Cubic critical, wide range

Percentage Accurate: 17.7% → 98.9%

Time: 24.7s

Alternatives: 8

Speedup: 23.2×

Specification

\[\left(\left(4.930380657631324 \cdot 10^{-32} < a \land a < 2.028240960365167 \cdot 10^{+31}\right) \land \left(4.930380657631324 \cdot 10^{-32} < b \land b < 2.028240960365167 \cdot 10^{+31}\right)\right) \land \left(4.930380657631324 \cdot 10^{-32} < c \land c < 2.028240960365167 \cdot 10^{+31}\right)\]

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: 17.7% 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: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{27 \cdot \left(\left(a \cdot \left(a \cdot a\right)\right) \cdot \left(c \cdot \left(c \cdot c\right)\right)\right) + \left(b \cdot b\right) \cdot \left(-27 \cdot \left(\left(a \cdot c\right) \cdot \left(a \cdot c\right)\right) + 9 \cdot \left(a \cdot \left(\left(b \cdot b\right) \cdot c\right)\right)\right)}{\left(9 \cdot \left(\left(a \cdot a\right) \cdot \left(c \cdot c\right)\right) + \left(b \cdot b\right) \cdot \left(\left(a \cdot c\right) \cdot -9 + 3 \cdot \left(b \cdot b\right)\right)\right) \cdot \left(b + \sqrt{b \cdot b + a \cdot \left(c \cdot -3\right)}\right)}}{a \cdot -3} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/
  (/
   (+
    (* 27.0 (* (* a (* a a)) (* c (* c c))))
    (* (* b b) (+ (* -27.0 (* (* a c) (* a c))) (* 9.0 (* a (* (* b b) c))))))
   (*
    (+
     (* 9.0 (* (* a a) (* c c)))
     (* (* b b) (+ (* (* a c) -9.0) (* 3.0 (* b b)))))
    (+ b (sqrt (+ (* b b) (* a (* c -3.0)))))))
  (* a -3.0)))

C

double code(double a, double b, double c) {
	return (((27.0 * ((a * (a * a)) * (c * (c * c)))) + ((b * b) * ((-27.0 * ((a * c) * (a * c))) + (9.0 * (a * ((b * b) * c)))))) / (((9.0 * ((a * a) * (c * c))) + ((b * b) * (((a * c) * -9.0) + (3.0 * (b * b))))) * (b + sqrt(((b * b) + (a * (c * -3.0))))))) / (a * -3.0);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((27.0d0 * ((a * (a * a)) * (c * (c * c)))) + ((b * b) * (((-27.0d0) * ((a * c) * (a * c))) + (9.0d0 * (a * ((b * b) * c)))))) / (((9.0d0 * ((a * a) * (c * c))) + ((b * b) * (((a * c) * (-9.0d0)) + (3.0d0 * (b * b))))) * (b + sqrt(((b * b) + (a * (c * (-3.0d0)))))))) / (a * (-3.0d0))
end function

Java

public static double code(double a, double b, double c) {
	return (((27.0 * ((a * (a * a)) * (c * (c * c)))) + ((b * b) * ((-27.0 * ((a * c) * (a * c))) + (9.0 * (a * ((b * b) * c)))))) / (((9.0 * ((a * a) * (c * c))) + ((b * b) * (((a * c) * -9.0) + (3.0 * (b * b))))) * (b + Math.sqrt(((b * b) + (a * (c * -3.0))))))) / (a * -3.0);
}

Python

def code(a, b, c):
	return (((27.0 * ((a * (a * a)) * (c * (c * c)))) + ((b * b) * ((-27.0 * ((a * c) * (a * c))) + (9.0 * (a * ((b * b) * c)))))) / (((9.0 * ((a * a) * (c * c))) + ((b * b) * (((a * c) * -9.0) + (3.0 * (b * b))))) * (b + math.sqrt(((b * b) + (a * (c * -3.0))))))) / (a * -3.0)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(Float64(27.0 * Float64(Float64(a * Float64(a * a)) * Float64(c * Float64(c * c)))) + Float64(Float64(b * b) * Float64(Float64(-27.0 * Float64(Float64(a * c) * Float64(a * c))) + Float64(9.0 * Float64(a * Float64(Float64(b * b) * c)))))) / Float64(Float64(Float64(9.0 * Float64(Float64(a * a) * Float64(c * c))) + Float64(Float64(b * b) * Float64(Float64(Float64(a * c) * -9.0) + Float64(3.0 * Float64(b * b))))) * Float64(b + sqrt(Float64(Float64(b * b) + Float64(a * Float64(c * -3.0))))))) / Float64(a * -3.0))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (((27.0 * ((a * (a * a)) * (c * (c * c)))) + ((b * b) * ((-27.0 * ((a * c) * (a * c))) + (9.0 * (a * ((b * b) * c)))))) / (((9.0 * ((a * a) * (c * c))) + ((b * b) * (((a * c) * -9.0) + (3.0 * (b * b))))) * (b + sqrt(((b * b) + (a * (c * -3.0))))))) / (a * -3.0);
end

