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

Percentage Accurate: 84.9% → 92.1%

Time: 20.7s

Alternatives: 26

Speedup: 0.7×

• 50.8% 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: 84.9% 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: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+22} \lor \neg \left(x \leq 1.5 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(-27 \cdot \frac{j \cdot k}{x} + \left(-4 \cdot i + \left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2e+22) (not (<= x 1.5e-24)))
   (*
    x
    (+
     (* -27.0 (/ (* j k) x))
     (+
      (* -4.0 i)
      (+ (* -4.0 (/ (* a t) x)) (+ (* 18.0 (* t (* y z))) (/ (* b c) x))))))
   (-
    (-
     (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
     (* i (* x 4.0)))
    (* k (* j 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 <= -2e+22) || !(x <= 1.5e-24)) {
		tmp = x * ((-27.0 * ((j * k) / x)) + ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x)))));
	} else {
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 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 <= (-2d+22)) .or. (.not. (x <= 1.5d-24))) then
        tmp = x * (((-27.0d0) * ((j * k) / x)) + (((-4.0d0) * i) + (((-4.0d0) * ((a * t) / x)) + ((18.0d0 * (t * (y * z))) + ((b * c) / x)))))
    else
        tmp = (((b * c) + ((t * (z * (y * (x * 18.0d0)))) - (t * (a * 4.0d0)))) - (i * (x * 4.0d0))) - (k * (j * 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 <= -2e+22) || !(x <= 1.5e-24)) {
		tmp = x * ((-27.0 * ((j * k) / x)) + ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x)))));
	} else {
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2e+22) or not (x <= 1.5e-24):
		tmp = x * ((-27.0 * ((j * k) / x)) + ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x)))))
	else:
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2e+22) || !(x <= 1.5e-24))
		tmp = Float64(x * Float64(Float64(-27.0 * Float64(Float64(j * k) / x)) + Float64(Float64(-4.0 * i) + Float64(Float64(-4.0 * Float64(Float64(a * t) / x)) + Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(Float64(b * c) / x))))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 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 <= -2e+22) || ~((x <= 1.5e-24)))
		tmp = x * ((-27.0 * ((j * k) / x)) + ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x)))));
	else
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2e+22], N[Not[LessEqual[x, 1.5e-24]], $MachinePrecision]], N[(x * N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * i), $MachinePrecision] + N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2e22 or 1.49999999999999998e-24 < x

   1. Initial program 80.7%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x around inf 95.1%

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

   if -2e22 < x < 1.49999999999999998e-24

   1. Initial program 93.2%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+22} \lor \neg \left(x \leq 1.5 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(-27 \cdot \frac{j \cdot k}{x} + \left(-4 \cdot i + \left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_4 := k \cdot \left(j \cdot 27\right)\\ t_5 := t \cdot \left(z \cdot \left(-4 \cdot \frac{a}{z} + 18 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;t\_4 \leq -10:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{-109}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-16}:\\ \;\;\;\;t\_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* -27.0 j)))
        (t_2 (+ (* b c) t_1))
        (t_3 (- (* b c) (* 4.0 (* x i))))
        (t_4 (* k (* j 27.0)))
        (t_5 (* t (* z (+ (* -4.0 (/ a z)) (* 18.0 (* x y)))))))
   (if (<= t_4 -10.0)
     t_2
     (if (<= t_4 -1e-83)
       t_5
       (if (<= t_4 2e-318)
         t_3
         (if (<= t_4 2e-147)
           (* t (+ (* -4.0 a) (* 18.0 (* x (* y z)))))
           (if (<= t_4 5e-109)
             t_3
             (if (<= t_4 2e-16)
               (+ t_1 (* 18.0 (* (* y z) (* x t))))
               (if (<= t_4 2e+74) t_5 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 = k * (-27.0 * j);
	double t_2 = (b * c) + t_1;
	double t_3 = (b * c) - (4.0 * (x * i));
	double t_4 = k * (j * 27.0);
	double t_5 = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))));
	double tmp;
	if (t_4 <= -10.0) {
		tmp = t_2;
	} else if (t_4 <= -1e-83) {
		tmp = t_5;
	} else if (t_4 <= 2e-318) {
		tmp = t_3;
	} else if (t_4 <= 2e-147) {
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	} else if (t_4 <= 5e-109) {
		tmp = t_3;
	} else if (t_4 <= 2e-16) {
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	} else if (t_4 <= 2e+74) {
		tmp = t_5;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = k * ((-27.0d0) * j)
    t_2 = (b * c) + t_1
    t_3 = (b * c) - (4.0d0 * (x * i))
    t_4 = k * (j * 27.0d0)
    t_5 = t * (z * (((-4.0d0) * (a / z)) + (18.0d0 * (x * y))))
    if (t_4 <= (-10.0d0)) then
        tmp = t_2
    else if (t_4 <= (-1d-83)) then
        tmp = t_5
    else if (t_4 <= 2d-318) then
        tmp = t_3
    else if (t_4 <= 2d-147) then
        tmp = t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z))))
    else if (t_4 <= 5d-109) then
        tmp = t_3
    else if (t_4 <= 2d-16) then
        tmp = t_1 + (18.0d0 * ((y * z) * (x * t)))
    else if (t_4 <= 2d+74) then
        tmp = t_5
    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 = k * (-27.0 * j);
	double t_2 = (b * c) + t_1;
	double t_3 = (b * c) - (4.0 * (x * i));
	double t_4 = k * (j * 27.0);
	double t_5 = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))));
	double tmp;
	if (t_4 <= -10.0) {
		tmp = t_2;
	} else if (t_4 <= -1e-83) {
		tmp = t_5;
	} else if (t_4 <= 2e-318) {
		tmp = t_3;
	} else if (t_4 <= 2e-147) {
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	} else if (t_4 <= 5e-109) {
		tmp = t_3;
	} else if (t_4 <= 2e-16) {
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	} else if (t_4 <= 2e+74) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (-27.0 * j)
	t_2 = (b * c) + t_1
	t_3 = (b * c) - (4.0 * (x * i))
	t_4 = k * (j * 27.0)
	t_5 = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))))
	tmp = 0
	if t_4 <= -10.0:
		tmp = t_2
	elif t_4 <= -1e-83:
		tmp = t_5
	elif t_4 <= 2e-318:
		tmp = t_3
	elif t_4 <= 2e-147:
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))))
	elif t_4 <= 5e-109:
		tmp = t_3
	elif t_4 <= 2e-16:
		tmp = t_1 + (18.0 * ((y * z) * (x * t)))
	elif t_4 <= 2e+74:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(-27.0 * j))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_4 = Float64(k * Float64(j * 27.0))
	t_5 = Float64(t * Float64(z * Float64(Float64(-4.0 * Float64(a / z)) + Float64(18.0 * Float64(x * y)))))
	tmp = 0.0
	if (t_4 <= -10.0)
		tmp = t_2;
	elseif (t_4 <= -1e-83)
		tmp = t_5;
	elseif (t_4 <= 2e-318)
		tmp = t_3;
	elseif (t_4 <= 2e-147)
		tmp = Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (t_4 <= 5e-109)
		tmp = t_3;
	elseif (t_4 <= 2e-16)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))));
	elseif (t_4 <= 2e+74)
		tmp = t_5;
	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 = k * (-27.0 * j);
	t_2 = (b * c) + t_1;
	t_3 = (b * c) - (4.0 * (x * i));
	t_4 = k * (j * 27.0);
	t_5 = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))));
	tmp = 0.0;
	if (t_4 <= -10.0)
		tmp = t_2;
	elseif (t_4 <= -1e-83)
		tmp = t_5;
	elseif (t_4 <= 2e-318)
		tmp = t_3;
	elseif (t_4 <= 2e-147)
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	elseif (t_4 <= 5e-109)
		tmp = t_3;
	elseif (t_4 <= 2e-16)
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	elseif (t_4 <= 2e+74)
		tmp = t_5;
	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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(z * N[(N[(-4.0 * N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -10.0], t$95$2, If[LessEqual[t$95$4, -1e-83], t$95$5, If[LessEqual[t$95$4, 2e-318], t$95$3, If[LessEqual[t$95$4, 2e-147], N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e-109], t$95$3, If[LessEqual[t$95$4, 2e-16], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+74], t$95$5, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10 or 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.8%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 69.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 2e-16 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   1. Initial program 92.2%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 91.9%

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

   6. Taylor expanded in t around inf 81.7%

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

   7. Taylor expanded in z around inf 82.3%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000024e-318 or 1.9999999999999999e-147 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e-109

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 88.0%

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

   4. Taylor expanded in a around inf 83.2%

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

      1. associate-*r* 83.2%

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

      2. *-commutative 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in j around 0 83.2%

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

   8. Taylor expanded in a around 0 71.4%

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

   if 2.0000024e-318 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e-147

   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 96.0%

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

   5. Taylor expanded in t around inf 67.9%

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

   6. Taylor expanded in t around inf 63.9%

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

   if 5.0000000000000002e-109 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-16

   1. Initial program 71.7%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in y around inf 58.1%

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

      1. *-commutative 58.1%

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

      2. associate-*r* 64.9%

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

      3. *-commutative 64.9%

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

   7. Simplified 64.9%

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

      1. associate-*l* 64.9%

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

   9. Applied egg-rr 64.9%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)} + k \cdot \left(j \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-4 \cdot \frac{a}{z} + 18 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-16}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-4 \cdot \frac{a}{z} + 18 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	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[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $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 95.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 34.8%

