Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Percentage Accurate: 85.0% → 90.1%

Time: 28.2s

Alternatives: 24

Speedup: 0.5×

• 50.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(b \cdot c + t\_1\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<=
        (-
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
          (* (* x 4.0) i))
         (* k (* j 27.0)))
        INFINITY)
     (- (+ (* b c) t_1) (+ (* 4.0 (* t a)) (* 27.0 (* j k))))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - (k * (j * 27.0))) <= ((double) INFINITY)) {
		tmp = ((b * c) + t_1) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - (k * (j * 27.0))) <= Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + t_1) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - (k * (j * 27.0))) <= math.inf:
		tmp = ((b * c) + t_1) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 27.0))) <= Inf)
		tmp = Float64(Float64(Float64(b * c) + t_1) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - (k * (j * 27.0))) <= Inf)
		tmp = ((b * c) + t_1) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 95.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.9%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.2%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + t\_2\\ \mathbf{elif}\;b \cdot c \leq -4.1 \cdot 10^{-10}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.18 \cdot 10^{-204}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 3.55 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* t (* a -4.0)))))
   (if (<= (* b c) -1.15e+139)
     (- (* b c) (* x (* 4.0 i)))
     (if (<= (* b c) -2.9e+47)
       (+ (* b c) (* (* t a) -4.0))
       (if (<= (* b c) -3.6e+14)
         (+ (* 18.0 (* (* y z) (* x t))) t_2)
         (if (<= (* b c) -4.1e-10)
           t_3
           (if (<= (* b c) -2.9e-44)
             t_1
             (if (<= (* b c) -1.18e-204)
               t_3
               (if (<= (* b c) 3.55e-68)
                 t_1
                 (if (<= (* b c) 3.2e-39)
                   t_3
                   (if (<= (* b c) 1.75e+143) t_1 (+ (* b c) t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -1.15e+139) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if ((b * c) <= -2.9e+47) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if ((b * c) <= -3.6e+14) {
		tmp = (18.0 * ((y * z) * (x * t))) + t_2;
	} else if ((b * c) <= -4.1e-10) {
		tmp = t_3;
	} else if ((b * c) <= -2.9e-44) {
		tmp = t_1;
	} else if ((b * c) <= -1.18e-204) {
		tmp = t_3;
	} else if ((b * c) <= 3.55e-68) {
		tmp = t_1;
	} else if ((b * c) <= 3.2e-39) {
		tmp = t_3;
	} else if ((b * c) <= 1.75e+143) {
		tmp = t_1;
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (t * (a * (-4.0d0)))
    if ((b * c) <= (-1.15d+139)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if ((b * c) <= (-2.9d+47)) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if ((b * c) <= (-3.6d+14)) then
        tmp = (18.0d0 * ((y * z) * (x * t))) + t_2
    else if ((b * c) <= (-4.1d-10)) then
        tmp = t_3
    else if ((b * c) <= (-2.9d-44)) then
        tmp = t_1
    else if ((b * c) <= (-1.18d-204)) then
        tmp = t_3
    else if ((b * c) <= 3.55d-68) then
        tmp = t_1
    else if ((b * c) <= 3.2d-39) then
        tmp = t_3
    else if ((b * c) <= 1.75d+143) then
        tmp = t_1
    else
        tmp = (b * c) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -1.15e+139) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if ((b * c) <= -2.9e+47) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if ((b * c) <= -3.6e+14) {
		tmp = (18.0 * ((y * z) * (x * t))) + t_2;
	} else if ((b * c) <= -4.1e-10) {
		tmp = t_3;
	} else if ((b * c) <= -2.9e-44) {
		tmp = t_1;
	} else if ((b * c) <= -1.18e-204) {
		tmp = t_3;
	} else if ((b * c) <= 3.55e-68) {
		tmp = t_1;
	} else if ((b * c) <= 3.2e-39) {
		tmp = t_3;
	} else if ((b * c) <= 1.75e+143) {
		tmp = t_1;
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (t * (a * -4.0))
	tmp = 0
	if (b * c) <= -1.15e+139:
		tmp = (b * c) - (x * (4.0 * i))
	elif (b * c) <= -2.9e+47:
		tmp = (b * c) + ((t * a) * -4.0)
	elif (b * c) <= -3.6e+14:
		tmp = (18.0 * ((y * z) * (x * t))) + t_2
	elif (b * c) <= -4.1e-10:
		tmp = t_3
	elif (b * c) <= -2.9e-44:
		tmp = t_1
	elif (b * c) <= -1.18e-204:
		tmp = t_3
	elif (b * c) <= 3.55e-68:
		tmp = t_1
	elif (b * c) <= 3.2e-39:
		tmp = t_3
	elif (b * c) <= 1.75e+143:
		tmp = t_1
	else:
		tmp = (b * c) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(t * Float64(a * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -1.15e+139)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (Float64(b * c) <= -2.9e+47)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (Float64(b * c) <= -3.6e+14)
		tmp = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + t_2);
	elseif (Float64(b * c) <= -4.1e-10)
		tmp = t_3;
	elseif (Float64(b * c) <= -2.9e-44)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.18e-204)
		tmp = t_3;
	elseif (Float64(b * c) <= 3.55e-68)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.2e-39)
		tmp = t_3;
	elseif (Float64(b * c) <= 1.75e+143)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (t * (a * -4.0));
	tmp = 0.0;
	if ((b * c) <= -1.15e+139)
		tmp = (b * c) - (x * (4.0 * i));
	elseif ((b * c) <= -2.9e+47)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif ((b * c) <= -3.6e+14)
		tmp = (18.0 * ((y * z) * (x * t))) + t_2;
	elseif ((b * c) <= -4.1e-10)
		tmp = t_3;
	elseif ((b * c) <= -2.9e-44)
		tmp = t_1;
	elseif ((b * c) <= -1.18e-204)
		tmp = t_3;
	elseif ((b * c) <= 3.55e-68)
		tmp = t_1;
	elseif ((b * c) <= 3.2e-39)
		tmp = t_3;
	elseif ((b * c) <= 1.75e+143)
		tmp = t_1;
	else
		tmp = (b * c) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.15e+139], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.9e+47], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e+14], N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.1e-10], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -2.9e-44], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.18e-204], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 3.55e-68], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.2e-39], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 1.75e+143], t$95$1, N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.15e139

   1. Initial program 73.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Taylor expanded in i around inf 72.7%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

      2. *-commutative 72.7%

         \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   8. Simplified 72.7%

      \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   if -1.15e139 < (*.f64 b c) < -2.8999999999999998e47

   1. Initial program 92.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 85.1%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in x around 0 74.2%

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

   if -2.8999999999999998e47 < (*.f64 b c) < -3.6e14

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 72.6%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 85.6%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -3.6e14 < (*.f64 b c) < -4.0999999999999998e-10 or -2.9000000000000001e-44 < (*.f64 b c) < -1.17999999999999995e-204 or 3.5500000000000001e-68 < (*.f64 b c) < 3.1999999999999998e-39

   1. Initial program 95.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 74.2%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 74.2%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 74.2%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 74.2%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 74.2%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 74.2%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 74.2%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 74.2%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 74.2%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 74.2%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if -4.0999999999999998e-10 < (*.f64 b c) < -2.9000000000000001e-44 or -1.17999999999999995e-204 < (*.f64 b c) < 3.5500000000000001e-68 or 3.1999999999999998e-39 < (*.f64 b c) < 1.75000000000000004e143

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 65.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if 1.75000000000000004e143 < (*.f64 b c)

