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

Percentage Accurate: 85.4% → 91.9%

Time: 19.6s

Alternatives: 23

Speedup: 0.8×

• 50.5% 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: 85.4% 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: 91.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY) t_1 (* x (+ (* 18.0 (* z (* y t))) (* i -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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	}
	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) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 97.8%

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

   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 19.4%

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

   5. Taylor expanded in y around inf 16.1%

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

   6. Taylor expanded in x around inf 67.8%

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

      1. cancel-sign-sub-inv 67.8%

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

      2. associate-*r* 67.8%

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

      3. metadata-eval 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 94.2%

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

Alternative 2: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+139} \lor \neg \left(t\_1 \leq 3.2 \cdot 10^{-31}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+139) (not (<= t_1 3.2e-31)))
     (- (+ (* b c) (* -4.0 (* x i))) (+ (* 4.0 (* t a)) (* 27.0 (* j k))))
     (-
      (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
      (* 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 t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+139) || !(t_1 <= 3.2e-31)) {
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+139)) .or. (.not. (t_1 <= 3.2d-31))) then
        tmp = ((b * c) + ((-4.0d0) * (x * i))) - ((4.0d0 * (t * a)) + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (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 t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+139) || !(t_1 <= 3.2e-31)) {
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+139) or not (t_1 <= 3.2e-31):
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+139) || !(t_1 <= 3.2e-31))
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - 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)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+139) || ~((t_1 <= 3.2e-31)))
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+139], N[Not[LessEqual[t$95$1, 3.2e-31]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000007e139 or 3.20000000000000018e-31 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.3%

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

   3. Taylor expanded in x around 0 81.4%

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

   4. Taylor expanded in y around 0 85.8%

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

   if -2.00000000000000007e139 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.20000000000000018e-31

   1. Initial program 88.8%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in j around 0 89.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+139} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 3.2 \cdot 10^{-31}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 10^{+235}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{j}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* (* j 27.0) k) 1e+235)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* j (+ (* k -27.0) (* 18.0 (/ (* t (* x (* y z))) j))))))

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 (((j * 27.0) * k) <= 1e+235) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)));
	}
	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 (((j * 27.0d0) * k) <= 1d+235) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = j * ((k * (-27.0d0)) + (18.0d0 * ((t * (x * (y * z))) / j)))
    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 (((j * 27.0) * k) <= 1e+235) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((j * 27.0) * k) <= 1e+235:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(j * 27.0) * k) <= 1e+235)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(j * Float64(Float64(k * -27.0) + Float64(18.0 * Float64(Float64(t * Float64(x * Float64(y * z))) / j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((j * 27.0) * k) <= 1e+235)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision], 1e+235], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(k * -27.0), $MachinePrecision] + N[(18.0 * N[(N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e235

   1. Initial program 86.8%

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

   3. Simplified 88.6%

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

   if 1.0000000000000001e235 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.6%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in j around inf 89.5%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{j}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 10^{+235}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{j}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 10^{+235}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{j}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* (* j 27.0) k) 1e+235)
   (-
    (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
    (+ (* 4.0 (* t a)) (* 27.0 (* j k))))
   (* j (+ (* k -27.0) (* 18.0 (/ (* t (* x (* y z))) j))))))

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 (((j * 27.0) * k) <= 1e+235) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)));
	}
	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 (((j * 27.0d0) * k) <= 1d+235) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - ((4.0d0 * (t * a)) + (27.0d0 * (j * k)))
    else
        tmp = j * ((k * (-27.0d0)) + (18.0d0 * ((t * (x * (y * z))) / j)))
    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 (((j * 27.0) * k) <= 1e+235) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((j * 27.0) * k) <= 1e+235:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	else:
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(j * 27.0) * k) <= 1e+235)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(j * Float64(Float64(k * -27.0) + Float64(18.0 * Float64(Float64(t * Float64(x * Float64(y * z))) / j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((j * 27.0) * k) <= 1e+235)
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	else
		tmp = j * ((k * -27.0) + (18.0 * ((t * (x * (y * z))) / j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision], 1e+235], 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[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(k * -27.0), $MachinePrecision] + N[(18.0 * N[(N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e235