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

   5. Taylor expanded in t around inf 52.4%

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

   6. Taylor expanded in t around inf 65.4%

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

4. Final simplification 93.1%

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

Alternative 4: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_3 \leq -10:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_1 + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t\_3 \leq 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* -27.0 j))) (t_2 (+ (* b c) t_1)) (t_3 (* k (* j 27.0))))
   (if (<= t_3 -10.0)
     t_2
     (if (<= t_3 -1e-83)
       (+ t_1 (* -4.0 (* a t)))
       (if (<= t_3 5e-109)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_3 2e+74)
           (* (* 18.0 (* y z)) (* x t))
           (if (<= t_3 1e+125) t_2 (+ t_1 (* -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 = k * (-27.0 * j);
	double t_2 = (b * c) + t_1;
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -10.0) {
		tmp = t_2;
	} else if (t_3 <= -1e-83) {
		tmp = t_1 + (-4.0 * (a * t));
	} else if (t_3 <= 5e-109) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_3 <= 2e+74) {
		tmp = (18.0 * (y * z)) * (x * t);
	} else if (t_3 <= 1e+125) {
		tmp = t_2;
	} else {
		tmp = t_1 + (-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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * ((-27.0d0) * j)
    t_2 = (b * c) + t_1
    t_3 = k * (j * 27.0d0)
    if (t_3 <= (-10.0d0)) then
        tmp = t_2
    else if (t_3 <= (-1d-83)) then
        tmp = t_1 + ((-4.0d0) * (a * t))
    else if (t_3 <= 5d-109) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_3 <= 2d+74) then
        tmp = (18.0d0 * (y * z)) * (x * t)
    else if (t_3 <= 1d+125) then
        tmp = t_2
    else
        tmp = t_1 + ((-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 = k * (-27.0 * j);
	double t_2 = (b * c) + t_1;
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -10.0) {
		tmp = t_2;
	} else if (t_3 <= -1e-83) {
		tmp = t_1 + (-4.0 * (a * t));
	} else if (t_3 <= 5e-109) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_3 <= 2e+74) {
		tmp = (18.0 * (y * z)) * (x * t);
	} else if (t_3 <= 1e+125) {
		tmp = t_2;
	} else {
		tmp = t_1 + (-4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (-27.0 * j)
	t_2 = (b * c) + t_1
	t_3 = k * (j * 27.0)
	tmp = 0
	if t_3 <= -10.0:
		tmp = t_2
	elif t_3 <= -1e-83:
		tmp = t_1 + (-4.0 * (a * t))
	elif t_3 <= 5e-109:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_3 <= 2e+74:
		tmp = (18.0 * (y * z)) * (x * t)
	elif t_3 <= 1e+125:
		tmp = t_2
	else:
		tmp = t_1 + (-4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(-27.0 * j))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= -10.0)
		tmp = t_2;
	elseif (t_3 <= -1e-83)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(a * t)));
	elseif (t_3 <= 5e-109)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_3 <= 2e+74)
		tmp = Float64(Float64(18.0 * Float64(y * z)) * Float64(x * t));
	elseif (t_3 <= 1e+125)
		tmp = t_2;
	else
		tmp = Float64(t_1 + 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 = k * (-27.0 * j);
	t_2 = (b * c) + t_1;
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (t_3 <= -10.0)
		tmp = t_2;
	elseif (t_3 <= -1e-83)
		tmp = t_1 + (-4.0 * (a * t));
	elseif (t_3 <= 5e-109)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_3 <= 2e+74)
		tmp = (18.0 * (y * z)) * (x * t);
	elseif (t_3 <= 1e+125)
		tmp = t_2;
	else
		tmp = t_1 + (-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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -10.0], t$95$2, If[LessEqual[t$95$3, -1e-83], N[(t$95$1 + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e-109], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+74], N[(N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+125], t$95$2, N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10 or 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   1. Initial program 84.8%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in b around inf 70.8%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83

   1. Initial program 93.7%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 57.1%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e-109

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf 87.1%

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

   4. Taylor expanded in a around inf 79.6%

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

      1. associate-*r* 79.6%

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

      2. *-commutative 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in j around 0 78.6%

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

   8. Taylor expanded in a around 0 63.5%

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

   if 5.0000000000000002e-109 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   1. Initial program 79.2%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in y around inf 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*r* 58.9%

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

      3. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*r* 51.2%

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

      3. associate-*l* 51.3%

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

   10. Applied egg-rr 51.3%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in i around inf 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right) + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + k \cdot \left(-27 \cdot j\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-4 \cdot \frac{a}{z} + 18 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* k (* -27.0 j)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -10.0)
     t_1
     (if (<= t_2 -1e-83)
       (* t (* z (+ (* -4.0 (/ a z)) (* 18.0 (* x y)))))
       (if (<= t_2 2e-318)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_2 2e+74)
           (* t (+ (* -4.0 a) (* 18.0 (* x (* y z)))))
           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) + (k * (-27.0 * j));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1;
	} else if (t_2 <= -1e-83) {
		tmp = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))));
	} else if (t_2 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 2e+74) {
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (k * ((-27.0d0) * j))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-10.0d0)) then
        tmp = t_1
    else if (t_2 <= (-1d-83)) then
        tmp = t * (z * (((-4.0d0) * (a / z)) + (18.0d0 * (x * y))))
    else if (t_2 <= 2d-318) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_2 <= 2d+74) then
        tmp = t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z))))
    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) + (k * (-27.0 * j));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1;
	} else if (t_2 <= -1e-83) {
		tmp = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))));
	} else if (t_2 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 2e+74) {
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (k * (-27.0 * j))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_1
	elif t_2 <= -1e-83:
		tmp = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))))
	elif t_2 <= 2e-318:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_2 <= 2e+74:
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))))
	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(k * Float64(-27.0 * j)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = t_1;
	elseif (t_2 <= -1e-83)
		tmp = Float64(t * Float64(z * Float64(Float64(-4.0 * Float64(a / z)) + Float64(18.0 * Float64(x * y)))));
	elseif (t_2 <= 2e-318)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_2 <= 2e+74)
		tmp = Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))));
	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) + (k * (-27.0 * j));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_1;
	elseif (t_2 <= -1e-83)
		tmp = t * (z * ((-4.0 * (a / z)) + (18.0 * (x * y))));
	elseif (t_2 <= 2e-318)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_2 <= 2e+74)
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], t$95$1, If[LessEqual[t$95$2, -1e-83], N[(t * N[(z * N[(N[(-4.0 * N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-318], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+74], N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10 or 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.8%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 69.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83

   1. Initial program 93.7%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 93.1%

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

   6. Taylor expanded in t around inf 76.6%

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

   7. Taylor expanded in z around inf 77.4%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000024e-318

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf 88.2%

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

   4. Taylor expanded in a around inf 81.6%

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

      1. associate-*r* 81.6%

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

      2. *-commutative 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in j around 0 81.6%

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

   8. Taylor expanded in a around 0 71.3%

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

   if 2.0000024e-318 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   1. Initial program 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around inf 66.4%

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

   6. Taylor expanded in t around inf 61.2%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-4 \cdot \frac{a}{z} + 18 \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + k \cdot \left(-27 \cdot j\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* k (* -27.0 j))))
        (t_2 (* k (* j 27.0)))
        (t_3 (* t (+ (* -4.0 a) (* 18.0 (* x (* y z)))))))
   (if (<= t_2 -10.0)
     t_1
     (if (<= t_2 -1e-83)
       t_3
       (if (<= t_2 2e-318)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_2 2e+74) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (k * (-27.0 * j));
	double t_2 = k * (j * 27.0);
	double t_3 = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1;
	} else if (t_2 <= -1e-83) {
		tmp = t_3;
	} else if (t_2 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 2e+74) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) + (k * ((-27.0d0) * j))
    t_2 = k * (j * 27.0d0)
    t_3 = t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z))))
    if (t_2 <= (-10.0d0)) then
        tmp = t_1
    else if (t_2 <= (-1d-83)) then
        tmp = t_3
    else if (t_2 <= 2d-318) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_2 <= 2d+74) then
        tmp = t_3
    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) + (k * (-27.0 * j));
	double t_2 = k * (j * 27.0);
	double t_3 = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1;
	} else if (t_2 <= -1e-83) {
		tmp = t_3;
	} else if (t_2 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 2e+74) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (k * (-27.0 * j))
	t_2 = k * (j * 27.0)
	t_3 = t * ((-4.0 * a) + (18.0 * (x * (y * z))))
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_1
	elif t_2 <= -1e-83:
		tmp = t_3
	elif t_2 <= 2e-318:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_2 <= 2e+74:
		tmp = t_3
	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(k * Float64(-27.0 * j)))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = t_1;
	elseif (t_2 <= -1e-83)
		tmp = t_3;
	elseif (t_2 <= 2e-318)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_2 <= 2e+74)
		tmp = t_3;
	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) + (k * (-27.0 * j));
	t_2 = k * (j * 27.0);
	t_3 = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_1;
	elseif (t_2 <= -1e-83)
		tmp = t_3;
	elseif (t_2 <= 2e-318)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_2 <= 2e+74)
		tmp = t_3;
	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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], t$95$1, If[LessEqual[t$95$2, -1e-83], t$95$3, If[LessEqual[t$95$2, 2e-318], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+74], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10 or 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.8%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 69.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 2.0000024e-318 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   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 88.8%

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

   5. Taylor expanded in t around inf 72.4%

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

   6. Taylor expanded in t around inf 64.7%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000024e-318

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf 88.2%

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

   4. Taylor expanded in a around inf 81.6%

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

      1. associate-*r* 81.6%

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

      2. *-commutative 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in j around 0 81.6%