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 82.1%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -4.1 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.18 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.55 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.18 \cdot 10^{+45}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -22500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.4 \cdot 10^{-204}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{-39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* t (* a -4.0)))))
   (if (<= (* b c) -5.2e+140)
     (- (* b c) (* x (* 4.0 i)))
     (if (<= (* b c) -1.18e+45)
       (+ (* b c) (* (* t a) -4.0))
       (if (<= (* b c) -22500000000000.0)
         t_1
         (if (<= (* b c) -1.4e-204)
           t_3
           (if (<= (* b c) 1.3e-69)
             t_1
             (if (<= (* b c) 1.4e-39)
               t_3
               (if (<= (* b c) 4.2e+149) t_1 (+ (* b c) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -5.2e+140) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if ((b * c) <= -1.18e+45) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if ((b * c) <= -22500000000000.0) {
		tmp = t_1;
	} else if ((b * c) <= -1.4e-204) {
		tmp = t_3;
	} else if ((b * c) <= 1.3e-69) {
		tmp = t_1;
	} else if ((b * c) <= 1.4e-39) {
		tmp = t_3;
	} else if ((b * c) <= 4.2e+149) {
		tmp = t_1;
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (t * (a * (-4.0d0)))
    if ((b * c) <= (-5.2d+140)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if ((b * c) <= (-1.18d+45)) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if ((b * c) <= (-22500000000000.0d0)) then
        tmp = t_1
    else if ((b * c) <= (-1.4d-204)) then
        tmp = t_3
    else if ((b * c) <= 1.3d-69) then
        tmp = t_1
    else if ((b * c) <= 1.4d-39) then
        tmp = t_3
    else if ((b * c) <= 4.2d+149) then
        tmp = t_1
    else
        tmp = (b * c) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -5.2e+140) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if ((b * c) <= -1.18e+45) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if ((b * c) <= -22500000000000.0) {
		tmp = t_1;
	} else if ((b * c) <= -1.4e-204) {
		tmp = t_3;
	} else if ((b * c) <= 1.3e-69) {
		tmp = t_1;
	} else if ((b * c) <= 1.4e-39) {
		tmp = t_3;
	} else if ((b * c) <= 4.2e+149) {
		tmp = t_1;
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (t * (a * -4.0))
	tmp = 0
	if (b * c) <= -5.2e+140:
		tmp = (b * c) - (x * (4.0 * i))
	elif (b * c) <= -1.18e+45:
		tmp = (b * c) + ((t * a) * -4.0)
	elif (b * c) <= -22500000000000.0:
		tmp = t_1
	elif (b * c) <= -1.4e-204:
		tmp = t_3
	elif (b * c) <= 1.3e-69:
		tmp = t_1
	elif (b * c) <= 1.4e-39:
		tmp = t_3
	elif (b * c) <= 4.2e+149:
		tmp = t_1
	else:
		tmp = (b * c) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(t * Float64(a * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -5.2e+140)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (Float64(b * c) <= -1.18e+45)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (Float64(b * c) <= -22500000000000.0)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.4e-204)
		tmp = t_3;
	elseif (Float64(b * c) <= 1.3e-69)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.4e-39)
		tmp = t_3;
	elseif (Float64(b * c) <= 4.2e+149)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (t * (a * -4.0));
	tmp = 0.0;
	if ((b * c) <= -5.2e+140)
		tmp = (b * c) - (x * (4.0 * i));
	elseif ((b * c) <= -1.18e+45)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif ((b * c) <= -22500000000000.0)
		tmp = t_1;
	elseif ((b * c) <= -1.4e-204)
		tmp = t_3;
	elseif ((b * c) <= 1.3e-69)
		tmp = t_1;
	elseif ((b * c) <= 1.4e-39)
		tmp = t_3;
	elseif ((b * c) <= 4.2e+149)
		tmp = t_1;
	else
		tmp = (b * c) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.2e+140], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.18e+45], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -22500000000000.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.4e-204], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 1.3e-69], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.4e-39], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+149], t$95$1, N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -5.2000000000000002e140

   1. Initial program 73.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Taylor expanded in i around inf 72.7%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

      2. *-commutative 72.7%

         \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   8. Simplified 72.7%

      \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   if -5.2000000000000002e140 < (*.f64 b c) < -1.17999999999999993e45

   1. Initial program 92.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 85.1%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in x around 0 74.2%

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

   if -1.17999999999999993e45 < (*.f64 b c) < -2.25e13 or -1.4e-204 < (*.f64 b c) < 1.3000000000000001e-69 or 1.4000000000000001e-39 < (*.f64 b c) < 4.2000000000000003e149

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 65.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -2.25e13 < (*.f64 b c) < -1.4e-204 or 1.3000000000000001e-69 < (*.f64 b c) < 1.4000000000000001e-39

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 64.8%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 64.8%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 64.8%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 64.8%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 64.8%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 64.8%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 64.8%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 64.8%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 64.8%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 64.8%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if 4.2000000000000003e149 < (*.f64 b c)

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 82.1%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.18 \cdot 10^{+45}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -22500000000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.4 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + t\_1\right)\\ t_3 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-32}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (- (+ (* b c) (* (* t a) -4.0)) (+ (* 27.0 (* j k)) t_1)))
        (t_3 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -4e+140)
     t_3
     (if (<= t -1.7e-84)
       t_2
       (if (<= t 3.4e-32)
         (-
          (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
          (* k (* j 27.0)))
         (if (<= t 1.9e+50) t_2 (- t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1);
	double t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -4e+140) {
		tmp = t_3;
	} else if (t <= -1.7e-84) {
		tmp = t_2;
	} else if (t <= 3.4e-32) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (k * (j * 27.0));
	} else if (t <= 1.9e+50) {
		tmp = t_2;
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = ((b * c) + ((t * a) * (-4.0d0))) - ((27.0d0 * (j * k)) + t_1)
    t_3 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-4d+140)) then
        tmp = t_3
    else if (t <= (-1.7d-84)) then
        tmp = t_2
    else if (t <= 3.4d-32) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - (k * (j * 27.0d0))
    else if (t <= 1.9d+50) then
        tmp = t_2
    else
        tmp = t_3 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1);
	double t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -4e+140) {
		tmp = t_3;
	} else if (t <= -1.7e-84) {
		tmp = t_2;
	} else if (t <= 3.4e-32) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (k * (j * 27.0));
	} else if (t <= 1.9e+50) {
		tmp = t_2;
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1)
	t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -4e+140:
		tmp = t_3
	elif t <= -1.7e-84:
		tmp = t_2
	elif t <= 3.4e-32:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (k * (j * 27.0))
	elif t <= 1.9e+50:
		tmp = t_2
	else:
		tmp = t_3 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(Float64(27.0 * Float64(j * k)) + t_1))
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -4e+140)
		tmp = t_3;
	elseif (t <= -1.7e-84)
		tmp = t_2;
	elseif (t <= 3.4e-32)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 1.9e+50)
		tmp = t_2;
	else
		tmp = Float64(t_3 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1);
	t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -4e+140)
		tmp = t_3;
	elseif (t <= -1.7e-84)
		tmp = t_2;
	elseif (t <= 3.4e-32)
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (k * (j * 27.0));
	elseif (t <= 1.9e+50)
		tmp = t_2;
	else
		tmp = t_3 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+140], t$95$3, If[LessEqual[t, -1.7e-84], t$95$2, If[LessEqual[t, 3.4e-32], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+50], t$95$2, N[(t$95$3 - t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.00000000000000024e140

   1. Initial program 72.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 81.5%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in i around 0 84.2%

      \[\leadsto \color{blue}{b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -4.00000000000000024e140 < t < -1.7000000000000001e-84 or 3.39999999999999978e-32 < t < 1.89999999999999994e50

   1. Initial program 94.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 94.3%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if -1.7000000000000001e-84 < t < 3.39999999999999978e-32

   1. Initial program 87.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.1%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 91.4%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. metadata-eval 91.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(--27\right)} \cdot \left(j \cdot k\right) \]

      2. distribute-lft-neg-in 91.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(--27 \cdot \left(j \cdot k\right)\right)} \]

      3. associate-*r* 91.5%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(-\color{blue}{\left(-27 \cdot j\right) \cdot k}\right) \]

      4. *-commutative 91.5%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(-\color{blue}{k \cdot \left(-27 \cdot j\right)}\right) \]

      5. distribute-rgt-neg-in 91.5%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{k \cdot \left(--27 \cdot j\right)} \]

      6. distribute-lft-neg-in 91.5%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \color{blue}{\left(\left(--27\right) \cdot j\right)} \]

      7. metadata-eval 91.5%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(\color{blue}{27} \cdot j\right) \]