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0 88.2%

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

   if 1.0000000000000001e235 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.6%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in j around inf 89.5%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{j}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 10^{+235}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{j}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+155}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -7.8e+123)
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
   (if (<= x 2.8e+155)
     (- (+ (* b c) (* -4.0 (* x i))) (+ (* 4.0 (* t a)) (* 27.0 (* j k))))
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 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 (x <= -7.8e+123) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 2.8e+155) {
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * 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 (x <= (-7.8d+123)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= 2.8d+155) then
        tmp = ((b * c) + ((-4.0d0) * (x * i))) - ((4.0d0 * (t * a)) + (27.0d0 * (j * k)))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * 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 (x <= -7.8e+123) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 2.8e+155) {
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -7.8e+123:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= 2.8e+155:
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -7.8e+123)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= 2.8e+155)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -7.8e+123)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= 2.8e+155)
		tmp = ((b * c) + (-4.0 * (x * i))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -7.8e+123], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+155], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.79999999999999986e123

   1. Initial program 73.2%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 70.6%

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

   6. Taylor expanded in x around inf 84.3%

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

      1. cancel-sign-sub-inv 84.3%

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

      2. associate-*r* 84.3%

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

      3. metadata-eval 84.3%

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

   8. Simplified 84.3%

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

   if -7.79999999999999986e123 < x < 2.80000000000000016e155

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0 86.9%

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

   4. Taylor expanded in y around 0 83.1%

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

   if 2.80000000000000016e155 < x

   1. Initial program 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x around inf 78.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+155}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+134}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -2.7e+51)
     (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
     (if (<= x 1.55e-10)
       (+ (* b c) t_1)
       (if (<= x 9.2e+134)
         (+ t_1 (* 18.0 (* t (* x (* y z)))))
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 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 t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -2.7e+51) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 1.55e-10) {
		tmp = (b * c) + t_1;
	} else if (x <= 9.2e+134) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * 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) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-2.7d+51)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= 1.55d-10) then
        tmp = (b * c) + t_1
    else if (x <= 9.2d+134) then
        tmp = t_1 + (18.0d0 * (t * (x * (y * z))))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * 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 t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -2.7e+51) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 1.55e-10) {
		tmp = (b * c) + t_1;
	} else if (x <= 9.2e+134) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if x <= -2.7e+51:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= 1.55e-10:
		tmp = (b * c) + t_1
	elif x <= 9.2e+134:
		tmp = t_1 + (18.0 * (t * (x * (y * z))))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	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 (x <= -2.7e+51)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= 1.55e-10)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 9.2e+134)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	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 (x <= -2.7e+51)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= 1.55e-10)
		tmp = (b * c) + t_1;
	elseif (x <= 9.2e+134)
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	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[x, -2.7e+51], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-10], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 9.2e+134], N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.69999999999999992e51

   1. Initial program 75.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 72.3%

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

   6. Taylor expanded in x around inf 72.6%

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

      1. cancel-sign-sub-inv 72.6%

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

      2. associate-*r* 72.6%

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

      3. metadata-eval 72.6%

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

   8. Simplified 72.6%

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

   if -2.69999999999999992e51 < x < 1.55000000000000008e-10

   1. Initial program 92.7%

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

   3. Simplified 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 b around inf 63.7%

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

   if 1.55000000000000008e-10 < x < 9.1999999999999992e134

   1. Initial program 88.9%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 71.5%

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

      1. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   if 9.1999999999999992e134 < x