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

   8. Taylor expanded in a around 0 71.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.8 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-288}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2.9e+136)
   (* b c)
   (if (<= (* b c) -4.8e-41)
     (* x (* 18.0 (* y (* t z))))
     (if (<= (* b c) 7e-288)
       (* -4.0 (* x i))
       (if (<= (* b c) 3.5e-72)
         (* j (* -27.0 k))
         (if (<= (* b c) 3.7e-18)
           (* x (* 18.0 (* z (* t y))))
           (if (<= (* b c) 1.9e+151) (* -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 ((b * c) <= -2.9e+136) {
		tmp = b * c;
	} else if ((b * c) <= -4.8e-41) {
		tmp = x * (18.0 * (y * (t * z)));
	} else if ((b * c) <= 7e-288) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3.5e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 3.7e-18) {
		tmp = x * (18.0 * (z * (t * y)));
	} else if ((b * c) <= 1.9e+151) {
		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 ((b * c) <= (-2.9d+136)) then
        tmp = b * c
    else if ((b * c) <= (-4.8d-41)) then
        tmp = x * (18.0d0 * (y * (t * z)))
    else if ((b * c) <= 7d-288) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 3.5d-72) then
        tmp = j * ((-27.0d0) * k)
    else if ((b * c) <= 3.7d-18) then
        tmp = x * (18.0d0 * (z * (t * y)))
    else if ((b * c) <= 1.9d+151) 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 ((b * c) <= -2.9e+136) {
		tmp = b * c;
	} else if ((b * c) <= -4.8e-41) {
		tmp = x * (18.0 * (y * (t * z)));
	} else if ((b * c) <= 7e-288) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3.5e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 3.7e-18) {
		tmp = x * (18.0 * (z * (t * y)));
	} else if ((b * c) <= 1.9e+151) {
		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 (b * c) <= -2.9e+136:
		tmp = b * c
	elif (b * c) <= -4.8e-41:
		tmp = x * (18.0 * (y * (t * z)))
	elif (b * c) <= 7e-288:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 3.5e-72:
		tmp = j * (-27.0 * k)
	elif (b * c) <= 3.7e-18:
		tmp = x * (18.0 * (z * (t * y)))
	elif (b * c) <= 1.9e+151:
		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 (Float64(b * c) <= -2.9e+136)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -4.8e-41)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(t * z))));
	elseif (Float64(b * c) <= 7e-288)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 3.5e-72)
		tmp = Float64(j * Float64(-27.0 * k));
	elseif (Float64(b * c) <= 3.7e-18)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(t * y))));
	elseif (Float64(b * c) <= 1.9e+151)
		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 ((b * c) <= -2.9e+136)
		tmp = b * c;
	elseif ((b * c) <= -4.8e-41)
		tmp = x * (18.0 * (y * (t * z)));
	elseif ((b * c) <= 7e-288)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 3.5e-72)
		tmp = j * (-27.0 * k);
	elseif ((b * c) <= 3.7e-18)
		tmp = x * (18.0 * (z * (t * y)));
	elseif ((b * c) <= 1.9e+151)
		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[LessEqual[N[(b * c), $MachinePrecision], -2.9e+136], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.8e-41], N[(x * N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7e-288], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.5e-72], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.7e-18], N[(x * N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.9e+151], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -2.89999999999999974e136 or 1.9e151 < (*.f64 b c)

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 81.7%

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

   4. Taylor expanded in a around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in b around inf 59.4%

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

   if -2.89999999999999974e136 < (*.f64 b c) < -4.80000000000000044e-41

   1. Initial program 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-*r* 71.5%

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

      3. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 46.3%

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

      4. *-commutative 46.3%

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

      5. associate-*l* 46.3%

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

      6. *-commutative 46.3%

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

      7. associate-*r* 46.4%

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

      8. *-commutative 46.4%

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

   10. Simplified 46.4%

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

   if -4.80000000000000044e-41 < (*.f64 b c) < 7.0000000000000006e-288

   1. Initial program 90.1%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in i around inf 61.0%

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

      1. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in x around inf 38.3%

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

   if 7.0000000000000006e-288 < (*.f64 b c) < 3.5e-72

   1. Initial program 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in k around inf 44.9%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 44.9%

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

   7. Simplified 44.9%

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

   if 3.5e-72 < (*.f64 b c) < 3.7000000000000003e-18

   1. Initial program 87.3%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. associate-*r* 44.1%

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

      3. *-commutative 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in y around inf 36.1%

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

      1. *-commutative 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-*l* 36.1%

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

      4. *-commutative 36.1%

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

      5. associate-*l* 36.1%

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

      6. *-commutative 36.1%

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

      7. associate-*r* 36.3%

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

      8. *-commutative 36.3%

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

   10. Simplified 36.3%

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

       1. associate-*r* 36.2%

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

   12. Applied egg-rr 36.2%

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

   if 3.7000000000000003e-18 < (*.f64 b c) < 1.9e151

   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 93.0%

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

   5. Taylor expanded in k around inf 40.9%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.8 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-288}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-290}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.66 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* 18.0 (* y (* t z))))))
   (if (<= (* b c) -1.25e+136)
     (* b c)
     (if (<= (* b c) -5.2e-39)
       t_1
       (if (<= (* b c) 1.9e-290)
         (* -4.0 (* x i))
         (if (<= (* b c) 1.66e-74)
           (* j (* -27.0 k))
           (if (<= (* b c) 4e-18)
             t_1
             (if (<= (* b c) 1.75e+149) (* -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 t_1 = x * (18.0 * (y * (t * z)));
	double tmp;
	if ((b * c) <= -1.25e+136) {
		tmp = b * c;
	} else if ((b * c) <= -5.2e-39) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e-290) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 1.66e-74) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 4e-18) {
		tmp = t_1;
	} else if ((b * c) <= 1.75e+149) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (18.0d0 * (y * (t * z)))
    if ((b * c) <= (-1.25d+136)) then
        tmp = b * c
    else if ((b * c) <= (-5.2d-39)) then
        tmp = t_1
    else if ((b * c) <= 1.9d-290) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 1.66d-74) then
        tmp = j * ((-27.0d0) * k)
    else if ((b * c) <= 4d-18) then
        tmp = t_1
    else if ((b * c) <= 1.75d+149) 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 t_1 = x * (18.0 * (y * (t * z)));
	double tmp;
	if ((b * c) <= -1.25e+136) {
		tmp = b * c;
	} else if ((b * c) <= -5.2e-39) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e-290) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 1.66e-74) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 4e-18) {
		tmp = t_1;
	} else if ((b * c) <= 1.75e+149) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (18.0 * (y * (t * z)))
	tmp = 0
	if (b * c) <= -1.25e+136:
		tmp = b * c
	elif (b * c) <= -5.2e-39:
		tmp = t_1
	elif (b * c) <= 1.9e-290:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 1.66e-74:
		tmp = j * (-27.0 * k)
	elif (b * c) <= 4e-18:
		tmp = t_1
	elif (b * c) <= 1.75e+149:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(18.0 * Float64(y * Float64(t * z))))
	tmp = 0.0
	if (Float64(b * c) <= -1.25e+136)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5.2e-39)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.9e-290)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 1.66e-74)
		tmp = Float64(j * Float64(-27.0 * k));
	elseif (Float64(b * c) <= 4e-18)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.75e+149)
		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)
	t_1 = x * (18.0 * (y * (t * z)));
	tmp = 0.0;
	if ((b * c) <= -1.25e+136)
		tmp = b * c;
	elseif ((b * c) <= -5.2e-39)
		tmp = t_1;
	elseif ((b * c) <= 1.9e-290)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 1.66e-74)
		tmp = j * (-27.0 * k);
	elseif ((b * c) <= 4e-18)
		tmp = t_1;
	elseif ((b * c) <= 1.75e+149)
		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_] := Block[{t$95$1 = N[(x * N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+136], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.2e-39], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.9e-290], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.66e-74], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e-18], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.75e+149], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.25e136 or 1.75000000000000006e149 < (*.f64 b c)

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 81.7%

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

   4. Taylor expanded in a around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in b around inf 59.4%

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

   if -1.25e136 < (*.f64 b c) < -5.2e-39 or 1.65999999999999995e-74 < (*.f64 b c) < 4.0000000000000003e-18

   1. Initial program 91.6%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around inf 58.1%

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

      1. *-commutative 58.1%

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

      2. associate-*r* 62.2%

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

      3. *-commutative 62.2%

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

   7. Simplified 62.2%

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

   8. Taylor expanded in y around inf 40.8%

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

      1. *-commutative 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*l* 42.9%

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

      4. *-commutative 42.9%

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

      5. associate-*l* 42.9%

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

      6. *-commutative 42.9%

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

      7. associate-*r* 43.0%

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

      8. *-commutative 43.0%

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

   10. Simplified 43.0%

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

   if -5.2e-39 < (*.f64 b c) < 1.89999999999999988e-290

   1. Initial program 90.1%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in i around inf 61.0%

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

      1. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in x around inf 38.3%

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

   if 1.89999999999999988e-290 < (*.f64 b c) < 1.65999999999999995e-74

   1. Initial program 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in k around inf 44.9%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 44.9%