   6. Simplified 91.5%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{k \cdot \left(27 \cdot j\right)} \]

   if 1.89999999999999994e50 < t

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 85.7%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-84}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-32}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+50}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t\_2 - t \cdot \left(a \cdot 4\right)\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;t\_2 - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2 (+ (* b c) t_1))
        (t_3 (- t_2 (* t (* a 4.0)))))
   (if (<= x -9.8e+122)
     t_1
     (if (<= x -1.15e+64)
       t_3
       (if (<= x -1.4e-25)
         (- t_2 (* k (* j 27.0)))
         (if (<= x 3.7e+30)
           (-
            (+ (* b c) (* (* t a) -4.0))
            (+ (* 27.0 (* j k)) (* 4.0 (* x i))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (b * c) + t_1;
	double t_3 = t_2 - (t * (a * 4.0));
	double tmp;
	if (x <= -9.8e+122) {
		tmp = t_1;
	} else if (x <= -1.15e+64) {
		tmp = t_3;
	} else if (x <= -1.4e-25) {
		tmp = t_2 - (k * (j * 27.0));
	} else if (x <= 3.7e+30) {
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = (b * c) + t_1
    t_3 = t_2 - (t * (a * 4.0d0))
    if (x <= (-9.8d+122)) then
        tmp = t_1
    else if (x <= (-1.15d+64)) then
        tmp = t_3
    else if (x <= (-1.4d-25)) then
        tmp = t_2 - (k * (j * 27.0d0))
    else if (x <= 3.7d+30) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (b * c) + t_1;
	double t_3 = t_2 - (t * (a * 4.0));
	double tmp;
	if (x <= -9.8e+122) {
		tmp = t_1;
	} else if (x <= -1.15e+64) {
		tmp = t_3;
	} else if (x <= -1.4e-25) {
		tmp = t_2 - (k * (j * 27.0));
	} else if (x <= 3.7e+30) {
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = (b * c) + t_1
	t_3 = t_2 - (t * (a * 4.0))
	tmp = 0
	if x <= -9.8e+122:
		tmp = t_1
	elif x <= -1.15e+64:
		tmp = t_3
	elif x <= -1.4e-25:
		tmp = t_2 - (k * (j * 27.0))
	elif x <= 3.7e+30:
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t_2 - Float64(t * Float64(a * 4.0)))
	tmp = 0.0
	if (x <= -9.8e+122)
		tmp = t_1;
	elseif (x <= -1.15e+64)
		tmp = t_3;
	elseif (x <= -1.4e-25)
		tmp = Float64(t_2 - Float64(k * Float64(j * 27.0)));
	elseif (x <= 3.7e+30)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = (b * c) + t_1;
	t_3 = t_2 - (t * (a * 4.0));
	tmp = 0.0;
	if (x <= -9.8e+122)
		tmp = t_1;
	elseif (x <= -1.15e+64)
		tmp = t_3;
	elseif (x <= -1.4e-25)
		tmp = t_2 - (k * (j * 27.0));
	elseif (x <= 3.7e+30)
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.8e+122], t$95$1, If[LessEqual[x, -1.15e+64], t$95$3, If[LessEqual[x, -1.4e-25], N[(t$95$2 - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+30], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.7999999999999995e122

   1. Initial program 60.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.9%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -9.7999999999999995e122 < x < -1.15e64 or 3.70000000000000016e30 < x

   1. Initial program 76.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 94.2%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(4 \cdot t + 27 \cdot \frac{j \cdot k}{a}\right)} \]

   5. Taylor expanded in a around inf 92.9%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 92.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(a \cdot t\right) \cdot 4} \]

      2. associate-*r* 92.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(t \cdot 4\right)} \]

      3. *-commutative 92.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(t \cdot 4\right) \cdot a} \]

      4. associate-*l* 92.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 92.9%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -1.15e64 < x < -1.39999999999999994e-25

   1. Initial program 91.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.1%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 95.4%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. metadata-eval 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(--27\right)} \cdot \left(j \cdot k\right) \]

      2. distribute-lft-neg-in 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(--27 \cdot \left(j \cdot k\right)\right)} \]

      3. associate-*r* 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(-\color{blue}{\left(-27 \cdot j\right) \cdot k}\right) \]

      4. *-commutative 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(-\color{blue}{k \cdot \left(-27 \cdot j\right)}\right) \]

      5. distribute-rgt-neg-in 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{k \cdot \left(--27 \cdot j\right)} \]

      6. distribute-lft-neg-in 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \color{blue}{\left(\left(--27\right) \cdot j\right)} \]

      7. metadata-eval 95.4%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(\color{blue}{27} \cdot j\right) \]

   6. Simplified 95.4%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{k \cdot \left(27 \cdot j\right)} \]

   if -1.39999999999999994e-25 < x < 3.70000000000000016e30

   1. Initial program 95.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 88.3%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t \cdot \left(a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.35 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -7.5 \cdot 10^{-216}:\\ \;\;\;\;t\_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-313}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.36 \cdot 10^{+88}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + -4 \cdot \frac{t \cdot a}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -1.35e+144)
     (- (* b c) (* x (* 4.0 i)))
     (if (<= (* b c) -7.5e-216)
       (+ t_1 (* t (* a -4.0)))
       (if (<= (* b c) -4e-313)
         (+ t_1 (* -4.0 (* x i)))
         (if (<= (* b c) 1.36e+88)
           (* j (+ (* k -27.0) (* -4.0 (/ (* t a) j))))
           (+ (* b c) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.35e+144) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if ((b * c) <= -7.5e-216) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= -4e-313) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 1.36e+88) {
		tmp = j * ((k * -27.0) + (-4.0 * ((t * a) / j)));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-1.35d+144)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if ((b * c) <= (-7.5d-216)) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if ((b * c) <= (-4d-313)) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if ((b * c) <= 1.36d+88) then
        tmp = j * ((k * (-27.0d0)) + ((-4.0d0) * ((t * a) / j)))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.35e+144) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if ((b * c) <= -7.5e-216) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= -4e-313) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 1.36e+88) {
		tmp = j * ((k * -27.0) + (-4.0 * ((t * a) / j)));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -1.35e+144:
		tmp = (b * c) - (x * (4.0 * i))
	elif (b * c) <= -7.5e-216:
		tmp = t_1 + (t * (a * -4.0))
	elif (b * c) <= -4e-313:
		tmp = t_1 + (-4.0 * (x * i))
	elif (b * c) <= 1.36e+88:
		tmp = j * ((k * -27.0) + (-4.0 * ((t * a) / j)))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.35e+144)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (Float64(b * c) <= -7.5e-216)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (Float64(b * c) <= -4e-313)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 1.36e+88)
		tmp = Float64(j * Float64(Float64(k * -27.0) + Float64(-4.0 * Float64(Float64(t * a) / j))));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1.35e+144)
		tmp = (b * c) - (x * (4.0 * i));
	elseif ((b * c) <= -7.5e-216)
		tmp = t_1 + (t * (a * -4.0));
	elseif ((b * c) <= -4e-313)
		tmp = t_1 + (-4.0 * (x * i));
	elseif ((b * c) <= 1.36e+88)
		tmp = j * ((k * -27.0) + (-4.0 * ((t * a) / j)));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.35e+144], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.5e-216], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4e-313], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.36e+88], N[(j * N[(N[(k * -27.0), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.35000000000000008e144

   1. Initial program 73.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Taylor expanded in i around inf 72.7%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

      2. *-commutative 72.7%

         \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   8. Simplified 72.7%

      \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   if -1.35000000000000008e144 < (*.f64 b c) < -7.50000000000000064e-216

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 57.8%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 57.8%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 57.8%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 57.8%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 57.8%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 57.8%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 57.8%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 57.8%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 57.8%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 57.8%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if -7.50000000000000064e-216 < (*.f64 b c) < -4.0000000000037e-313

   1. Initial program 92.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 78.0%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   if -4.0000000000037e-313 < (*.f64 b c) < 1.3600000000000001e88

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 47.1%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 47.1%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 47.1%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 47.1%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 47.1%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 47.1%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 47.1%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 47.1%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   8. Taylor expanded in j around inf 49.5%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k + -4 \cdot \frac{a \cdot t}{j}\right)} \]

   if 1.3600000000000001e88 < (*.f64 b c)