   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 78.9%

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

   5. Taylor expanded in 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 4 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -1.35 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -7.1 \cdot 10^{-308}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-267}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= k -1.35e-139)
     t_1
     (if (<= k -7.1e-308)
       (- (* b c) (* 4.0 (* x i)))
       (if (<= k 7.6e-267)
         (* (* y z) (* 18.0 (* x t)))
         (if (<= k 1.25e+101) (+ (* b c) (* -4.0 (* t a))) 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) + (j * (k * -27.0));
	double tmp;
	if (k <= -1.35e-139) {
		tmp = t_1;
	} else if (k <= -7.1e-308) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 7.6e-267) {
		tmp = (y * z) * (18.0 * (x * t));
	} else if (k <= 1.25e+101) {
		tmp = (b * c) + (-4.0 * (t * a));
	} 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) + (j * (k * (-27.0d0)))
    if (k <= (-1.35d-139)) then
        tmp = t_1
    else if (k <= (-7.1d-308)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (k <= 7.6d-267) then
        tmp = (y * z) * (18.0d0 * (x * t))
    else if (k <= 1.25d+101) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    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) + (j * (k * -27.0));
	double tmp;
	if (k <= -1.35e-139) {
		tmp = t_1;
	} else if (k <= -7.1e-308) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 7.6e-267) {
		tmp = (y * z) * (18.0 * (x * t));
	} else if (k <= 1.25e+101) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if k <= -1.35e-139:
		tmp = t_1
	elif k <= -7.1e-308:
		tmp = (b * c) - (4.0 * (x * i))
	elif k <= 7.6e-267:
		tmp = (y * z) * (18.0 * (x * t))
	elif k <= 1.25e+101:
		tmp = (b * c) + (-4.0 * (t * a))
	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(j * Float64(k * -27.0)))
	tmp = 0.0
	if (k <= -1.35e-139)
		tmp = t_1;
	elseif (k <= -7.1e-308)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (k <= 7.6e-267)
		tmp = Float64(Float64(y * z) * Float64(18.0 * Float64(x * t)));
	elseif (k <= 1.25e+101)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	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) + (j * (k * -27.0));
	tmp = 0.0;
	if (k <= -1.35e-139)
		tmp = t_1;
	elseif (k <= -7.1e-308)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (k <= 7.6e-267)
		tmp = (y * z) * (18.0 * (x * t));
	elseif (k <= 1.25e+101)
		tmp = (b * c) + (-4.0 * (t * a));
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.35e-139], t$95$1, If[LessEqual[k, -7.1e-308], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.6e-267], N[(N[(y * z), $MachinePrecision] * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.25e+101], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.3499999999999999e-139 or 1.24999999999999997e101 < k

   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 87.4%

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

   5. Taylor expanded in b around inf 55.6%

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

   if -1.3499999999999999e-139 < k < -7.10000000000000005e-308

   1. Initial program 90.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around 0 52.5%

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

   6. Taylor expanded in i around inf 52.5%

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

      1. *-commutative 52.5%

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

   8. Simplified 52.5%

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

   if -7.10000000000000005e-308 < k < 7.60000000000000006e-267

   1. Initial program 60.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in y around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in x around inf 60.5%

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

      1. associate-*r* 60.5%

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

      2. associate-*r* 60.5%

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

   10. Simplified 60.5%

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

   if 7.60000000000000006e-267 < k < 1.24999999999999997e101

   1. Initial program 85.3%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around 0 66.4%

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

   6. Taylor expanded in j around 0 57.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-139}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -7.1 \cdot 10^{-308}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-267}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \leq -0.00087:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-232} \lor \neg \left(a \leq 3.9 \cdot 10^{+262}\right):\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= a -0.00087)
     (+ (* b c) (* -4.0 (* t a)))
     (if (or (<= a -1.05e-232) (not (<= a 3.9e+262)))
       (+ t_1 (* x (* i -4.0)))
       (+ (* 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 (a <= -0.00087) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((a <= -1.05e-232) || !(a <= 3.9e+262)) {
		tmp = t_1 + (x * (i * -4.0));
	} 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 (a <= (-0.00087d0)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if ((a <= (-1.05d-232)) .or. (.not. (a <= 3.9d+262))) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    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 (a <= -0.00087) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((a <= -1.05e-232) || !(a <= 3.9e+262)) {
		tmp = t_1 + (x * (i * -4.0));
	} 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 a <= -0.00087:
		tmp = (b * c) + (-4.0 * (t * a))
	elif (a <= -1.05e-232) or not (a <= 3.9e+262):
		tmp = t_1 + (x * (i * -4.0))
	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 (a <= -0.00087)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif ((a <= -1.05e-232) || !(a <= 3.9e+262))
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	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 (a <= -0.00087)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif ((a <= -1.05e-232) || ~((a <= 3.9e+262)))
		tmp = t_1 + (x * (i * -4.0));
	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[a, -0.00087], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.05e-232], N[Not[LessEqual[a, 3.9e+262]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.70000000000000005e-4