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

   7. Simplified 44.9%

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

   if 4.0000000000000003e-18 < (*.f64 b c) < 1.75000000000000006e149

   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 93.0%

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

   5. Taylor expanded in k around inf 40.9%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-290}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.66 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.75 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{-304}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.08 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.95 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.75e+135)
   (* b c)
   (if (<= (* b c) -1.95e-8)
     (* t (* (* y z) (* x 18.0)))
     (if (<= (* b c) 2.5e-304)
       (* -4.0 (* x i))
       (if (<= (* b c) 1.08e-72)
         (* j (* -27.0 k))
         (if (<= (* b c) 1.95e-18)
           (* t (* 18.0 (* x (* y z))))
           (if (<= (* b c) 3.9e+149) (* -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 ((b * c) <= -1.75e+135) {
		tmp = b * c;
	} else if ((b * c) <= -1.95e-8) {
		tmp = t * ((y * z) * (x * 18.0));
	} else if ((b * c) <= 2.5e-304) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 1.08e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 1.95e-18) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 3.9e+149) {
		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 ((b * c) <= (-1.75d+135)) then
        tmp = b * c
    else if ((b * c) <= (-1.95d-8)) then
        tmp = t * ((y * z) * (x * 18.0d0))
    else if ((b * c) <= 2.5d-304) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 1.08d-72) then
        tmp = j * ((-27.0d0) * k)
    else if ((b * c) <= 1.95d-18) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else if ((b * c) <= 3.9d+149) 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 ((b * c) <= -1.75e+135) {
		tmp = b * c;
	} else if ((b * c) <= -1.95e-8) {
		tmp = t * ((y * z) * (x * 18.0));
	} else if ((b * c) <= 2.5e-304) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 1.08e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 1.95e-18) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 3.9e+149) {
		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 (b * c) <= -1.75e+135:
		tmp = b * c
	elif (b * c) <= -1.95e-8:
		tmp = t * ((y * z) * (x * 18.0))
	elif (b * c) <= 2.5e-304:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 1.08e-72:
		tmp = j * (-27.0 * k)
	elif (b * c) <= 1.95e-18:
		tmp = t * (18.0 * (x * (y * z)))
	elif (b * c) <= 3.9e+149:
		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 (Float64(b * c) <= -1.75e+135)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.95e-8)
		tmp = Float64(t * Float64(Float64(y * z) * Float64(x * 18.0)));
	elseif (Float64(b * c) <= 2.5e-304)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 1.08e-72)
		tmp = Float64(j * Float64(-27.0 * k));
	elseif (Float64(b * c) <= 1.95e-18)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 3.9e+149)
		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 ((b * c) <= -1.75e+135)
		tmp = b * c;
	elseif ((b * c) <= -1.95e-8)
		tmp = t * ((y * z) * (x * 18.0));
	elseif ((b * c) <= 2.5e-304)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 1.08e-72)
		tmp = j * (-27.0 * k);
	elseif ((b * c) <= 1.95e-18)
		tmp = t * (18.0 * (x * (y * z)));
	elseif ((b * c) <= 3.9e+149)
		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[LessEqual[N[(b * c), $MachinePrecision], -1.75e+135], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.95e-8], N[(t * N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.5e-304], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.08e-72], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.95e-18], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.9e+149], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.7500000000000001e135 or 3.8999999999999999e149 < (*.f64 b c)

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 81.7%

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

   4. Taylor expanded in a around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in b around inf 59.4%

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

   if -1.7500000000000001e135 < (*.f64 b c) < -1.94999999999999992e-8

   1. Initial program 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 68.6%

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

   6. Taylor expanded in t around inf 58.4%

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

   7. Taylor expanded in x around inf 47.6%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -1.94999999999999992e-8 < (*.f64 b c) < 2.49999999999999983e-304

   1. Initial program 90.5%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in i around inf 61.3%

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

      1. *-commutative 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in x around inf 36.8%

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

   if 2.49999999999999983e-304 < (*.f64 b c) < 1.07999999999999998e-72

   1. Initial program 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in k around inf 44.9%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 44.9%

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

   7. Simplified 44.9%

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

   if 1.07999999999999998e-72 < (*.f64 b c) < 1.95000000000000002e-18

   1. Initial program 87.3%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 56.4%

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

   6. Taylor expanded in t around inf 56.4%

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

   7. Taylor expanded in x around inf 36.2%

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

   if 1.95000000000000002e-18 < (*.f64 b c) < 3.8999999999999999e149

   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 93.0%

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

   5. Taylor expanded in k around inf 40.9%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.75 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{-304}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.08 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.95 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;18 \cdot \left(t \cdot t\_1\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-306}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(18 \cdot t\_1\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= (* b c) -6.2e+136)
     (* b c)
     (if (<= (* b c) -6.5e-9)
       (* 18.0 (* t t_1))
       (if (<= (* b c) 1.05e-306)
         (* -4.0 (* x i))
         (if (<= (* b c) 3e-73)
           (* j (* -27.0 k))
           (if (<= (* b c) 1.65e-17)
             (* t (* 18.0 t_1))
             (if (<= (* b c) 3.9e+149) (* -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 t_1 = x * (y * z);
	double tmp;
	if ((b * c) <= -6.2e+136) {
		tmp = b * c;
	} else if ((b * c) <= -6.5e-9) {
		tmp = 18.0 * (t * t_1);
	} else if ((b * c) <= 1.05e-306) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3e-73) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 1.65e-17) {
		tmp = t * (18.0 * t_1);
	} else if ((b * c) <= 3.9e+149) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if ((b * c) <= (-6.2d+136)) then
        tmp = b * c
    else if ((b * c) <= (-6.5d-9)) then
        tmp = 18.0d0 * (t * t_1)
    else if ((b * c) <= 1.05d-306) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 3d-73) then
        tmp = j * ((-27.0d0) * k)
    else if ((b * c) <= 1.65d-17) then
        tmp = t * (18.0d0 * t_1)
    else if ((b * c) <= 3.9d+149) 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 t_1 = x * (y * z);
	double tmp;
	if ((b * c) <= -6.2e+136) {
		tmp = b * c;
	} else if ((b * c) <= -6.5e-9) {
		tmp = 18.0 * (t * t_1);
	} else if ((b * c) <= 1.05e-306) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3e-73) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 1.65e-17) {
		tmp = t * (18.0 * t_1);
	} else if ((b * c) <= 3.9e+149) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	tmp = 0
	if (b * c) <= -6.2e+136:
		tmp = b * c
	elif (b * c) <= -6.5e-9:
		tmp = 18.0 * (t * t_1)
	elif (b * c) <= 1.05e-306:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 3e-73:
		tmp = j * (-27.0 * k)
	elif (b * c) <= 1.65e-17:
		tmp = t * (18.0 * t_1)
	elif (b * c) <= 3.9e+149:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (Float64(b * c) <= -6.2e+136)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -6.5e-9)
		tmp = Float64(18.0 * Float64(t * t_1));
	elseif (Float64(b * c) <= 1.05e-306)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 3e-73)
		tmp = Float64(j * Float64(-27.0 * k));
	elseif (Float64(b * c) <= 1.65e-17)
		tmp = Float64(t * Float64(18.0 * t_1));
	elseif (Float64(b * c) <= 3.9e+149)
		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)
	t_1 = x * (y * z);
	tmp = 0.0;
	if ((b * c) <= -6.2e+136)
		tmp = b * c;
	elseif ((b * c) <= -6.5e-9)
		tmp = 18.0 * (t * t_1);
	elseif ((b * c) <= 1.05e-306)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 3e-73)
		tmp = j * (-27.0 * k);
	elseif ((b * c) <= 1.65e-17)
		tmp = t * (18.0 * t_1);
	elseif ((b * c) <= 3.9e+149)
		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_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.2e+136], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.5e-9], N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.05e-306], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3e-73], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-17], N[(t * N[(18.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.9e+149], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -6.19999999999999967e136 or 3.8999999999999999e149 < (*.f64 b c)

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 81.7%

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

   4. Taylor expanded in a around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in b around inf 59.4%

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

   if -6.19999999999999967e136 < (*.f64 b c) < -6.5000000000000003e-9

   1. Initial program 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*r* 68.4%

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

      3. *-commutative 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in y around inf 47.6%

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

   if -6.5000000000000003e-9 < (*.f64 b c) < 1.0500000000000001e-306

   1. Initial program 90.5%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in i around inf 61.3%

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

      1. *-commutative 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in x around inf 36.8%

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

   if 1.0500000000000001e-306 < (*.f64 b c) < 3e-73

   1. Initial program 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in k around inf 44.9%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 44.9%

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

   7. Simplified 44.9%

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

   if 3e-73 < (*.f64 b c) < 1.65e-17

   1. Initial program 87.3%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 56.4%

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

   6. Taylor expanded in t around inf 56.4%

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

   7. Taylor expanded in x around inf 36.2%

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

   if 1.65e-17 < (*.f64 b c) < 3.8999999999999999e149

   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 93.0%

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

   5. Taylor expanded in k around inf 40.9%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-306}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -3.4 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-288}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))))
   (if (<= (* b c) -3.4e+135)
     (* b c)
     (if (<= (* b c) -2.5e-8)
       t_1
       (if (<= (* b c) 1.6e-288)
         (* -4.0 (* x i))
         (if (<= (* b c) 5.5e-72)
           (* j (* -27.0 k))
           (if (<= (* b c) 4e-18)
             t_1
             (if (<= (* b c) 1.15e+149) (* -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 t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -3.4e+135) {
		tmp = b * c;
	} else if ((b * c) <= -2.5e-8) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-288) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 5.5e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 4e-18) {
		tmp = t_1;
	} else if ((b * c) <= 1.15e+149) {
		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) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    if ((b * c) <= (-3.4d+135)) then
        tmp = b * c
    else if ((b * c) <= (-2.5d-8)) then
        tmp = t_1
    else if ((b * c) <= 1.6d-288) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 5.5d-72) then
        tmp = j * ((-27.0d0) * k)
    else if ((b * c) <= 4d-18) then
        tmp = t_1
    else if ((b * c) <= 1.15d+149) 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 t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -3.4e+135) {
		tmp = b * c;
	} else if ((b * c) <= -2.5e-8) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-288) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 5.5e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 4e-18) {
		tmp = t_1;
	} else if ((b * c) <= 1.15e+149) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if (b * c) <= -3.4e+135:
		tmp = b * c
	elif (b * c) <= -2.5e-8:
		tmp = t_1
	elif (b * c) <= 1.6e-288:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 5.5e-72:
		tmp = j * (-27.0 * k)
	elif (b * c) <= 4e-18:
		tmp = t_1
	elif (b * c) <= 1.15e+149:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -3.4e+135)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.5e-8)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e-288)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 5.5e-72)
		tmp = Float64(j * Float64(-27.0 * k));
	elseif (Float64(b * c) <= 4e-18)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.15e+149)
		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)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -3.4e+135)
		tmp = b * c;
	elseif ((b * c) <= -2.5e-8)
		tmp = t_1;
	elseif ((b * c) <= 1.6e-288)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 5.5e-72)
		tmp = j * (-27.0 * k);
	elseif ((b * c) <= 4e-18)
		tmp = t_1;
	elseif ((b * c) <= 1.15e+149)
		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_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.4e+135], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.5e-8], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e-288], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.5e-72], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e-18], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.15e+149], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -3.4000000000000001e135 or 1.1499999999999999e149 < (*.f64 b c)