   1. Initial program 85.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 73.8%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.35 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -7.5 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-313}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.36 \cdot 10^{+88}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + -4 \cdot \frac{t \cdot a}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 33.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+261}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+139}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)) (t_2 (* x (* i -4.0))))
   (if (<= (* b c) -1.25e+261)
     (* b c)
     (if (<= (* b c) -7e-219)
       t_1
       (if (<= (* b c) 0.0)
         t_2
         (if (<= (* b c) 5.8e+88)
           t_1
           (if (<= (* b c) 1.4e+139) t_2 (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -1.25e+261) {
		tmp = b * c;
	} else if ((b * c) <= -7e-219) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t_2;
	} else if ((b * c) <= 5.8e+88) {
		tmp = t_1;
	} else if ((b * c) <= 1.4e+139) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    t_2 = x * (i * (-4.0d0))
    if ((b * c) <= (-1.25d+261)) then
        tmp = b * c
    else if ((b * c) <= (-7d-219)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t_2
    else if ((b * c) <= 5.8d+88) then
        tmp = t_1
    else if ((b * c) <= 1.4d+139) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -1.25e+261) {
		tmp = b * c;
	} else if ((b * c) <= -7e-219) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t_2;
	} else if ((b * c) <= 5.8e+88) {
		tmp = t_1;
	} else if ((b * c) <= 1.4e+139) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	t_2 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -1.25e+261:
		tmp = b * c
	elif (b * c) <= -7e-219:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t_2
	elif (b * c) <= 5.8e+88:
		tmp = t_1
	elif (b * c) <= 1.4e+139:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.25e+261)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7e-219)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = t_2;
	elseif (Float64(b * c) <= 5.8e+88)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.4e+139)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -1.25e+261)
		tmp = b * c;
	elseif ((b * c) <= -7e-219)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t_2;
	elseif ((b * c) <= 5.8e+88)
		tmp = t_1;
	elseif ((b * c) <= 1.4e+139)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+261], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7e-219], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 5.8e+88], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.4e+139], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.25e261 or 1.3999999999999999e139 < (*.f64 b c)

   1. Initial program 82.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 76.0%

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

   if -1.25e261 < (*.f64 b c) < -7.00000000000000022e-219 or -0.0 < (*.f64 b c) < 5.7999999999999999e88

   1. Initial program 86.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.5%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 35.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 35.1%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

   6. Simplified 35.1%

      \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot -4} \]

   if -7.00000000000000022e-219 < (*.f64 b c) < -0.0 or 5.7999999999999999e88 < (*.f64 b c) < 1.3999999999999999e139

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 37.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 37.6%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      2. metadata-eval 37.6%

         \[\leadsto \left(\color{blue}{\left(-4\right)} \cdot i\right) \cdot x \]

      3. distribute-lft-neg-in 37.6%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x \]

      4. distribute-lft-neg-in 37.6%

         \[\leadsto \color{blue}{-\left(4 \cdot i\right) \cdot x} \]

      5. *-commutative 37.6%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      6. distribute-rgt-neg-in 37.6%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      7. distribute-lft-neg-in 37.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      8. metadata-eval 37.6%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

      9. *-commutative 37.6%

         \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{x \cdot \left(i \cdot -4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+261}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7 \cdot 10^{-219}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{+88}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c + t\_2\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* x (* 4.0 i))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* t (* a -4.0)))))
   (if (<= t -3.1e+153)
     (* x (* 18.0 (* z (* y t))))
     (if (<= t -5.2e+97)
       t_3
       (if (<= t -1.1e-120)
         t_1
         (if (<= t 1.8e-208) (+ (* b c) t_2) (if (<= t 5.4e+76) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if (t <= -3.1e+153) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (t <= -5.2e+97) {
		tmp = t_3;
	} else if (t <= -1.1e-120) {
		tmp = t_1;
	} else if (t <= 1.8e-208) {
		tmp = (b * c) + t_2;
	} else if (t <= 5.4e+76) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) - (x * (4.0d0 * i))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (t * (a * (-4.0d0)))
    if (t <= (-3.1d+153)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if (t <= (-5.2d+97)) then
        tmp = t_3
    else if (t <= (-1.1d-120)) then
        tmp = t_1
    else if (t <= 1.8d-208) then
        tmp = (b * c) + t_2
    else if (t <= 5.4d+76) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if (t <= -3.1e+153) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (t <= -5.2e+97) {
		tmp = t_3;
	} else if (t <= -1.1e-120) {
		tmp = t_1;
	} else if (t <= 1.8e-208) {
		tmp = (b * c) + t_2;
	} else if (t <= 5.4e+76) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (x * (4.0 * i))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (t * (a * -4.0))
	tmp = 0
	if t <= -3.1e+153:
		tmp = x * (18.0 * (z * (y * t)))
	elif t <= -5.2e+97:
		tmp = t_3
	elif t <= -1.1e-120:
		tmp = t_1
	elif t <= 1.8e-208:
		tmp = (b * c) + t_2
	elif t <= 5.4e+76:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(t * Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -3.1e+153)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (t <= -5.2e+97)
		tmp = t_3;
	elseif (t <= -1.1e-120)
		tmp = t_1;
	elseif (t <= 1.8e-208)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (t <= 5.4e+76)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (x * (4.0 * i));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (t * (a * -4.0));
	tmp = 0.0;
	if (t <= -3.1e+153)
		tmp = x * (18.0 * (z * (y * t)));
	elseif (t <= -5.2e+97)
		tmp = t_3;
	elseif (t <= -1.1e-120)
		tmp = t_1;
	elseif (t <= 1.8e-208)
		tmp = (b * c) + t_2;
	elseif (t <= 5.4e+76)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+153], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e+97], t$95$3, If[LessEqual[t, -1.1e-120], t$95$1, If[LessEqual[t, 1.8e-208], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, 5.4e+76], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.1e153

   1. Initial program 74.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 64.4%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around inf 61.0%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 63.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)}\right) \]

      2. *-commutative 63.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)}\right) \]

   8. Simplified 63.7%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]

   if -3.1e153 < t < -5.2e97 or 5.3999999999999998e76 < t

   1. Initial program 81.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 60.7%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 60.7%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 60.7%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 60.7%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 60.7%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 60.7%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 60.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 60.7%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if -5.2e97 < t < -1.10000000000000006e-120 or 1.7999999999999999e-208 < t < 5.3999999999999998e76

   1. Initial program 89.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.9%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Taylor expanded in i around inf 61.7%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 61.7%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

      2. *-commutative 61.7%

         \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   8. Simplified 61.7%

      \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   if -1.10000000000000006e-120 < t < 1.7999999999999999e-208

   1. Initial program 88.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 71.6%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;z \leq 1.05 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 25000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))))
   (if (<= z 1.05e-230)
     t_1
     (if (<= z 7.2e-170)
       (* x (* i -4.0))
       (if (<= z 25000000000.0)
         t_1
         (if (<= z 1.3e+51)
           (* k (* j -27.0))
           (if (<= z 3e+162) t_1 (* 18.0 (* (* y z) (* x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (z <= 1.05e-230) {
		tmp = t_1;
	} else if (z <= 7.2e-170) {
		tmp = x * (i * -4.0);
	} else if (z <= 25000000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e+51) {
		tmp = k * (j * -27.0);
	} else if (z <= 3e+162) {
		tmp = t_1;
	} else {
		tmp = 18.0 * ((y * z) * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((t * a) * (-4.0d0))
    if (z <= 1.05d-230) then
        tmp = t_1
    else if (z <= 7.2d-170) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 25000000000.0d0) then
        tmp = t_1
    else if (z <= 1.3d+51) then
        tmp = k * (j * (-27.0d0))
    else if (z <= 3d+162) then
        tmp = t_1
    else
        tmp = 18.0d0 * ((y * z) * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (z <= 1.05e-230) {
		tmp = t_1;
	} else if (z <= 7.2e-170) {
		tmp = x * (i * -4.0);
	} else if (z <= 25000000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e+51) {
		tmp = k * (j * -27.0);
	} else if (z <= 3e+162) {
		tmp = t_1;
	} else {
		tmp = 18.0 * ((y * z) * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + ((t * a) * -4.0)
	tmp = 0
	if z <= 1.05e-230:
		tmp = t_1
	elif z <= 7.2e-170:
		tmp = x * (i * -4.0)
	elif z <= 25000000000.0:
		tmp = t_1
	elif z <= 1.3e+51:
		tmp = k * (j * -27.0)
	elif z <= 3e+162:
		tmp = t_1
	else:
		tmp = 18.0 * ((y * z) * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (z <= 1.05e-230)
		tmp = t_1;
	elseif (z <= 7.2e-170)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 25000000000.0)
		tmp = t_1;
	elseif (z <= 1.3e+51)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (z <= 3e+162)
		tmp = t_1;
	else
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	tmp = 0.0;
	if (z <= 1.05e-230)
		tmp = t_1;
	elseif (z <= 7.2e-170)
		tmp = x * (i * -4.0);
	elseif (z <= 25000000000.0)
		tmp = t_1;
	elseif (z <= 1.3e+51)
		tmp = k * (j * -27.0);
	elseif (z <= 3e+162)
		tmp = t_1;
	else
		tmp = 18.0 * ((y * z) * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1.05e-230], t$95$1, If[LessEqual[z, 7.2e-170], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 25000000000.0], t$95$1, If[LessEqual[z, 1.3e+51], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+162], t$95$1, N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 1.0499999999999999e-230 or 7.2000000000000006e-170 < z < 2.5e10 or 1.3000000000000001e51 < z < 2.9999999999999998e162