   1. Initial program 86.3%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 74.6%

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

   6. Taylor expanded in j around 0 66.1%

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

   if -8.70000000000000005e-4 < a < -1.05e-232 or 3.89999999999999985e262 < a

   1. Initial program 88.2%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in i around inf 61.3%

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

      1. *-commutative 61.3%

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

      2. *-commutative 61.3%

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

      3. associate-*l* 61.3%

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

      4. *-commutative 61.3%

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

   7. Simplified 61.3%

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

   if -1.05e-232 < a < 3.89999999999999985e262

   1. Initial program 85.0%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in b around inf 58.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00087:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-232} \lor \neg \left(a \leq 3.9 \cdot 10^{+262}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 31.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+15}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.35e-103)
   (* j (* k -27.0))
   (if (<= k -2.4e-223)
     (* b c)
     (if (<= k 8e+15)
       (* 18.0 (* t (* x (* y z))))
       (if (<= k 2.25e+108) (* x (* i -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 (k <= -1.35e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= -2.4e-223) {
		tmp = b * c;
	} else if (k <= 8e+15) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (k <= 2.25e+108) {
		tmp = x * (i * -4.0);
	} else {
		tmp = -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 (k <= (-1.35d-103)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= (-2.4d-223)) then
        tmp = b * c
    else if (k <= 8d+15) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (k <= 2.25d+108) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = (-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 (k <= -1.35e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= -2.4e-223) {
		tmp = b * c;
	} else if (k <= 8e+15) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (k <= 2.25e+108) {
		tmp = x * (i * -4.0);
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.35e-103:
		tmp = j * (k * -27.0)
	elif k <= -2.4e-223:
		tmp = b * c
	elif k <= 8e+15:
		tmp = 18.0 * (t * (x * (y * z)))
	elif k <= 2.25e+108:
		tmp = x * (i * -4.0)
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.35e-103)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= -2.4e-223)
		tmp = Float64(b * c);
	elseif (k <= 8e+15)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (k <= 2.25e+108)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = 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 (k <= -1.35e-103)
		tmp = j * (k * -27.0);
	elseif (k <= -2.4e-223)
		tmp = b * c;
	elseif (k <= 8e+15)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (k <= 2.25e+108)
		tmp = x * (i * -4.0);
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.35e-103], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.4e-223], N[(b * c), $MachinePrecision], If[LessEqual[k, 8e+15], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.25e+108], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.35000000000000005e-103

   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 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 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-*r* 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if -1.35000000000000005e-103 < k < -2.39999999999999985e-223

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in b around inf 47.1%

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

   if -2.39999999999999985e-223 < k < 8e15

   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 85.9%

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

   4. Taylor expanded in y around inf 28.3%

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

   if 8e15 < k < 2.25e108

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 85.7%

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

   4. Taylor expanded in i around inf 33.4%

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

      1. associate-*r* 33.4%

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

      2. *-commutative 33.4%

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

   6. Simplified 33.4%

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

   if 2.25e108 < k

   1. Initial program 82.9%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in j around inf 50.4%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+15}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+117} \lor \neg \left(t \leq 1.15 \cdot 10^{+120}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -4e+117) (not (<= t 1.15e+120)))
   (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))
   (- (* b c) (+ (* 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 <= -4e+117) || !(t <= 1.15e+120)) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else {
		tmp = (b * c) - ((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 <= (-4d+117)) .or. (.not. (t <= 1.15d+120))) then
        tmp = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    else
        tmp = (b * c) - ((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 <= -4e+117) || !(t <= 1.15e+120)) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else {
		tmp = (b * c) - ((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 <= -4e+117) or not (t <= 1.15e+120):
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	else:
		tmp = (b * c) - ((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 <= -4e+117) || !(t <= 1.15e+120))
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)));
	else
		tmp = Float64(Float64(b * c) - 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 <= -4e+117) || ~((t <= 1.15e+120)))
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	else
		tmp = (b * c) - ((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, -4e+117], N[Not[LessEqual[t, 1.15e+120]], $MachinePrecision]], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $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 < -4.0000000000000002e117 or 1.14999999999999996e120 < t

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 74.2%

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

   4. Taylor expanded in t around inf 75.1%

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

      1. cancel-sign-sub-inv 75.1%

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

      2. metadata-eval 75.1%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if -4.0000000000000002e117 < t < 1.14999999999999996e120

   1. Initial program 90.3%

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

   3. Simplified 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 t around 0 76.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+117} \lor \neg \left(t \leq 1.15 \cdot 10^{+120}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -7e+89)
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
   (if (<= x 8.2e+65)
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 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 (x <= -7e+89) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 8.2e+65) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * 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 (x <= (-7d+89)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= 8.2d+65) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * 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 (x <= -7e+89) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 8.2e+65) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -7e+89:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= 8.2e+65:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -7e+89)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= 8.2e+65)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -7e+89)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= 8.2e+65)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -7e+89], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+65], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000001e89