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 81.7%

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

   4. Taylor expanded in a around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in b around inf 59.4%

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

   if -3.4000000000000001e135 < (*.f64 b c) < -2.4999999999999999e-8 or 5.49999999999999994e-72 < (*.f64 b c) < 4.0000000000000003e-18

   1. Initial program 91.0%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. associate-*r* 59.6%

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

      3. *-commutative 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in y around inf 43.4%

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

   if -2.4999999999999999e-8 < (*.f64 b c) < 1.6e-288

   1. Initial program 90.5%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in i around inf 61.3%

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

      1. *-commutative 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in x around inf 36.8%

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

   if 1.6e-288 < (*.f64 b c) < 5.49999999999999994e-72

   1. Initial program 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in k around inf 44.9%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 44.9%

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

   7. Simplified 44.9%

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

   if 4.0000000000000003e-18 < (*.f64 b c) < 1.1499999999999999e149

   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 93.0%

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

   5. Taylor expanded in k around inf 40.9%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.4 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-288}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{-18}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+149}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -3.7 \cdot 10^{+143}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 6.6 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 7.6 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* -4.0 (* x i))))
   (if (<= (* b c) -3.7e+143)
     (* b c)
     (if (<= (* b c) -1.95e-49)
       t_1
       (if (<= (* b c) 5.5e-301)
         t_2
         (if (<= (* b c) 9.5e-72)
           (* j (* -27.0 k))
           (if (<= (* b c) 6.6e-31)
             t_2
             (if (<= (* b c) 7.6e+151) t_1 (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -3.7e+143) {
		tmp = b * c;
	} else if ((b * c) <= -1.95e-49) {
		tmp = t_1;
	} else if ((b * c) <= 5.5e-301) {
		tmp = t_2;
	} else if ((b * c) <= 9.5e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 6.6e-31) {
		tmp = t_2;
	} else if ((b * c) <= 7.6e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (-4.0d0) * (x * i)
    if ((b * c) <= (-3.7d+143)) then
        tmp = b * c
    else if ((b * c) <= (-1.95d-49)) then
        tmp = t_1
    else if ((b * c) <= 5.5d-301) then
        tmp = t_2
    else if ((b * c) <= 9.5d-72) then
        tmp = j * ((-27.0d0) * k)
    else if ((b * c) <= 6.6d-31) then
        tmp = t_2
    else if ((b * c) <= 7.6d+151) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -3.7e+143) {
		tmp = b * c;
	} else if ((b * c) <= -1.95e-49) {
		tmp = t_1;
	} else if ((b * c) <= 5.5e-301) {
		tmp = t_2;
	} else if ((b * c) <= 9.5e-72) {
		tmp = j * (-27.0 * k);
	} else if ((b * c) <= 6.6e-31) {
		tmp = t_2;
	} else if ((b * c) <= 7.6e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -3.7e+143:
		tmp = b * c
	elif (b * c) <= -1.95e-49:
		tmp = t_1
	elif (b * c) <= 5.5e-301:
		tmp = t_2
	elif (b * c) <= 9.5e-72:
		tmp = j * (-27.0 * k)
	elif (b * c) <= 6.6e-31:
		tmp = t_2
	elif (b * c) <= 7.6e+151:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -3.7e+143)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.95e-49)
		tmp = t_1;
	elseif (Float64(b * c) <= 5.5e-301)
		tmp = t_2;
	elseif (Float64(b * c) <= 9.5e-72)
		tmp = Float64(j * Float64(-27.0 * k));
	elseif (Float64(b * c) <= 6.6e-31)
		tmp = t_2;
	elseif (Float64(b * c) <= 7.6e+151)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -3.7e+143)
		tmp = b * c;
	elseif ((b * c) <= -1.95e-49)
		tmp = t_1;
	elseif ((b * c) <= 5.5e-301)
		tmp = t_2;
	elseif ((b * c) <= 9.5e-72)
		tmp = j * (-27.0 * k);
	elseif ((b * c) <= 6.6e-31)
		tmp = t_2;
	elseif ((b * c) <= 7.6e+151)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.7e+143], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.95e-49], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5.5e-301], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 9.5e-72], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.6e-31], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 7.6e+151], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.7000000000000002e143 or 7.6000000000000001e151 < (*.f64 b c)

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 83.3%

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

   4. Taylor expanded in a around inf 82.2%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in b around inf 61.1%

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

   if -3.7000000000000002e143 < (*.f64 b c) < -1.95000000000000006e-49 or 6.5999999999999998e-31 < (*.f64 b c) < 7.6000000000000001e151

   1. Initial program 88.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in k around inf 33.7%

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

   if -1.95000000000000006e-49 < (*.f64 b c) < 5.50000000000000005e-301 or 9.4999999999999998e-72 < (*.f64 b c) < 6.5999999999999998e-31

   1. Initial program 89.1%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in i around inf 59.6%

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

      1. *-commutative 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in x around inf 39.2%

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

   if 5.50000000000000005e-301 < (*.f64 b c) < 9.4999999999999998e-72

   1. Initial program 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in k around inf 43.5%

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

      1. associate-*r* 43.6%

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

      2. *-commutative 43.6%

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

      3. associate-*r* 43.5%

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

   7. Simplified 43.5%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.7 \cdot 10^{+143}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-49}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-301}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 6.6 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 7.6 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -2.1 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* -4.0 (* x i))))
   (if (<= (* b c) -2.1e+141)
     (* b c)
     (if (<= (* b c) -1.6e-52)
       t_1
       (if (<= (* b c) 1.55e-291)
         t_2
         (if (<= (* b c) 1.1e-71)
           t_1
           (if (<= (* b c) 2.3e-32)
             t_2
             (if (<= (* b c) 6.5e+151) t_1 (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -2.1e+141) {
		tmp = b * c;
	} else if ((b * c) <= -1.6e-52) {
		tmp = t_1;
	} else if ((b * c) <= 1.55e-291) {
		tmp = t_2;
	} else if ((b * c) <= 1.1e-71) {
		tmp = t_1;
	} else if ((b * c) <= 2.3e-32) {
		tmp = t_2;
	} else if ((b * c) <= 6.5e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (-4.0d0) * (x * i)
    if ((b * c) <= (-2.1d+141)) then
        tmp = b * c
    else if ((b * c) <= (-1.6d-52)) then
        tmp = t_1
    else if ((b * c) <= 1.55d-291) then
        tmp = t_2
    else if ((b * c) <= 1.1d-71) then
        tmp = t_1
    else if ((b * c) <= 2.3d-32) then
        tmp = t_2
    else if ((b * c) <= 6.5d+151) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -2.1e+141) {
		tmp = b * c;
	} else if ((b * c) <= -1.6e-52) {
		tmp = t_1;
	} else if ((b * c) <= 1.55e-291) {
		tmp = t_2;
	} else if ((b * c) <= 1.1e-71) {
		tmp = t_1;
	} else if ((b * c) <= 2.3e-32) {
		tmp = t_2;
	} else if ((b * c) <= 6.5e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -2.1e+141:
		tmp = b * c
	elif (b * c) <= -1.6e-52:
		tmp = t_1
	elif (b * c) <= 1.55e-291:
		tmp = t_2
	elif (b * c) <= 1.1e-71:
		tmp = t_1
	elif (b * c) <= 2.3e-32:
		tmp = t_2
	elif (b * c) <= 6.5e+151:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -2.1e+141)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.6e-52)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.55e-291)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.1e-71)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.3e-32)
		tmp = t_2;
	elseif (Float64(b * c) <= 6.5e+151)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -2.1e+141)
		tmp = b * c;
	elseif ((b * c) <= -1.6e-52)
		tmp = t_1;
	elseif ((b * c) <= 1.55e-291)
		tmp = t_2;
	elseif ((b * c) <= 1.1e-71)
		tmp = t_1;
	elseif ((b * c) <= 2.3e-32)
		tmp = t_2;
	elseif ((b * c) <= 6.5e+151)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.1e+141], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.6e-52], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.55e-291], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.1e-71], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.3e-32], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 6.5e+151], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.0999999999999998e141 or 6.5000000000000002e151 < (*.f64 b c)

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 83.3%

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

   4. Taylor expanded in a around inf 82.2%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in b around inf 61.1%

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

   if -2.0999999999999998e141 < (*.f64 b c) < -1.60000000000000005e-52 or 1.55000000000000006e-291 < (*.f64 b c) < 1.09999999999999999e-71 or 2.3000000000000001e-32 < (*.f64 b c) < 6.5000000000000002e151

   1. Initial program 87.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in k around inf 36.9%

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

   if -1.60000000000000005e-52 < (*.f64 b c) < 1.55000000000000006e-291 or 1.09999999999999999e-71 < (*.f64 b c) < 2.3000000000000001e-32