   1. Initial program 85.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 78.7%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in x around 0 50.3%

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

   if 1.0499999999999999e-230 < z < 7.2000000000000006e-170

   1. Initial program 75.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.7%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 51.1%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 51.1%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      2. metadata-eval 51.1%

         \[\leadsto \left(\color{blue}{\left(-4\right)} \cdot i\right) \cdot x \]

      3. distribute-lft-neg-in 51.1%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x \]

      4. distribute-lft-neg-in 51.1%

         \[\leadsto \color{blue}{-\left(4 \cdot i\right) \cdot x} \]

      5. *-commutative 51.1%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      6. distribute-rgt-neg-in 51.1%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      7. distribute-lft-neg-in 51.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      8. metadata-eval 51.1%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

      9. *-commutative 51.1%

         \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{x \cdot \left(i \cdot -4\right)} \]

   if 2.5e10 < z < 1.3000000000000001e51

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 46.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.3%

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. *-commutative 46.3%

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} \]

   7. Simplified 46.3%

      \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} \]

   if 2.9999999999999998e162 < z

   1. Initial program 75.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 70.6%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 70.6%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(4 \cdot t + 27 \cdot \frac{j \cdot k}{a}\right)} \]

   5. Taylor expanded in a around inf 65.9%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(a \cdot t\right) \cdot 4} \]

      2. associate-*r* 65.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(t \cdot 4\right)} \]

      3. *-commutative 65.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(t \cdot 4\right) \cdot a} \]

      4. associate-*l* 65.9%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 65.9%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   8. Taylor expanded in y around inf 68.0%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 72.2%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

   10. Simplified 72.2%

       \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 25000000000:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ t_2 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* x (* 4.0 i)))) (t_2 (* x (* 18.0 (* z (* y t))))))
   (if (<= t -9e+203)
     t_2
     (if (<= t -1.9e+93)
       (+ (* b c) (* (* t a) -4.0))
       (if (<= t -5.9e-123)
         t_1
         (if (<= t 1.3e-208)
           (+ (* b c) (* j (* k -27.0)))
           (if (<= t 4.4e+104) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double t_2 = x * (18.0 * (z * (y * t)));
	double tmp;
	if (t <= -9e+203) {
		tmp = t_2;
	} else if (t <= -1.9e+93) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t <= -5.9e-123) {
		tmp = t_1;
	} else if (t <= 1.3e-208) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 4.4e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (x * (4.0d0 * i))
    t_2 = x * (18.0d0 * (z * (y * t)))
    if (t <= (-9d+203)) then
        tmp = t_2
    else if (t <= (-1.9d+93)) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (t <= (-5.9d-123)) then
        tmp = t_1
    else if (t <= 1.3d-208) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 4.4d+104) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double t_2 = x * (18.0 * (z * (y * t)));
	double tmp;
	if (t <= -9e+203) {
		tmp = t_2;
	} else if (t <= -1.9e+93) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t <= -5.9e-123) {
		tmp = t_1;
	} else if (t <= 1.3e-208) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 4.4e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (x * (4.0 * i))
	t_2 = x * (18.0 * (z * (y * t)))
	tmp = 0
	if t <= -9e+203:
		tmp = t_2
	elif t <= -1.9e+93:
		tmp = (b * c) + ((t * a) * -4.0)
	elif t <= -5.9e-123:
		tmp = t_1
	elif t <= 1.3e-208:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 4.4e+104:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	t_2 = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))))
	tmp = 0.0
	if (t <= -9e+203)
		tmp = t_2;
	elseif (t <= -1.9e+93)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (t <= -5.9e-123)
		tmp = t_1;
	elseif (t <= 1.3e-208)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 4.4e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (x * (4.0 * i));
	t_2 = x * (18.0 * (z * (y * t)));
	tmp = 0.0;
	if (t <= -9e+203)
		tmp = t_2;
	elseif (t <= -1.9e+93)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (t <= -5.9e-123)
		tmp = t_1;
	elseif (t <= 1.3e-208)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 4.4e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+203], t$95$2, If[LessEqual[t, -1.9e+93], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.9e-123], t$95$1, If[LessEqual[t, 1.3e-208], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+104], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.0000000000000006e203 or 4.40000000000000001e104 < t

   1. Initial program 72.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around inf 53.5%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 53.6%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)}\right) \]

      2. *-commutative 53.6%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)}\right) \]

   8. Simplified 53.6%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]

   if -9.0000000000000006e203 < t < -1.8999999999999999e93

   1. Initial program 92.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 81.9%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in x around 0 68.1%

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

   if -1.8999999999999999e93 < t < -5.89999999999999988e-123 or 1.30000000000000008e-208 < t < 4.40000000000000001e104

   1. Initial program 89.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.2%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Taylor expanded in i around inf 60.6%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

      2. *-commutative 60.6%

         \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   8. Simplified 60.6%

      \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   if -5.89999999999999988e-123 < t < 1.30000000000000008e-208

   1. Initial program 88.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 71.6%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2.15 \cdot 10^{+231}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.12 \cdot 10^{-39}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= (* b c) -2.15e+231)
     (* b c)
     (if (<= (* b c) 1.02e-235)
       t_1
       (if (<= (* b c) 1.12e-39)
         (* k (* j -27.0))
         (if (<= (* b c) 8e+137) t_1 (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -2.15e+231) {
		tmp = b * c;
	} else if ((b * c) <= 1.02e-235) {
		tmp = t_1;
	} else if ((b * c) <= 1.12e-39) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 8e+137) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if ((b * c) <= (-2.15d+231)) then
        tmp = b * c
    else if ((b * c) <= 1.02d-235) then
        tmp = t_1
    else if ((b * c) <= 1.12d-39) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 8d+137) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -2.15e+231) {
		tmp = b * c;
	} else if ((b * c) <= 1.02e-235) {
		tmp = t_1;
	} else if ((b * c) <= 1.12e-39) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 8e+137) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -2.15e+231:
		tmp = b * c
	elif (b * c) <= 1.02e-235:
		tmp = t_1
	elif (b * c) <= 1.12e-39:
		tmp = k * (j * -27.0)
	elif (b * c) <= 8e+137:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.15e+231)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.02e-235)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.12e-39)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 8e+137)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2.15e+231)
		tmp = b * c;
	elseif ((b * c) <= 1.02e-235)
		tmp = t_1;
	elseif ((b * c) <= 1.12e-39)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 8e+137)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.15e+231], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.02e-235], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.12e-39], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8e+137], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.14999999999999988e231 or 8.0000000000000003e137 < (*.f64 b c)

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.7%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 73.3%

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

   if -2.14999999999999988e231 < (*.f64 b c) < 1.02e-235 or 1.12e-39 < (*.f64 b c) < 8.0000000000000003e137

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.1%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 28.4%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 28.4%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      2. metadata-eval 28.4%

         \[\leadsto \left(\color{blue}{\left(-4\right)} \cdot i\right) \cdot x \]

      3. distribute-lft-neg-in 28.4%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x \]

      4. distribute-lft-neg-in 28.4%

         \[\leadsto \color{blue}{-\left(4 \cdot i\right) \cdot x} \]

      5. *-commutative 28.4%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      6. distribute-rgt-neg-in 28.4%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      7. distribute-lft-neg-in 28.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      8. metadata-eval 28.4%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