   1. Initial program 72.5%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 70.5%

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

   6. Taylor expanded in x around inf 79.1%

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

      1. cancel-sign-sub-inv 79.1%

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

      2. associate-*r* 79.1%

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

      3. metadata-eval 79.1%

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

   8. Simplified 79.1%

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

   if -7.0000000000000001e89 < x < 8.2000000000000003e65

   1. Initial program 92.5%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around 0 79.7%

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

   if 8.2000000000000003e65 < x

   1. Initial program 76.3%

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

   3. Simplified 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 74.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.3 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-228}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+110}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.3e-103)
   (* j (* k -27.0))
   (if (<= k -3.9e-228)
     (* b c)
     (if (<= k 1.5e+110) (* (* y z) (* 18.0 (* x t))) (* -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 (k <= -1.3e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= -3.9e-228) {
		tmp = b * c;
	} else if (k <= 1.5e+110) {
		tmp = (y * z) * (18.0 * (x * t));
	} else {
		tmp = -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 (k <= (-1.3d-103)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= (-3.9d-228)) then
        tmp = b * c
    else if (k <= 1.5d+110) then
        tmp = (y * z) * (18.0d0 * (x * t))
    else
        tmp = (-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 (k <= -1.3e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= -3.9e-228) {
		tmp = b * c;
	} else if (k <= 1.5e+110) {
		tmp = (y * z) * (18.0 * (x * t));
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.3e-103:
		tmp = j * (k * -27.0)
	elif k <= -3.9e-228:
		tmp = b * c
	elif k <= 1.5e+110:
		tmp = (y * z) * (18.0 * (x * t))
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.3e-103)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= -3.9e-228)
		tmp = Float64(b * c);
	elseif (k <= 1.5e+110)
		tmp = Float64(Float64(y * z) * Float64(18.0 * Float64(x * t)));
	else
		tmp = 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 (k <= -1.3e-103)
		tmp = j * (k * -27.0);
	elseif (k <= -3.9e-228)
		tmp = b * c;
	elseif (k <= 1.5e+110)
		tmp = (y * z) * (18.0 * (x * t));
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.3e-103], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.9e-228], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.5e+110], N[(N[(y * z), $MachinePrecision] * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.29999999999999998e-103

   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 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 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-*r* 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if -1.29999999999999998e-103 < k < -3.90000000000000029e-228

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in b around inf 47.1%

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

   if -3.90000000000000029e-228 < k < 1.50000000000000004e110

   1. Initial program 83.9%

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

   3. Simplified 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 34.7%

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

      1. *-commutative 34.7%

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

   7. Simplified 34.7%

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

   8. Taylor expanded in x around inf 29.4%

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

      1. associate-*r* 29.4%

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

      2. associate-*r* 29.4%

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

   10. Simplified 29.4%

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

   if 1.50000000000000004e110 < k

   1. Initial program 82.9%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in j around inf 50.4%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.3 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-228}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+110}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-228}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+109}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.35e-103)
   (* j (* k -27.0))
   (if (<= k -6e-228)
     (* b c)
     (if (<= k 6e+109) (* 18.0 (* (* y z) (* x t))) (* -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 (k <= -1.35e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= -6e-228) {
		tmp = b * c;
	} else if (k <= 6e+109) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else {
		tmp = -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 (k <= (-1.35d-103)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= (-6d-228)) then
        tmp = b * c
    else if (k <= 6d+109) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else
        tmp = (-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 (k <= -1.35e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= -6e-228) {
		tmp = b * c;
	} else if (k <= 6e+109) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.35e-103:
		tmp = j * (k * -27.0)
	elif k <= -6e-228:
		tmp = b * c
	elif k <= 6e+109:
		tmp = 18.0 * ((y * z) * (x * t))
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.35e-103)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= -6e-228)
		tmp = Float64(b * c);
	elseif (k <= 6e+109)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	else
		tmp = 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 (k <= -1.35e-103)
		tmp = j * (k * -27.0);
	elseif (k <= -6e-228)
		tmp = b * c;
	elseif (k <= 6e+109)
		tmp = 18.0 * ((y * z) * (x * t));
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.35e-103], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6e-228], N[(b * c), $MachinePrecision], If[LessEqual[k, 6e+109], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.35000000000000005e-103

   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 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 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-*r* 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if -1.35000000000000005e-103 < k < -5.9999999999999999e-228