   1. Initial program 89.1%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in i around inf 59.6%

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

      1. *-commutative 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in x around inf 39.2%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.1 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-52}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{-291}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + k \cdot \left(-27 \cdot j\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot 18\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* k (* -27.0 j)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -10.0)
     t_1
     (if (<= t_2 -1e-83)
       (* (* t (* y z)) (* x 18.0))
       (if (<= t_2 5e-109)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_2 2e+74) (* (* 18.0 (* y z)) (* x t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (k * (-27.0 * j));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1;
	} else if (t_2 <= -1e-83) {
		tmp = (t * (y * z)) * (x * 18.0);
	} else if (t_2 <= 5e-109) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 2e+74) {
		tmp = (18.0 * (y * z)) * (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (k * ((-27.0d0) * j))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-10.0d0)) then
        tmp = t_1
    else if (t_2 <= (-1d-83)) then
        tmp = (t * (y * z)) * (x * 18.0d0)
    else if (t_2 <= 5d-109) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_2 <= 2d+74) then
        tmp = (18.0d0 * (y * z)) * (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (k * (-27.0 * j));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1;
	} else if (t_2 <= -1e-83) {
		tmp = (t * (y * z)) * (x * 18.0);
	} else if (t_2 <= 5e-109) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 2e+74) {
		tmp = (18.0 * (y * z)) * (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (k * (-27.0 * j))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_1
	elif t_2 <= -1e-83:
		tmp = (t * (y * z)) * (x * 18.0)
	elif t_2 <= 5e-109:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_2 <= 2e+74:
		tmp = (18.0 * (y * z)) * (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(k * Float64(-27.0 * j)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = t_1;
	elseif (t_2 <= -1e-83)
		tmp = Float64(Float64(t * Float64(y * z)) * Float64(x * 18.0));
	elseif (t_2 <= 5e-109)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_2 <= 2e+74)
		tmp = Float64(Float64(18.0 * Float64(y * z)) * Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (k * (-27.0 * j));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_1;
	elseif (t_2 <= -1e-83)
		tmp = (t * (y * z)) * (x * 18.0);
	elseif (t_2 <= 5e-109)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_2 <= 2e+74)
		tmp = (18.0 * (y * z)) * (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], t$95$1, If[LessEqual[t$95$2, -1e-83], N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-109], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+74], N[(N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10 or 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.8%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 69.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83

   1. Initial program 93.7%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*r* 65.8%

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

      3. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in y around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 55.0%

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

      4. associate-*r* 55.0%

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

      5. *-commutative 55.0%

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

      6. associate-*r* 55.0%

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

      7. *-commutative 55.0%

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

      8. associate-*r* 55.0%

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

      9. *-commutative 55.0%

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

      10. associate-*l* 55.0%

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

      11. *-commutative 55.0%

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

   10. Applied egg-rr 55.0%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e-109

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf 87.1%

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

   4. Taylor expanded in a around inf 79.6%

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

      1. associate-*r* 79.6%

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

      2. *-commutative 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in j around 0 78.6%

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

   8. Taylor expanded in a around 0 63.5%

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

   if 5.0000000000000002e-109 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   1. Initial program 79.2%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in y around inf 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*r* 58.9%

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

      3. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*r* 51.2%

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

      3. associate-*l* 51.3%

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

   10. Applied egg-rr 51.3%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot 18\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= x -1e+109)
     (- (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (* 4.0 (* x i))) t_1)
     (if (<= x 1.15e+112)
       (-
        (-
         (+ (* b c) (- (* (* x (* 18.0 y)) (* t z)) (* t (* a 4.0))))
         (* i (* x 4.0)))
        t_1)
       (- (* x (- (* 18.0 (* t (* y z))) (* i 4.0))) 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 = k * (j * 27.0);
	double tmp;
	if (x <= -1e+109) {
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i))) - t_1;
	} else if (x <= 1.15e+112) {
		tmp = (((b * c) + (((x * (18.0 * y)) * (t * z)) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - 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 = k * (j * 27.0d0)
    if (x <= (-1d+109)) then
        tmp = (((b * c) + (18.0d0 * (t * (x * (y * z))))) - (4.0d0 * (x * i))) - t_1
    else if (x <= 1.15d+112) then
        tmp = (((b * c) + (((x * (18.0d0 * y)) * (t * z)) - (t * (a * 4.0d0)))) - (i * (x * 4.0d0))) - t_1
    else
        tmp = (x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))) - 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 = k * (j * 27.0);
	double tmp;
	if (x <= -1e+109) {
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i))) - t_1;
	} else if (x <= 1.15e+112) {
		tmp = (((b * c) + (((x * (18.0 * y)) * (t * z)) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if x <= -1e+109:
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i))) - t_1
	elif x <= 1.15e+112:
		tmp = (((b * c) + (((x * (18.0 * y)) * (t * z)) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1
	else:
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (x <= -1e+109)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (x <= 1.15e+112)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(Float64(x * Float64(18.0 * y)) * Float64(t * z)) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - t_1);
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (x <= -1e+109)
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i))) - t_1;
	elseif (x <= 1.15e+112)
		tmp = (((b * c) + (((x * (18.0 * y)) * (t * z)) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	else
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+109], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.15e+112], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999982e108

   1. Initial program 76.0%

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

   3. Taylor expanded in a around 0 84.3%

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

   if -9.99999999999999982e108 < x < 1.15e112

   1. Initial program 93.7%

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

      1. associate-*l* 89.8%

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

      2. associate-*l* 89.8%

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

   4. Applied egg-rr 89.8%

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

   if 1.15e112 < x

   1. Initial program 69.0%

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

   3. Taylor expanded in x around inf 91.8%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_2\right) - t\_1\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-77}:\\ \;\;\;\;\left(b \cdot c - \left(t\_2 + \left(a \cdot t\right) \cdot 4\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+116}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2 (* 4.0 (* x i)))
        (t_3 (- (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) t_2) t_1)))
   (if (<= x -1.6e-53)
     t_3
     (if (<= x 1.45e-77)
       (- (- (* b c) (+ t_2 (* (* a t) 4.0))) t_1)
       (if (<= x 3e+116)
         t_3
         (- (* x (- (* 18.0 (* t (* y z))) (* i 4.0))) 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 = k * (j * 27.0);
	double t_2 = 4.0 * (x * i);
	double t_3 = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1;
	double tmp;
	if (x <= -1.6e-53) {
		tmp = t_3;
	} else if (x <= 1.45e-77) {
		tmp = ((b * c) - (t_2 + ((a * t) * 4.0))) - t_1;
	} else if (x <= 3e+116) {
		tmp = t_3;
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = 4.0d0 * (x * i)
    t_3 = (((b * c) + (18.0d0 * (t * (x * (y * z))))) - t_2) - t_1
    if (x <= (-1.6d-53)) then
        tmp = t_3
    else if (x <= 1.45d-77) then
        tmp = ((b * c) - (t_2 + ((a * t) * 4.0d0))) - t_1
    else if (x <= 3d+116) then
        tmp = t_3
    else
        tmp = (x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))) - 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 = k * (j * 27.0);
	double t_2 = 4.0 * (x * i);
	double t_3 = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1;
	double tmp;
	if (x <= -1.6e-53) {
		tmp = t_3;
	} else if (x <= 1.45e-77) {
		tmp = ((b * c) - (t_2 + ((a * t) * 4.0))) - t_1;
	} else if (x <= 3e+116) {
		tmp = t_3;
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = 4.0 * (x * i)
	t_3 = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1
	tmp = 0
	if x <= -1.6e-53:
		tmp = t_3
	elif x <= 1.45e-77:
		tmp = ((b * c) - (t_2 + ((a * t) * 4.0))) - t_1
	elif x <= 3e+116:
		tmp = t_3
	else:
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - t_2) - t_1)
	tmp = 0.0
	if (x <= -1.6e-53)
		tmp = t_3;
	elseif (x <= 1.45e-77)
		tmp = Float64(Float64(Float64(b * c) - Float64(t_2 + Float64(Float64(a * t) * 4.0))) - t_1);
	elseif (x <= 3e+116)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = 4.0 * (x * i);
	t_3 = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1;
	tmp = 0.0;
	if (x <= -1.6e-53)
		tmp = t_3;
	elseif (x <= 1.45e-77)
		tmp = ((b * c) - (t_2 + ((a * t) * 4.0))) - t_1;
	elseif (x <= 3e+116)
		tmp = t_3;
	else
		tmp = (x * ((18.0 * (t * (y * z))) - (i * 4.0))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -1.6e-53], t$95$3, If[LessEqual[x, 1.45e-77], N[(N[(N[(b * c), $MachinePrecision] - N[(t$95$2 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3e+116], t$95$3, N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e-53 or 1.4499999999999999e-77 < x < 2.9999999999999999e116