      9. *-commutative 28.4%

         \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   6. Simplified 28.4%

      \[\leadsto \color{blue}{x \cdot \left(i \cdot -4\right)} \]

   if 1.02e-235 < (*.f64 b c) < 1.12e-39

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 35.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.2%

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. *-commutative 35.2%

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} \]

   7. Simplified 35.2%

      \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.15 \cdot 10^{+231}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.12 \cdot 10^{-39}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+261}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.8 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9 \cdot 10^{-64}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)))
   (if (<= (* b c) -1.25e+261)
     (* b c)
     (if (<= (* b c) -5.8e-213)
       t_1
       (if (<= (* b c) 9e-64)
         (* 18.0 (* t (* x (* y z))))
         (if (<= (* b c) 3.1e+88) t_1 (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double tmp;
	if ((b * c) <= -1.25e+261) {
		tmp = b * c;
	} else if ((b * c) <= -5.8e-213) {
		tmp = t_1;
	} else if ((b * c) <= 9e-64) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 3.1e+88) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    if ((b * c) <= (-1.25d+261)) then
        tmp = b * c
    else if ((b * c) <= (-5.8d-213)) then
        tmp = t_1
    else if ((b * c) <= 9d-64) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= 3.1d+88) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double tmp;
	if ((b * c) <= -1.25e+261) {
		tmp = b * c;
	} else if ((b * c) <= -5.8e-213) {
		tmp = t_1;
	} else if ((b * c) <= 9e-64) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 3.1e+88) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	tmp = 0
	if (b * c) <= -1.25e+261:
		tmp = b * c
	elif (b * c) <= -5.8e-213:
		tmp = t_1
	elif (b * c) <= 9e-64:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= 3.1e+88:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	tmp = 0.0
	if (Float64(b * c) <= -1.25e+261)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5.8e-213)
		tmp = t_1;
	elseif (Float64(b * c) <= 9e-64)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 3.1e+88)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	tmp = 0.0;
	if ((b * c) <= -1.25e+261)
		tmp = b * c;
	elseif ((b * c) <= -5.8e-213)
		tmp = t_1;
	elseif ((b * c) <= 9e-64)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= 3.1e+88)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+261], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.8e-213], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9e-64], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.1e+88], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.25e261 or 3.1000000000000001e88 < (*.f64 b c)

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 87.0%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 69.0%

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

   if -1.25e261 < (*.f64 b c) < -5.7999999999999999e-213 or 9.00000000000000019e-64 < (*.f64 b c) < 3.1000000000000001e88

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.4%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

   6. Simplified 38.0%

      \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot -4} \]

   if -5.7999999999999999e-213 < (*.f64 b c) < 9.00000000000000019e-64

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.6%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in y around inf 38.6%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+261}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.8 \cdot 10^{-213}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 9 \cdot 10^{-64}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{+88}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+261}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.3 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-61}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)))
   (if (<= (* b c) -1.25e+261)
     (* b c)
     (if (<= (* b c) -1.3e-217)
       t_1
       (if (<= (* b c) 7.5e-61)
         (* 18.0 (* (* y z) (* x t)))
         (if (<= (* b c) 4.3e+88) t_1 (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double tmp;
	if ((b * c) <= -1.25e+261) {
		tmp = b * c;
	} else if ((b * c) <= -1.3e-217) {
		tmp = t_1;
	} else if ((b * c) <= 7.5e-61) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if ((b * c) <= 4.3e+88) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    if ((b * c) <= (-1.25d+261)) then
        tmp = b * c
    else if ((b * c) <= (-1.3d-217)) then
        tmp = t_1
    else if ((b * c) <= 7.5d-61) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if ((b * c) <= 4.3d+88) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double tmp;
	if ((b * c) <= -1.25e+261) {
		tmp = b * c;
	} else if ((b * c) <= -1.3e-217) {
		tmp = t_1;
	} else if ((b * c) <= 7.5e-61) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if ((b * c) <= 4.3e+88) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	tmp = 0
	if (b * c) <= -1.25e+261:
		tmp = b * c
	elif (b * c) <= -1.3e-217:
		tmp = t_1
	elif (b * c) <= 7.5e-61:
		tmp = 18.0 * ((y * z) * (x * t))
	elif (b * c) <= 4.3e+88:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	tmp = 0.0
	if (Float64(b * c) <= -1.25e+261)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.3e-217)
		tmp = t_1;
	elseif (Float64(b * c) <= 7.5e-61)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (Float64(b * c) <= 4.3e+88)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	tmp = 0.0;
	if ((b * c) <= -1.25e+261)
		tmp = b * c;
	elseif ((b * c) <= -1.3e-217)
		tmp = t_1;
	elseif ((b * c) <= 7.5e-61)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif ((b * c) <= 4.3e+88)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+261], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.3e-217], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 7.5e-61], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.3e+88], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.25e261 or 4.29999999999999974e88 < (*.f64 b c)

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 87.0%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 69.0%

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

   if -1.25e261 < (*.f64 b c) < -1.29999999999999997e-217 or 7.50000000000000047e-61 < (*.f64 b c) < 4.29999999999999974e88

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.4%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

   6. Simplified 38.0%

      \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot -4} \]

   if -1.29999999999999997e-217 < (*.f64 b c) < 7.50000000000000047e-61

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.6%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 89.7%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(4 \cdot t + 27 \cdot \frac{j \cdot k}{a}\right)} \]

   5. Taylor expanded in a around inf 80.0%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 80.0%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(a \cdot t\right) \cdot 4} \]

      2. associate-*r* 80.0%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(t \cdot 4\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(t \cdot 4\right) \cdot a} \]

      4. associate-*l* 80.0%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 80.0%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   8. Taylor expanded in y around inf 38.6%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.6%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

   10. Simplified 42.6%

       \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+261}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.3 \cdot 10^{-217}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-61}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{+88}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+153}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* t (* a -4.0)))))
   (if (<= t -7.2e+153)
     (+ (* 18.0 (* (* y z) (* x t))) t_1)
     (if (<= t -1.5e+103)
       t_2
       (if (<= t 1.2e+84)
         (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))
         (if (<= t 1.8e+226)
           (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (t * (a * -4.0));
	double tmp;
	if (t <= -7.2e+153) {
		tmp = (18.0 * ((y * z) * (x * t))) + t_1;
	} else if (t <= -1.5e+103) {
		tmp = t_2;
	} else if (t <= 1.2e+84) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else if (t <= 1.8e+226) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (t * (a * (-4.0d0)))
    if (t <= (-7.2d+153)) then
        tmp = (18.0d0 * ((y * z) * (x * t))) + t_1
    else if (t <= (-1.5d+103)) then
        tmp = t_2
    else if (t <= 1.2d+84) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    else if (t <= 1.8d+226) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (t * (a * -4.0));
	double tmp;
	if (t <= -7.2e+153) {
		tmp = (18.0 * ((y * z) * (x * t))) + t_1;
	} else if (t <= -1.5e+103) {
		tmp = t_2;
	} else if (t <= 1.2e+84) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else if (t <= 1.8e+226) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (t * (a * -4.0))
	tmp = 0
	if t <= -7.2e+153:
		tmp = (18.0 * ((y * z) * (x * t))) + t_1
	elif t <= -1.5e+103:
		tmp = t_2
	elif t <= 1.2e+84:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	elif t <= 1.8e+226:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(t * Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -7.2e+153)
		tmp = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + t_1);
	elseif (t <= -1.5e+103)
		tmp = t_2;
	elseif (t <= 1.2e+84)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	elseif (t <= 1.8e+226)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (t * (a * -4.0));
	tmp = 0.0;
	if (t <= -7.2e+153)
		tmp = (18.0 * ((y * z) * (x * t))) + t_1;
	elseif (t <= -1.5e+103)
		tmp = t_2;
	elseif (t <= 1.2e+84)
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	elseif (t <= 1.8e+226)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+153], N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -1.5e+103], t$95$2, If[LessEqual[t, 1.2e+84], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+226], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2000000000000001e153

   1. Initial program 74.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.0%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 69.0%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -7.2000000000000001e153 < t < -1.5e103 or 1.7999999999999999e226 < t