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in b around inf 47.1%

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

   if -5.9999999999999999e-228 < k < 6.00000000000000031e109

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 85.8%

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

   4. Taylor expanded in y around inf 29.4%

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

      1. associate-*r* 29.4%

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

   6. Simplified 29.4%

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

   if 6.00000000000000031e109 < k

   1. Initial program 82.9%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in j around inf 50.4%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-228}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+109}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+45} \lor \neg \left(x \leq 9.6 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -4.9e+45) (not (<= x 9.6e+54)))
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
   (+ (* 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 ((x <= -4.9e+45) || !(x <= 9.6e+54)) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = (b * c) + (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 ((x <= (-4.9d+45)) .or. (.not. (x <= 9.6d+54))) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else
        tmp = (b * c) + (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 ((x <= -4.9e+45) || !(x <= 9.6e+54)) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -4.9e+45) or not (x <= 9.6e+54):
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -4.9e+45) || !(x <= 9.6e+54))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(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 ((x <= -4.9e+45) || ~((x <= 9.6e+54)))
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -4.9e+45], N[Not[LessEqual[x, 9.6e+54]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9000000000000002e45 or 9.59999999999999993e54 < x

   1. Initial program 75.6%

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

   3. Simplified 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 y around inf 74.7%

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

   6. Taylor expanded in x around inf 72.3%

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

      1. cancel-sign-sub-inv 72.3%

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

      2. associate-*r* 72.3%

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

      3. metadata-eval 72.3%

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

   8. Simplified 72.3%

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

   if -4.9000000000000002e45 < x < 9.59999999999999993e54

   1. Initial program 93.2%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in b around inf 62.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+45} \lor \neg \left(x \leq 9.6 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+117} \lor \neg \left(t \leq 10^{+19}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.9e+117) (not (<= t 1e+19)))
   (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))
   (+ (* 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 ((t <= -2.9e+117) || !(t <= 1e+19)) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else {
		tmp = (b * c) + (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 ((t <= (-2.9d+117)) .or. (.not. (t <= 1d+19))) then
        tmp = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    else
        tmp = (b * c) + (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 ((t <= -2.9e+117) || !(t <= 1e+19)) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -2.9e+117) or not (t <= 1e+19):
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.9e+117) || !(t <= 1e+19))
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(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 ((t <= -2.9e+117) || ~((t <= 1e+19)))
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.9e+117], N[Not[LessEqual[t, 1e+19]], $MachinePrecision]], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000027e117 or 1e19 < t

   1. Initial program 78.5%

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

   3. Taylor expanded in x around 0 76.4%

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

   4. Taylor expanded in t around inf 71.1%

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

      1. cancel-sign-sub-inv 71.1%

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

      2. metadata-eval 71.1%

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

      3. associate-*r* 71.1%

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

      4. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   if -2.90000000000000027e117 < t < 1e19

   1. Initial program 90.2%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around inf 60.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+117} \lor \neg \left(t \leq 10^{+19}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.45e+50)
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
   (if (<= x 9.6e+54)
     (+ (* b c) (* j (* k -27.0)))
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 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 (x <= -1.45e+50) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 9.6e+54) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * 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 (x <= (-1.45d+50)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= 9.6d+54) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * 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 (x <= -1.45e+50) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 9.6e+54) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -1.45e+50:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= 9.6e+54:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.45e+50)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= 9.6e+54)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -1.45e+50)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= 9.6e+54)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.45e+50], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.6e+54], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e50

   1. Initial program 75.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 72.3%

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

   6. Taylor expanded in x around inf 72.6%

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

      1. cancel-sign-sub-inv 72.6%

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

      2. associate-*r* 72.6%

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

      3. metadata-eval 72.6%

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

   8. Simplified 72.6%

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

   if -1.45e50 < x < 9.59999999999999993e54

   1. Initial program 93.2%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in b around inf 62.4%

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

   if 9.59999999999999993e54 < x

   1. Initial program 75.7%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around inf 72.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 10^{+18}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.2e+117)
   (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))
   (if (<= t 1e+18)
     (+ (* b c) (* j (* k -27.0)))
     (* t (- (* 18.0 (* x (* y z))) (* 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 tmp;
	if (t <= -1.2e+117) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else if (t <= 1e+18) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (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) :: tmp
    if (t <= (-1.2d+117)) then
        tmp = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    else if (t <= 1d+18) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (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 tmp;
	if (t <= -1.2e+117) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else if (t <= 1e+18) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.2e+117:
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	elif t <= 1e+18:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.2e+117)
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)));
	elseif (t <= 1e+18)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.2e+117)
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	elseif (t <= 1e+18)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.2e+117], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+18], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1999999999999999e117