   1. Initial program 86.0%

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

   3. Taylor expanded in a around 0 85.2%

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

   if -1.6e-53 < x < 1.4499999999999999e-77

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 89.6%

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

   if 2.9999999999999999e116 < x

   1. Initial program 69.0%

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

   3. Taylor expanded in x around inf 91.8%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-53}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-77}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + \left(a \cdot t\right) \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+116}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83} \lor \neg \left(t\_2 \leq 10^{-25}\right):\\ \;\;\;\;t\_1 + -4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* -27.0 j))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -10.0)
     (+ (* b c) t_1)
     (if (or (<= t_2 -1e-83) (not (<= t_2 1e-25)))
       (+ t_1 (* -4.0 (* a t)))
       (- (* b c) (* 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 = k * (-27.0 * j);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = (b * c) + t_1;
	} else if ((t_2 <= -1e-83) || !(t_2 <= 1e-25)) {
		tmp = t_1 + (-4.0 * (a * t));
	} else {
		tmp = (b * c) - (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) :: t_2
    real(8) :: tmp
    t_1 = k * ((-27.0d0) * j)
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-10.0d0)) then
        tmp = (b * c) + t_1
    else if ((t_2 <= (-1d-83)) .or. (.not. (t_2 <= 1d-25))) then
        tmp = t_1 + ((-4.0d0) * (a * t))
    else
        tmp = (b * c) - (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 = k * (-27.0 * j);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = (b * c) + t_1;
	} else if ((t_2 <= -1e-83) || !(t_2 <= 1e-25)) {
		tmp = t_1 + (-4.0 * (a * t));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (-27.0 * j)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -10.0:
		tmp = (b * c) + t_1
	elif (t_2 <= -1e-83) or not (t_2 <= 1e-25):
		tmp = t_1 + (-4.0 * (a * t))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(-27.0 * j))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = Float64(Float64(b * c) + t_1);
	elseif ((t_2 <= -1e-83) || !(t_2 <= 1e-25))
		tmp = Float64(t_1 + Float64(-4.0 * Float64(a * t)));
	else
		tmp = Float64(Float64(b * c) - 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 = k * (-27.0 * j);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = (b * c) + t_1;
	elseif ((t_2 <= -1e-83) || ~((t_2 <= 1e-25)))
		tmp = t_1 + (-4.0 * (a * t));
	else
		tmp = (b * c) - (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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[t$95$2, -1e-83], N[Not[LessEqual[t$95$2, 1e-25]], $MachinePrecision]], N[(t$95$1 + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10

   1. Initial program 84.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 72.6%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 1.00000000000000004e-25 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 88.6%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 58.1%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e-25

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 84.1%

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

   4. Taylor expanded in a around inf 77.2%

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

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in j around 0 75.5%

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

   8. Taylor expanded in a around 0 61.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83} \lor \neg \left(k \cdot \left(j \cdot 27\right) \leq 10^{-25}\right):\\ \;\;\;\;k \cdot \left(-27 \cdot j\right) + -4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+149}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+125}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* -27.0 j))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+149)
     (+ (* b c) t_1)
     (if (<= t_2 1e+125)
       (- (+ (* b c) (* -4.0 (* a t))) (* 4.0 (* x i)))
       (+ t_1 (* -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 = k * (-27.0 * j);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+149) {
		tmp = (b * c) + t_1;
	} else if (t_2 <= 1e+125) {
		tmp = ((b * c) + (-4.0 * (a * t))) - (4.0 * (x * i));
	} else {
		tmp = t_1 + (-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) :: t_2
    real(8) :: tmp
    t_1 = k * ((-27.0d0) * j)
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+149)) then
        tmp = (b * c) + t_1
    else if (t_2 <= 1d+125) then
        tmp = ((b * c) + ((-4.0d0) * (a * t))) - (4.0d0 * (x * i))
    else
        tmp = t_1 + ((-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 = k * (-27.0 * j);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+149) {
		tmp = (b * c) + t_1;
	} else if (t_2 <= 1e+125) {
		tmp = ((b * c) + (-4.0 * (a * t))) - (4.0 * (x * i));
	} else {
		tmp = t_1 + (-4.0 * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (-27.0 * j)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+149:
		tmp = (b * c) + t_1
	elif t_2 <= 1e+125:
		tmp = ((b * c) + (-4.0 * (a * t))) - (4.0 * (x * i))
	else:
		tmp = t_1 + (-4.0 * (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(-27.0 * j))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+149)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t_2 <= 1e+125)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(t_1 + 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 = k * (-27.0 * j);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+149)
		tmp = (b * c) + t_1;
	elseif (t_2 <= 1e+125)
		tmp = ((b * c) + (-4.0 * (a * t))) - (4.0 * (x * i));
	else
		tmp = t_1 + (-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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+149], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e+125], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000005e149

   1. Initial program 81.9%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 85.5%

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

   if -1.00000000000000005e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   1. Initial program 88.8%

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

   3. Taylor expanded in a around inf 86.3%

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

   4. Taylor expanded in a around inf 76.8%

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

      1. associate-*r* 76.8%

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

      2. *-commutative 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in j around 0 70.1%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in i around inf 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+149}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+195}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + \left(a \cdot t\right) \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -27 \cdot \frac{j \cdot k}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.45e+135)
   (+ (* t (+ (* -4.0 a) (* x (* 18.0 (* y z))))) (* k (* -27.0 j)))
   (if (<= t 8.6e+195)
     (- (- (* b c) (+ (* 4.0 (* x i)) (* (* a t) 4.0))) (* k (* j 27.0)))
     (* t (+ (+ (* -4.0 a) (* 18.0 (* x (* y z)))) (* -27.0 (/ (* j k) 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 (t <= -1.45e+135) {
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	} else if (t <= 8.6e+195) {
		tmp = ((b * c) - ((4.0 * (x * i)) + ((a * t) * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / 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 (t <= (-1.45d+135)) then
        tmp = (t * (((-4.0d0) * a) + (x * (18.0d0 * (y * z))))) + (k * ((-27.0d0) * j))
    else if (t <= 8.6d+195) then
        tmp = ((b * c) - ((4.0d0 * (x * i)) + ((a * t) * 4.0d0))) - (k * (j * 27.0d0))
    else
        tmp = t * ((((-4.0d0) * a) + (18.0d0 * (x * (y * z)))) + ((-27.0d0) * ((j * k) / 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 (t <= -1.45e+135) {
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	} else if (t <= 8.6e+195) {
		tmp = ((b * c) - ((4.0 * (x * i)) + ((a * t) * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.45e+135:
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j))
	elif t <= 8.6e+195:
		tmp = ((b * c) - ((4.0 * (x * i)) + ((a * t) * 4.0))) - (k * (j * 27.0))
	else:
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.45e+135)
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(x * Float64(18.0 * Float64(y * z))))) + Float64(k * Float64(-27.0 * j)));
	elseif (t <= 8.6e+195)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(Float64(a * t) * 4.0))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(t * Float64(Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))) + Float64(-27.0 * Float64(Float64(j * k) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.45e+135)
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	elseif (t <= 8.6e+195)
		tmp = ((b * c) - ((4.0 * (x * i)) + ((a * t) * 4.0))) - (k * (j * 27.0));
	else
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.45e+135], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+195], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4499999999999999e135

   1. Initial program 71.3%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in t around inf 82.3%

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

      1. *-commutative 82.3%

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

   7. Applied egg-rr 82.3%

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

      1. associate-*l* 82.4%

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

   9. Simplified 82.4%

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

   if -1.4499999999999999e135 < t < 8.59999999999999962e195

   1. Initial program 90.6%

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

   3. Taylor expanded in y around 0 84.9%

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

   if 8.59999999999999962e195 < t

   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 89.3%

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

   5. Taylor expanded in t around inf 85.9%

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

   6. Taylor expanded in t around inf 89.4%

      \[\leadsto \color{blue}{t \cdot \left(-27 \cdot \frac{j \cdot k}{t} + \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+195}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + \left(a \cdot t\right) \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -27 \cdot \frac{j \cdot k}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+101}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -27 \cdot \frac{j \cdot k}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.32e+75)
   (+ (* t (+ (* -4.0 a) (* x (* 18.0 (* y z))))) (* k (* -27.0 j)))
   (if (<= t 6.2e+101)
     (- (- (* b c) (* 4.0 (* x i))) (* k (* j 27.0)))
     (* t (+ (+ (* -4.0 a) (* 18.0 (* x (* y z)))) (* -27.0 (/ (* j k) 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 (t <= -1.32e+75) {
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	} else if (t <= 6.2e+101) {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	} else {
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / 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 (t <= (-1.32d+75)) then
        tmp = (t * (((-4.0d0) * a) + (x * (18.0d0 * (y * z))))) + (k * ((-27.0d0) * j))
    else if (t <= 6.2d+101) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 27.0d0))
    else
        tmp = t * ((((-4.0d0) * a) + (18.0d0 * (x * (y * z)))) + ((-27.0d0) * ((j * k) / 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 (t <= -1.32e+75) {
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	} else if (t <= 6.2e+101) {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	} else {
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.32e+75:
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j))
	elif t <= 6.2e+101:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	else:
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.32e+75)
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(x * Float64(18.0 * Float64(y * z))))) + Float64(k * Float64(-27.0 * j)));
	elseif (t <= 6.2e+101)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(t * Float64(Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))) + Float64(-27.0 * Float64(Float64(j * k) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.32e+75)
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	elseif (t <= 6.2e+101)
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	else
		tmp = t * (((-4.0 * a) + (18.0 * (x * (y * z)))) + (-27.0 * ((j * k) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.32e+75], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+101], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3200000000000001e75

   1. Initial program 75.5%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in t around inf 78.4%

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

      1. *-commutative 78.4%

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

   7. Applied egg-rr 78.4%

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

      1. associate-*l* 78.6%

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

   9. Simplified 78.6%

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

   if -1.3200000000000001e75 < t < 6.19999999999999998e101

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 79.4%

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

   if 6.19999999999999998e101 < t

   1. Initial program 82.5%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in t around inf 82.7%

      \[\leadsto \color{blue}{t \cdot \left(-27 \cdot \frac{j \cdot k}{t} + \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+101}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -27 \cdot \frac{j \cdot k}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-254}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* k (* -27.0 j)))))
   (if (<= t -9.5e+125)
     (* x (* 18.0 (* y (* t z))))
     (if (<= t -1.25e-216)
       t_1
       (if (<= t -2.1e-254)
         (* -4.0 (* x i))
         (if (<= t 7.6e+130) t_1 (* t (* -4.0 a))))))))