   1. Initial program 84.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 81.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 81.6%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 81.6%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 81.6%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 81.6%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 81.6%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 81.6%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 81.6%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 81.6%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if -1.5e103 < t < 1.2e84

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 78.9%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if 1.2e84 < t < 1.7999999999999999e226

   1. Initial program 77.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.1%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+153}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+161}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + t\_1\\ \mathbf{elif}\;t \leq -108:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + t\_2\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* 4.0 (* x i))))
   (if (<= t -1.65e+161)
     (+ (* 18.0 (* (* y z) (* x t))) t_1)
     (if (<= t -108.0)
       (- (+ (* b c) (* (* t a) -4.0)) t_2)
       (if (<= t 2.2e+83)
         (- (* b c) (+ (* 27.0 (* j k)) t_2))
         (if (<= t 1.65e+228)
           (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
           (+ t_1 (* t (* a -4.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -1.65e+161) {
		tmp = (18.0 * ((y * z) * (x * t))) + t_1;
	} else if (t <= -108.0) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else if (t <= 2.2e+83) {
		tmp = (b * c) - ((27.0 * (j * k)) + t_2);
	} else if (t <= 1.65e+228) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = t_1 + (t * (a * -4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = 4.0d0 * (x * i)
    if (t <= (-1.65d+161)) then
        tmp = (18.0d0 * ((y * z) * (x * t))) + t_1
    else if (t <= (-108.0d0)) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_2
    else if (t <= 2.2d+83) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + t_2)
    else if (t <= 1.65d+228) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = t_1 + (t * (a * (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -1.65e+161) {
		tmp = (18.0 * ((y * z) * (x * t))) + t_1;
	} else if (t <= -108.0) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else if (t <= 2.2e+83) {
		tmp = (b * c) - ((27.0 * (j * k)) + t_2);
	} else if (t <= 1.65e+228) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = t_1 + (t * (a * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = 4.0 * (x * i)
	tmp = 0
	if t <= -1.65e+161:
		tmp = (18.0 * ((y * z) * (x * t))) + t_1
	elif t <= -108.0:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2
	elif t <= 2.2e+83:
		tmp = (b * c) - ((27.0 * (j * k)) + t_2)
	elif t <= 1.65e+228:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = t_1 + (t * (a * -4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -1.65e+161)
		tmp = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + t_1);
	elseif (t <= -108.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_2);
	elseif (t <= 2.2e+83)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + t_2));
	elseif (t <= 1.65e+228)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -1.65e+161)
		tmp = (18.0 * ((y * z) * (x * t))) + t_1;
	elseif (t <= -108.0)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	elseif (t <= 2.2e+83)
		tmp = (b * c) - ((27.0 * (j * k)) + t_2);
	elseif (t <= 1.65e+228)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = t_1 + (t * (a * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+161], N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -108.0], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 2.2e+83], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+228], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.64999999999999999e161

   1. Initial program 72.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 70.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 70.2%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 70.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -1.64999999999999999e161 < t < -108

   1. Initial program 96.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 85.0%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in y around 0 82.1%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)} \]

   if -108 < t < 2.19999999999999999e83

   1. Initial program 87.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 79.9%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if 2.19999999999999999e83 < t < 1.65000000000000003e228

   1. Initial program 77.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.1%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if 1.65000000000000003e228 < t

   1. Initial program 78.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 79.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 79.3%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      3. metadata-eval 79.3%

         \[\leadsto \left(a \cdot \color{blue}{\left(-4\right)}\right) \cdot t + j \cdot \left(k \cdot -27\right) \]

      4. distribute-rgt-neg-in 79.3%

         \[\leadsto \color{blue}{\left(-a \cdot 4\right)} \cdot t + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 79.3%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot 4\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-rgt-neg-in 79.3%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-4\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      7. metadata-eval 79.3%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{-4}\right) + j \cdot \left(k \cdot -27\right) \]

      8. *-commutative 79.3%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 79.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+161}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -108:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.95 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -2.95e+144)
     t_2
     (if (<= t 3.5e+50)
       (- (+ (* b c) (* (* t a) -4.0)) (+ (* 27.0 (* j k)) t_1))
       (- t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -2.95e+144) {
		tmp = t_2;
	} else if (t <= 3.5e+50) {
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-2.95d+144)) then
        tmp = t_2
    else if (t <= 3.5d+50) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - ((27.0d0 * (j * k)) + t_1)
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -2.95e+144) {
		tmp = t_2;
	} else if (t <= 3.5e+50) {
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -2.95e+144:
		tmp = t_2
	elif t <= 3.5e+50:
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1)
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -2.95e+144)
		tmp = t_2;
	elseif (t <= 3.5e+50)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(Float64(27.0 * Float64(j * k)) + t_1));
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -2.95e+144)
		tmp = t_2;
	elseif (t <= 3.5e+50)
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + t_1);
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.95e+144], t$95$2, If[LessEqual[t, 3.5e+50], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.94999999999999994e144

   1. Initial program 72.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 81.5%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in i around 0 84.2%

      \[\leadsto \color{blue}{b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -2.94999999999999994e144 < t < 3.50000000000000006e50

   1. Initial program 90.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 88.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if 3.50000000000000006e50 < t

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 85.7%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-6}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -4.2e+130)
     t_2
     (if (<= t -8e-6)
       (- (+ (* b c) (* (* t a) -4.0)) t_1)
       (if (<= t 2.5e+49) (- (* b c) (+ (* 27.0 (* j k)) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -4.2e+130) {
		tmp = t_2;
	} else if (t <= -8e-6) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (t <= 2.5e+49) {
		tmp = (b * c) - ((27.0 * (j * k)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-4.2d+130)) then
        tmp = t_2
    else if (t <= (-8d-6)) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_1
    else if (t <= 2.5d+49) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -4.2e+130) {
		tmp = t_2;
	} else if (t <= -8e-6) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (t <= 2.5e+49) {
		tmp = (b * c) - ((27.0 * (j * k)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -4.2e+130:
		tmp = t_2
	elif t <= -8e-6:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1
	elif t <= 2.5e+49:
		tmp = (b * c) - ((27.0 * (j * k)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -4.2e+130)
		tmp = t_2;
	elseif (t <= -8e-6)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_1);
	elseif (t <= 2.5e+49)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -4.2e+130)
		tmp = t_2;
	elseif (t <= -8e-6)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	elseif (t <= 2.5e+49)
		tmp = (b * c) - ((27.0 * (j * k)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+130], t$95$2, If[LessEqual[t, -8e-6], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.5e+49], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.19999999999999981e130 or 2.5000000000000002e49 < t

   1. Initial program 77.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 83.4%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in i around 0 80.8%

      \[\leadsto \color{blue}{b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -4.19999999999999981e130 < t < -7.99999999999999964e-6

   1. Initial program 99.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 85.6%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in y around 0 85.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)} \]

   if -7.99999999999999964e-6 < t < 2.5000000000000002e49

   1. Initial program 87.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.1%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-6}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+136} \lor \neg \left(t \leq 5.5 \cdot 10^{+106}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.05e+136) (not (<= t 5.5e+106)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (+ (* b c) (* (* t a) -4.0)) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.05e+136) || !(t <= 5.5e+106)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-2.05d+136)) .or. (.not. (t <= 5.5d+106))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.05e+136) || !(t <= 5.5e+106)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -2.05e+136) or not (t <= 5.5e+106):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.05e+136) || !(t <= 5.5e+106))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -2.05e+136) || ~((t <= 5.5e+106)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = ((b * c) + ((t * a) * -4.0)) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.05e+136], N[Not[LessEqual[t, 5.5e+106]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0499999999999999e136 or 5.5e106 < t

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 83.4%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in i around 0 83.7%

      \[\leadsto \color{blue}{b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -2.0499999999999999e136 < t < 5.5e106

   1. Initial program 90.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 88.1%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+136} \lor \neg \left(t \leq 5.5 \cdot 10^{+106}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-25} \lor \neg \left(x \leq 3500000000000\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.35e-25) (not (<= x 3500000000000.0)))
   (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
   (- (+ (* b c) (* (* t a) -4.0)) (* 27.0 (* j k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.35e-25) || !(x <= 3500000000000.0)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-1.35d-25)) .or. (.not. (x <= 3500000000000.0d0))) then
        tmp = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    else
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.35e-25) || !(x <= 3500000000000.0)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.35e-25) or not (x <= 3500000000000.0):
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	else:
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.35e-25) || !(x <= 3500000000000.0))
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.35e-25) || ~((x <= 3500000000000.0)))
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	else
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.35e-25], N[Not[LessEqual[x, 3500000000000.0]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000008e-25 or 3.5e12 < x