Wolfram

code[a_, b_, c_] := N[(N[(N[(N[(27.0 * N[(N[(a * N[(a * a), $MachinePrecision]), $MachinePrecision] * N[(c * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] * N[(N[(-27.0 * N[(N[(a * c), $MachinePrecision] * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(a * N[(N[(b * b), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(9.0 * N[(N[(a * a), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] * N[(N[(N[(a * c), $MachinePrecision] * -9.0), $MachinePrecision] + N[(3.0 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(b + N[Sqrt[N[(N[(b * b), $MachinePrecision] + N[(a * N[(c * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * -3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.1%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

7. Taylor expanded in b around 0 0

   \[\leadsto expr\]

9. Simplified 0

   \[\leadsto expr\]

10. Taylor expanded in b around 0 0

    \[\leadsto expr\]

12. Simplified 0

    \[\leadsto expr\]

13. Taylor expanded in b around 0 0

    \[\leadsto expr\]

15. Simplified 0

    \[\leadsto expr\]
16. Add Preprocessing

Alternative 2: 97.8% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 15.1%

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

3. Taylor expanded in a around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 3: 97.0% accurate, 3.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 15.1%

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

3. Taylor expanded in 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: 96.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \frac{-0.5}{\frac{b}{c}} - \frac{a}{\frac{-4 \cdot \left(\left(a \cdot b\right) \cdot c\right) + 2.6666666666666665 \cdot \left(b \cdot \left(b \cdot b\right)\right)}{c \cdot c}} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (-
  (/ -0.5 (/ b c))
  (/
   a
   (/
    (+ (* -4.0 (* (* a b) c)) (* 2.6666666666666665 (* b (* b b))))
    (* c c)))))

C

double code(double a, double b, double c) {
	return (-0.5 / (b / c)) - (a / (((-4.0 * ((a * b) * c)) + (2.6666666666666665 * (b * (b * b)))) / (c * c)));
}

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) / (b / c)) - (a / ((((-4.0d0) * ((a * b) * c)) + (2.6666666666666665d0 * (b * (b * b)))) / (c * c)))
end function

Java

public static double code(double a, double b, double c) {
	return (-0.5 / (b / c)) - (a / (((-4.0 * ((a * b) * c)) + (2.6666666666666665 * (b * (b * b)))) / (c * c)));
}

Python

def code(a, b, c):
	return (-0.5 / (b / c)) - (a / (((-4.0 * ((a * b) * c)) + (2.6666666666666665 * (b * (b * b)))) / (c * c)))

Julia

function code(a, b, c)
	return Float64(Float64(-0.5 / Float64(b / c)) - Float64(a / Float64(Float64(Float64(-4.0 * Float64(Float64(a * b) * c)) + Float64(2.6666666666666665 * Float64(b * Float64(b * b)))) / Float64(c * c))))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-0.5 / (b / c)) - (a / (((-4.0 * ((a * b) * c)) + (2.6666666666666665 * (b * (b * b)))) / (c * c)));
end

Wolfram

code[a_, b_, c_] := N[(N[(-0.5 / N[(b / c), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(N[(-4.0 * N[(N[(a * b), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] + N[(2.6666666666666665 * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.1%

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

3. Taylor expanded in a around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in b around -inf 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]

10. Applied egg-rr 0

    \[\leadsto expr\]

11. Taylor expanded in c around 0 0

    \[\leadsto expr\]

13. Simplified 0

    \[\leadsto expr\]
14. Add Preprocessing

Alternative 5: 95.4% 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 15.1%

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

3. Taylor expanded in a around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 6: 95.4% 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 15.1%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 7: 95.4% accurate, 7.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 15.1%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in c around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 8: 90.6% 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 15.1%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (a b c)
  :name "Cubic critical, wide range"
  :precision binary64
  :pre (and (and (and (< 4.930380657631324e-32 a) (< a 2.028240960365167e+31)) (and (< 4.930380657631324e-32 b) (< b 2.028240960365167e+31))) (and (< 4.930380657631324e-32 c) (< c 2.028240960365167e+31)))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))