   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 78.5%

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

   4. Taylor expanded in t around inf 74.4%

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

      1. cancel-sign-sub-inv 74.4%

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

      2. metadata-eval 74.4%

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

      3. associate-*r* 74.4%

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

      4. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   if -1.1999999999999999e117 < t < 1e18

   1. Initial program 90.2%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around inf 60.5%

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

   if 1e18 < t

   1. Initial program 80.4%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around inf 68.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 10^{+18}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.4 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{-38}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.56 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -2.4e-104)
   (* j (* k -27.0))
   (if (<= k 5.3e-38)
     (* b c)
     (if (<= k 1.56e+108) (* x (* i -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 (k <= -2.4e-104) {
		tmp = j * (k * -27.0);
	} else if (k <= 5.3e-38) {
		tmp = b * c;
	} else if (k <= 1.56e+108) {
		tmp = x * (i * -4.0);
	} else {
		tmp = -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 (k <= (-2.4d-104)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 5.3d-38) then
        tmp = b * c
    else if (k <= 1.56d+108) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = (-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 (k <= -2.4e-104) {
		tmp = j * (k * -27.0);
	} else if (k <= 5.3e-38) {
		tmp = b * c;
	} else if (k <= 1.56e+108) {
		tmp = x * (i * -4.0);
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -2.4e-104:
		tmp = j * (k * -27.0)
	elif k <= 5.3e-38:
		tmp = b * c
	elif k <= 1.56e+108:
		tmp = x * (i * -4.0)
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -2.4e-104)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 5.3e-38)
		tmp = Float64(b * c);
	elseif (k <= 1.56e+108)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = 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 (k <= -2.4e-104)
		tmp = j * (k * -27.0);
	elseif (k <= 5.3e-38)
		tmp = b * c;
	elseif (k <= 1.56e+108)
		tmp = x * (i * -4.0);
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -2.4e-104], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.3e-38], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.56e+108], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.4000000000000001e-104

   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 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 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-*r* 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if -2.4000000000000001e-104 < k < 5.30000000000000016e-38

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 90.9%

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

   4. Taylor expanded in b around inf 39.1%

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

   if 5.30000000000000016e-38 < k < 1.5599999999999999e108

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 82.3%

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

   4. Taylor expanded in i around inf 33.9%

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

      1. associate-*r* 33.9%

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

      2. *-commutative 33.9%

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

   6. Simplified 33.9%

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

   if 1.5599999999999999e108 < k

   1. Initial program 80.9%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in j around inf 49.2%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.4 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{-38}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.56 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+260}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))))
   (if (<= a -3.4e+30)
     (+ (* b c) t_1)
     (if (<= a 2.25e+260) (+ (* b c) (* j (* k -27.0))) 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 * (t * a);
	double tmp;
	if (a <= -3.4e+30) {
		tmp = (b * c) + t_1;
	} else if (a <= 2.25e+260) {
		tmp = (b * c) + (j * (k * -27.0));
	} 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 = (-4.0d0) * (t * a)
    if (a <= (-3.4d+30)) then
        tmp = (b * c) + t_1
    else if (a <= 2.25d+260) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    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 = -4.0 * (t * a);
	double tmp;
	if (a <= -3.4e+30) {
		tmp = (b * c) + t_1;
	} else if (a <= 2.25e+260) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	tmp = 0
	if a <= -3.4e+30:
		tmp = (b * c) + t_1
	elif a <= 2.25e+260:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (a <= -3.4e+30)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (a <= 2.25e+260)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	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 = -4.0 * (t * a);
	tmp = 0.0;
	if (a <= -3.4e+30)
		tmp = (b * c) + t_1;
	elseif (a <= 2.25e+260)
		tmp = (b * c) + (j * (k * -27.0));
	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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+30], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[a, 2.25e+260], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4000000000000002e30

