / b))))) / b

Julia

function code(a, b, c)
	return Float64(Float64(Float64(c * -0.5) + Float64(-0.375 * Float64(a * Float64(Float64(c / b) * Float64(c / b))))) / b)
end

MATLAB

function tmp = code(a, b, c)
	tmp = ((c * -0.5) + (-0.375 * (a * ((c / b) * (c / b))))) / b;
end

Wolfram

code[a_, b_, c_] := N[(N[(N[(c * -0.5), $MachinePrecision] + N[(-0.375 * N[(a * N[(N[(c / b), $MachinePrecision] * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 32.5%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 6: 90.4% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(\frac{-0.375}{b} \cdot \frac{a \cdot c}{b \cdot b} + \frac{-0.5}{b}\right) \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (* c (+ (* (/ -0.375 b) (/ (* a c) (* b b))) (/ -0.5 b))))

C

double code(double a, double b, double c) {
	return c * (((-0.375 / b) * ((a * c) / (b * b))) + (-0.5 / 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 * ((((-0.375d0) / b) * ((a * c) / (b * b))) + ((-0.5d0) / b))
end function

Java

public static double code(double a, double b, double c) {
	return c * (((-0.375 / b) * ((a * c) / (b * b))) + (-0.5 / b));
}

Python

def code(a, b, c):
	return c * (((-0.375 / b) * ((a * c) / (b * b))) + (-0.5 / b))

Julia

function code(a, b, c)
	return Float64(c * Float64(Float64(Float64(-0.375 / b) * Float64(Float64(a * c) / Float64(b * b))) + Float64(-0.5 / b)))
end

MATLAB

function tmp = code(a, b, c)
	tmp = c * (((-0.375 / b) * ((a * c) / (b * b))) + (-0.5 / b));
end

Wolfram

code[a_, b_, c_] := N[(c * N[(N[(N[(-0.375 / b), $MachinePrecision] * N[(N[(a * c), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.5%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

5. Taylor expanded in c around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 7: 81.4% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot \frac{c}{b} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* -0.5 (/ c b)))

C

double code(double a, double b, double c) {
	return -0.5 * (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 = (-0.5d0) * (c / b)
end function

Java

public static double code(double a, double b, double c) {
	return -0.5 * (c / b);
}

Python

def code(a, b, c):
	return -0.5 * (c / b)

Julia

function code(a, b, c)
	return Float64(-0.5 * Float64(c / b))
end

MATLAB

function tmp = code(a, b, c)
	tmp = -0.5 * (c / b);
end

Wolfram

code[a_, b_, c_] := N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.5%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 8: 3.2% accurate, 116.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 0.0)

C

double code(double a, double b, double c) {
	return 0.0;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = 0.0d0
end function

Java

public static double code(double a, double b, double c) {
	return 0.0;
}

Python

def code(a, b, c):
	return 0.0

Julia

function code(a, b, c)
	return 0.0
end

MATLAB

function tmp = code(a, b, c)
	tmp = 0.0;
end

Wolfram

code[a_, b_, c_] := 0.0

Derivation

1. Initial program 32.5%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

5. Taylor expanded in c around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (a b c)
  :name "Cubic critical, medium range"
  :precision binary64
  :pre (and (and (and (< 1.1102230246251565e-16 a) (< a 9007199254740992.0)) (and (< 1.1102230246251565e-16 b) (< b 9007199254740992.0))) (and (< 1.1102230246251565e-16 c) (< c 9007199254740992.0)))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))