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) + (k * (-27.0 * j));
	double tmp;
	if (t <= -9.5e+125) {
		tmp = x * (18.0 * (y * (t * z)));
	} else if (t <= -1.25e-216) {
		tmp = t_1;
	} else if (t <= -2.1e-254) {
		tmp = -4.0 * (x * i);
	} else if (t <= 7.6e+130) {
		tmp = t_1;
	} else {
		tmp = t * (-4.0 * a);
	}
	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) + (k * ((-27.0d0) * j))
    if (t <= (-9.5d+125)) then
        tmp = x * (18.0d0 * (y * (t * z)))
    else if (t <= (-1.25d-216)) then
        tmp = t_1
    else if (t <= (-2.1d-254)) then
        tmp = (-4.0d0) * (x * i)
    else if (t <= 7.6d+130) then
        tmp = t_1
    else
        tmp = t * ((-4.0d0) * a)
    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) + (k * (-27.0 * j));
	double tmp;
	if (t <= -9.5e+125) {
		tmp = x * (18.0 * (y * (t * z)));
	} else if (t <= -1.25e-216) {
		tmp = t_1;
	} else if (t <= -2.1e-254) {
		tmp = -4.0 * (x * i);
	} else if (t <= 7.6e+130) {
		tmp = t_1;
	} else {
		tmp = t * (-4.0 * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (k * (-27.0 * j))
	tmp = 0
	if t <= -9.5e+125:
		tmp = x * (18.0 * (y * (t * z)))
	elif t <= -1.25e-216:
		tmp = t_1
	elif t <= -2.1e-254:
		tmp = -4.0 * (x * i)
	elif t <= 7.6e+130:
		tmp = t_1
	else:
		tmp = t * (-4.0 * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(k * Float64(-27.0 * j)))
	tmp = 0.0
	if (t <= -9.5e+125)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(t * z))));
	elseif (t <= -1.25e-216)
		tmp = t_1;
	elseif (t <= -2.1e-254)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (t <= 7.6e+130)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-4.0 * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (k * (-27.0 * j));
	tmp = 0.0;
	if (t <= -9.5e+125)
		tmp = x * (18.0 * (y * (t * z)));
	elseif (t <= -1.25e-216)
		tmp = t_1;
	elseif (t <= -2.1e-254)
		tmp = -4.0 * (x * i);
	elseif (t <= 7.6e+130)
		tmp = t_1;
	else
		tmp = t * (-4.0 * a);
	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[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+125], N[(x * N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-216], t$95$1, If[LessEqual[t, -2.1e-254], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+130], t$95$1, N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.50000000000000041e125

   1. Initial program 70.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*r* 67.9%

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

      3. *-commutative 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*l* 61.2%

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

      4. *-commutative 61.2%

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

      5. associate-*l* 61.3%

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

      6. *-commutative 61.3%

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

      7. associate-*r* 58.9%

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

      8. *-commutative 58.9%

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

   10. Simplified 58.9%

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

   if -9.50000000000000041e125 < t < -1.25000000000000005e-216 or -2.09999999999999997e-254 < t < 7.6000000000000004e130

   1. Initial program 90.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in b around inf 58.1%

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

   if -1.25000000000000005e-216 < t < -2.09999999999999997e-254

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in i around inf 86.0%

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

      1. *-commutative 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in x around inf 76.6%

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

   if 7.6000000000000004e130 < t

   1. Initial program 82.1%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around inf 79.7%

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

   6. Taylor expanded in t around inf 82.3%

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

   7. Taylor expanded in a around inf 53.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-216}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-254}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 75.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+73} \lor \neg \left(t \leq 10^{+102}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.9e+73) (not (<= t 1e+102)))
   (+ (* t (+ (* -4.0 a) (* x (* 18.0 (* y z))))) (* k (* -27.0 j)))
   (- (- (* b c) (* 4.0 (* x i))) (* k (* j 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 <= -1.9e+73) || !(t <= 1e+102)) {
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 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 <= (-1.9d+73)) .or. (.not. (t <= 1d+102))) then
        tmp = (t * (((-4.0d0) * a) + (x * (18.0d0 * (y * z))))) + (k * ((-27.0d0) * j))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 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 <= -1.9e+73) || !(t <= 1e+102)) {
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.9e+73) or not (t <= 1e+102):
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.9e+73) || !(t <= 1e+102))
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(x * Float64(18.0 * Float64(y * z))))) + Float64(k * Float64(-27.0 * j)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 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 <= -1.9e+73) || ~((t <= 1e+102)))
		tmp = (t * ((-4.0 * a) + (x * (18.0 * (y * z))))) + (k * (-27.0 * j));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.9e+73], N[Not[LessEqual[t, 1e+102]], $MachinePrecision]], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.90000000000000011e73 or 9.99999999999999977e101 < t

   1. Initial program 79.2%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. *-commutative 79.4%

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

   7. Applied egg-rr 79.4%

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

      1. associate-*l* 79.5%

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

   9. Simplified 79.5%

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

   if -1.90000000000000011e73 < t < 9.99999999999999977e101

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 79.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+73} \lor \neg \left(t \leq 10^{+102}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 75.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+74} \lor \neg \left(t \leq 3.25 \cdot 10^{+103}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.05e+74) (not (<= t 3.25e+103)))
   (+ (* t (+ (* -4.0 a) (* 18.0 (* x (* y z))))) (* k (* -27.0 j)))
   (- (- (* b c) (* 4.0 (* x i))) (* k (* j 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 <= -2.05e+74) || !(t <= 3.25e+103)) {
		tmp = (t * ((-4.0 * a) + (18.0 * (x * (y * z))))) + (k * (-27.0 * j));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 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 <= (-2.05d+74)) .or. (.not. (t <= 3.25d+103))) then
        tmp = (t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z))))) + (k * ((-27.0d0) * j))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 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 <= -2.05e+74) || !(t <= 3.25e+103)) {
		tmp = (t * ((-4.0 * a) + (18.0 * (x * (y * z))))) + (k * (-27.0 * j));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -2.05e+74) or not (t <= 3.25e+103):
		tmp = (t * ((-4.0 * a) + (18.0 * (x * (y * z))))) + (k * (-27.0 * j))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.05e+74) || !(t <= 3.25e+103))
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z))))) + Float64(k * Float64(-27.0 * j)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 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 <= -2.05e+74) || ~((t <= 3.25e+103)))
		tmp = (t * ((-4.0 * a) + (18.0 * (x * (y * z))))) + (k * (-27.0 * j));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.05e+74], N[Not[LessEqual[t, 3.25e+103]], $MachinePrecision]], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05e74 or 3.25000000000000001e103 < t

   1. Initial program 79.2%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around inf 79.4%

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

   if -2.05e74 < t < 3.25000000000000001e103

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 79.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+74} \lor \neg \left(t \leq 3.25 \cdot 10^{+103}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 72.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+132} \lor \neg \left(t \leq 1.72 \cdot 10^{+106}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.6e+132) (not (<= t 1.72e+106)))
   (* t (+ (* -4.0 a) (* 18.0 (* x (* y z)))))
   (- (- (* b c) (* 4.0 (* x i))) (* k (* j 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 <= -3.6e+132) || !(t <= 1.72e+106)) {
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 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 <= (-3.6d+132)) .or. (.not. (t <= 1.72d+106))) then
        tmp = t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z))))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 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 <= -3.6e+132) || !(t <= 1.72e+106)) {
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -3.6e+132) or not (t <= 1.72e+106):
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3.6e+132) || !(t <= 1.72e+106))
		tmp = Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z)))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 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 <= -3.6e+132) || ~((t <= 1.72e+106)))
		tmp = t * ((-4.0 * a) + (18.0 * (x * (y * z))));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.6e+132], N[Not[LessEqual[t, 1.72e+106]], $MachinePrecision]], N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.60000000000000016e132 or 1.7200000000000001e106 < t

   1. Initial program 77.9%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 81.1%

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

   6. Taylor expanded in t around inf 80.6%

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

   if -3.60000000000000016e132 < t < 1.7200000000000001e106

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 78.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+132} \lor \neg \left(t \leq 1.72 \cdot 10^{+106}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 37.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+145} \lor \neg \left(b \cdot c \leq 6.2 \cdot 10^{+150}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -6.2e+145) (not (<= (* b c) 6.2e+150)))
   (* 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 (((b * c) <= -6.2e+145) || !((b * c) <= 6.2e+150)) {
		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 (((b * c) <= (-6.2d+145)) .or. (.not. ((b * c) <= 6.2d+150))) 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 (((b * c) <= -6.2e+145) || !((b * c) <= 6.2e+150)) {
		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 ((b * c) <= -6.2e+145) or not ((b * c) <= 6.2e+150):
		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 ((Float64(b * c) <= -6.2e+145) || !(Float64(b * c) <= 6.2e+150))
		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 (((b * c) <= -6.2e+145) || ~(((b * c) <= 6.2e+150)))
		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[Or[LessEqual[N[(b * c), $MachinePrecision], -6.2e+145], N[Not[LessEqual[N[(b * c), $MachinePrecision], 6.2e+150]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -6.19999999999999977e145 or 6.20000000000000028e150 < (*.f64 b c)

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 83.3%

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

   4. Taylor expanded in a around inf 82.2%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in b around inf 61.1%

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

   if -6.19999999999999977e145 < (*.f64 b c) < 6.20000000000000028e150

   1. Initial program 88.4%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in k around inf 30.1%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+145} \lor \neg \left(b \cdot c \leq 6.2 \cdot 10^{+150}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 24.0% 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 87.2%

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

3. Taylor expanded in a around inf 85.1%

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

4. Taylor expanded in a around inf 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Taylor expanded in b around inf 24.6%

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

Developer target: 88.8% 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 2024096 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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