   1. Initial program 85.4%

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

   3. Simplified 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 x around 0 73.2%

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

   6. Taylor expanded in j around 0 67.1%

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

   if -3.4000000000000002e30 < a < 2.25000000000000011e260

   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 90.3%

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

   5. Taylor expanded in b around inf 55.9%

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

   if 2.25000000000000011e260 < a

   1. Initial program 54.5%

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

   3. Taylor expanded in x around 0 54.5%

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

   4. Taylor expanded in a around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. *-commutative 55.6%

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

   6. Simplified 55.6%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+260}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -2.3e-8)
   (* 18.0 (* t (* x (* y z))))
   (if (<= z 2.7e+57)
     (+ (* b c) (* -4.0 (* t a)))
     (* (* y z) (* 18.0 (* 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 tmp;
	if (z <= -2.3e-8) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (z <= 2.7e+57) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (y * z) * (18.0 * (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) :: tmp
    if (z <= (-2.3d-8)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (z <= 2.7d+57) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (y * z) * (18.0d0 * (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 tmp;
	if (z <= -2.3e-8) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (z <= 2.7e+57) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (y * z) * (18.0 * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -2.3e-8:
		tmp = 18.0 * (t * (x * (y * z)))
	elif z <= 2.7e+57:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (y * z) * (18.0 * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -2.3e-8)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (z <= 2.7e+57)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(y * z) * Float64(18.0 * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -2.3e-8)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (z <= 2.7e+57)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (y * z) * (18.0 * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -2.3e-8], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+57], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3000000000000001e-8

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 83.6%

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

   4. Taylor expanded in y around inf 46.1%

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

   if -2.3000000000000001e-8 < z < 2.6999999999999998e57

   1. Initial program 87.4%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around 0 72.8%

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

   6. Taylor expanded in j around 0 51.2%

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

   if 2.6999999999999998e57 < z

   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 76.2%

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

   5. Taylor expanded in y around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in x around inf 50.3%

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

      1. associate-*r* 52.0%

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

      2. associate-*r* 52.0%

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

   10. Simplified 52.0%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103} \lor \neg \left(k \leq 2.4 \cdot 10^{+110}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -1.35e-103) (not (<= k 2.4e+110))) (* -27.0 (* j k)) (* 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 tmp;
	if ((k <= -1.35e-103) || !(k <= 2.4e+110)) {
		tmp = -27.0 * (j * k);
	} 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) :: tmp
    if ((k <= (-1.35d-103)) .or. (.not. (k <= 2.4d+110))) then
        tmp = (-27.0d0) * (j * k)
    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 tmp;
	if ((k <= -1.35e-103) || !(k <= 2.4e+110)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -1.35e-103) or not (k <= 2.4e+110):
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -1.35e-103) || !(k <= 2.4e+110))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -1.35e-103) || ~((k <= 2.4e+110)))
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -1.35e-103], N[Not[LessEqual[k, 2.4e+110]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -1.35000000000000005e-103 or 2.40000000000000012e110 < k

   1. Initial program 86.1%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in j around inf 43.0%

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

   if -1.35000000000000005e-103 < k < 2.40000000000000012e110

   1. Initial program 85.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 32.3%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103} \lor \neg \left(k \leq 2.4 \cdot 10^{+110}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.35e-103)
   (* j (* k -27.0))
   (if (<= k 3.8e+109) (* b c) (* -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 (k <= -1.35e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= 3.8e+109) {
		tmp = b * c;
	} else {
		tmp = -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 (k <= (-1.35d-103)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 3.8d+109) then
        tmp = b * c
    else
        tmp = (-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 (k <= -1.35e-103) {
		tmp = j * (k * -27.0);
	} else if (k <= 3.8e+109) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.35e-103:
		tmp = j * (k * -27.0)
	elif k <= 3.8e+109:
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.35e-103)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 3.8e+109)
		tmp = Float64(b * c);
	else
		tmp = 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 (k <= -1.35e-103)
		tmp = j * (k * -27.0);
	elseif (k <= 3.8e+109)
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.35e-103], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e+109], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.35000000000000005e-103

   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 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 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-*r* 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if -1.35000000000000005e-103 < k < 3.80000000000000039e109

   1. Initial program 85.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 32.3%

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

   if 3.80000000000000039e109 < k

   1. Initial program 82.9%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in j around inf 50.4%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 23.5% 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 85.9%

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

3. Taylor expanded in x around 0 86.3%

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

4. Taylor expanded in b around inf 26.6%

   \[\leadsto \color{blue}{b \cdot c} \]
5. Add Preprocessing

Developer Target 1: 89.6% 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 2024137 
(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
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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