   1. Initial program 75.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 87.3%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 86.6%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(4 \cdot t + 27 \cdot \frac{j \cdot k}{a}\right)} \]

   5. Taylor expanded in a around inf 85.7%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(a \cdot t\right) \cdot 4} \]

      2. associate-*r* 85.7%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(t \cdot 4\right)} \]

      3. *-commutative 85.7%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{\left(t \cdot 4\right) \cdot a} \]

      4. associate-*l* 85.7%

         \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 85.7%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   8. Taylor expanded in a around 0 82.3%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -1.35000000000000008e-25 < x < 3.5e12

   1. Initial program 95.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-25} \lor \neg \left(x \leq 3500000000000\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+68} \lor \neg \left(x \leq 3.6 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.6e+68) (not (<= x 3.6e+88)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (+ (* b c) (* (* t a) -4.0)) (* 27.0 (* j k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.6e+68) || !(x <= 3.6e+88)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2.6d+68)) .or. (.not. (x <= 3.6d+88))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.6e+68) || !(x <= 3.6e+88)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2.6e+68) or not (x <= 3.6e+88):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.6e+68) || !(x <= 3.6e+88))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2.6e+68) || ~((x <= 3.6e+88)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.6e+68], N[Not[LessEqual[x, 3.6e+88]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999998e68 or 3.6000000000000002e88 < x

   1. Initial program 67.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.9%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -2.5999999999999998e68 < x < 3.6000000000000002e88

   1. Initial program 95.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.8%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+68} \lor \neg \left(x \leq 3.6 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))))
   (if (<= a -5.6e+91)
     t_1
     (if (<= a 1.45e+16)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= a 4.2e+88) (* 18.0 (* y (* x (* z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (a <= -5.6e+91) {
		tmp = t_1;
	} else if (a <= 1.45e+16) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (a <= 4.2e+88) {
		tmp = 18.0 * (y * (x * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((t * a) * (-4.0d0))
    if (a <= (-5.6d+91)) then
        tmp = t_1
    else if (a <= 1.45d+16) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (a <= 4.2d+88) then
        tmp = 18.0d0 * (y * (x * (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (a <= -5.6e+91) {
		tmp = t_1;
	} else if (a <= 1.45e+16) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (a <= 4.2e+88) {
		tmp = 18.0 * (y * (x * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + ((t * a) * -4.0)
	tmp = 0
	if a <= -5.6e+91:
		tmp = t_1
	elif a <= 1.45e+16:
		tmp = (b * c) + (j * (k * -27.0))
	elif a <= 4.2e+88:
		tmp = 18.0 * (y * (x * (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (a <= -5.6e+91)
		tmp = t_1;
	elseif (a <= 1.45e+16)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (a <= 4.2e+88)
		tmp = Float64(18.0 * Float64(y * Float64(x * Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	tmp = 0.0;
	if (a <= -5.6e+91)
		tmp = t_1;
	elseif (a <= 1.45e+16)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (a <= 4.2e+88)
		tmp = 18.0 * (y * (x * (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+91], t$95$1, If[LessEqual[a, 1.45e+16], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+88], N[(18.0 * N[(y * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.5999999999999997e91 or 4.2e88 < a

   1. Initial program 82.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 81.5%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in x around 0 61.9%

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

   if -5.5999999999999997e91 < a < 1.45e16

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 53.3%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 1.45e16 < a < 4.2e88

   1. Initial program 70.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 82.2%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(4 \cdot t + 27 \cdot \frac{j \cdot k}{a}\right)} \]

   5. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto 18 \cdot \left(\left(t \cdot x\right) \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

      3. associate-*r* 55.3%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} \]

      4. associate-*r* 55.3%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot z\right)\right)} \cdot y\right) \]

      5. *-commutative 55.3%

         \[\leadsto 18 \cdot \left(\left(t \cdot \color{blue}{\left(z \cdot x\right)}\right) \cdot y\right) \]

      6. associate-*r* 55.2%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot y\right) \]

   7. Simplified 55.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(\left(t \cdot z\right) \cdot x\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 50.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))))
   (if (<= a -3.3e+91)
     t_1
     (if (<= a 8e+15)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= a 1.1e+90) (* 18.0 (* y (* x (* z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (a <= -3.3e+91) {
		tmp = t_1;
	} else if (a <= 8e+15) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (a <= 1.1e+90) {
		tmp = 18.0 * (y * (x * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((t * a) * (-4.0d0))
    if (a <= (-3.3d+91)) then
        tmp = t_1
    else if (a <= 8d+15) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (a <= 1.1d+90) then
        tmp = 18.0d0 * (y * (x * (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double tmp;
	if (a <= -3.3e+91) {
		tmp = t_1;
	} else if (a <= 8e+15) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (a <= 1.1e+90) {
		tmp = 18.0 * (y * (x * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + ((t * a) * -4.0)
	tmp = 0
	if a <= -3.3e+91:
		tmp = t_1
	elif a <= 8e+15:
		tmp = (b * c) - (27.0 * (j * k))
	elif a <= 1.1e+90:
		tmp = 18.0 * (y * (x * (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (a <= -3.3e+91)
		tmp = t_1;
	elseif (a <= 8e+15)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (a <= 1.1e+90)
		tmp = Float64(18.0 * Float64(y * Float64(x * Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	tmp = 0.0;
	if (a <= -3.3e+91)
		tmp = t_1;
	elseif (a <= 8e+15)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (a <= 1.1e+90)
		tmp = 18.0 * (y * (x * (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+91], t$95$1, If[LessEqual[a, 8e+15], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+90], N[(18.0 * N[(y * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.30000000000000017e91 or 1.09999999999999995e90 < a

   1. Initial program 82.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 81.5%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   6. Taylor expanded in x around 0 61.9%

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

   if -3.30000000000000017e91 < a < 8e15

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.2%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Taylor expanded in i around 0 53.4%

      \[\leadsto \color{blue}{b \cdot c - 27 \cdot \left(j \cdot k\right)} \]

   if 8e15 < a < 1.09999999999999995e90

   1. Initial program 70.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in a around inf 82.2%

      \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \color{blue}{a \cdot \left(4 \cdot t + 27 \cdot \frac{j \cdot k}{a}\right)} \]

   5. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

      2. *-commutative 60.4%

         \[\leadsto 18 \cdot \left(\left(t \cdot x\right) \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

      3. associate-*r* 55.3%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} \]

      4. associate-*r* 55.3%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot z\right)\right)} \cdot y\right) \]

      5. *-commutative 55.3%

         \[\leadsto 18 \cdot \left(\left(t \cdot \color{blue}{\left(z \cdot x\right)}\right) \cdot y\right) \]

      6. associate-*r* 55.2%

         \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot y\right) \]

   7. Simplified 55.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(\left(t \cdot z\right) \cdot x\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+91}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.75 \cdot 10^{+45} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+166}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.75e+45) (not (<= (* b c) 5e+166)))
   (* b c)
   (* (* j k) -27.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.75e+45) || !((b * c) <= 5e+166)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.75d+45)) .or. (.not. ((b * c) <= 5d+166))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.75e+45) || !((b * c) <= 5e+166)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.75e+45) or not ((b * c) <= 5e+166):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.75e+45) || !(Float64(b * c) <= 5e+166))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.75e+45) || ~(((b * c) <= 5e+166)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.75e+45], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5e+166]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.75e45 or 5.0000000000000002e166 < (*.f64 b c)

   1. Initial program 80.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.1%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 60.2%

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

   if -2.75e45 < (*.f64 b c) < 5.0000000000000002e166

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 22.6%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.75 \cdot 10^{+45} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+166}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 23.7% accurate, 10.3× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 84.9%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in x around 0 89.1%

   \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

4. Taylor expanded in b around inf 25.2%

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

5. Final simplification 25.2%

   \[\leadsto b \cdot c \]
6. Add Preprocessing

Developer target: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))