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

Percentage Accurate: 85.1% → 92.1%

Time: 22.2s

Alternatives: 21

Speedup: 1.0×

• 50.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.8%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) 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 25.0%

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

   4. Taylor expanded in x around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. cancel-sign-sub-inv 66.7%

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

      3. metadata-eval 66.7%

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

      4. associate-*r* 66.7%

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

      5. *-commutative 66.7%

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

      6. *-commutative 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 94.9%

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

Alternative 2: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+20} \lor \neg \left(t_2 \leq 4 \cdot 10^{+44}\right) \land t_2 \leq 10^{+113}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* -4.0 (* x i)) (* k (* j -27.0))))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (* b c) (* t (* a 4.0)))))
   (if (<= t_2 -2e+143)
     t_1
     (if (<= t_2 -2e-134)
       t_3
       (if (<= t_2 -1e-298)
         (* t (* 18.0 (* y (* x z))))
         (if (or (<= t_2 4e+20) (and (not (<= t_2 4e+44)) (<= t_2 1e+113)))
           t_3
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * (x * i)) + (k * (j * -27.0));
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) - (t * (a * 4.0));
	double tmp;
	if (t_2 <= -2e+143) {
		tmp = t_1;
	} else if (t_2 <= -2e-134) {
		tmp = t_3;
	} else if (t_2 <= -1e-298) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if ((t_2 <= 4e+20) || (!(t_2 <= 4e+44) && (t_2 <= 1e+113))) {
		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 = ((-4.0d0) * (x * i)) + (k * (j * (-27.0d0)))
    t_2 = (j * 27.0d0) * k
    t_3 = (b * c) - (t * (a * 4.0d0))
    if (t_2 <= (-2d+143)) then
        tmp = t_1
    else if (t_2 <= (-2d-134)) then
        tmp = t_3
    else if (t_2 <= (-1d-298)) then
        tmp = t * (18.0d0 * (y * (x * z)))
    else if ((t_2 <= 4d+20) .or. (.not. (t_2 <= 4d+44)) .and. (t_2 <= 1d+113)) 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 = (-4.0 * (x * i)) + (k * (j * -27.0));
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) - (t * (a * 4.0));
	double tmp;
	if (t_2 <= -2e+143) {
		tmp = t_1;
	} else if (t_2 <= -2e-134) {
		tmp = t_3;
	} else if (t_2 <= -1e-298) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if ((t_2 <= 4e+20) || (!(t_2 <= 4e+44) && (t_2 <= 1e+113))) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * (x * i)) + (k * (j * -27.0))
	t_2 = (j * 27.0) * k
	t_3 = (b * c) - (t * (a * 4.0))
	tmp = 0
	if t_2 <= -2e+143:
		tmp = t_1
	elif t_2 <= -2e-134:
		tmp = t_3
	elif t_2 <= -1e-298:
		tmp = t * (18.0 * (y * (x * z)))
	elif (t_2 <= 4e+20) or (not (t_2 <= 4e+44) and (t_2 <= 1e+113)):
		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(-4.0 * Float64(x * i)) + Float64(k * Float64(j * -27.0)))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))
	tmp = 0.0
	if (t_2 <= -2e+143)
		tmp = t_1;
	elseif (t_2 <= -2e-134)
		tmp = t_3;
	elseif (t_2 <= -1e-298)
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	elseif ((t_2 <= 4e+20) || (!(t_2 <= 4e+44) && (t_2 <= 1e+113)))
		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 = (-4.0 * (x * i)) + (k * (j * -27.0));
	t_2 = (j * 27.0) * k;
	t_3 = (b * c) - (t * (a * 4.0));
	tmp = 0.0;
	if (t_2 <= -2e+143)
		tmp = t_1;
	elseif (t_2 <= -2e-134)
		tmp = t_3;
	elseif (t_2 <= -1e-298)
		tmp = t * (18.0 * (y * (x * z)));
	elseif ((t_2 <= 4e+20) || (~((t_2 <= 4e+44)) && (t_2 <= 1e+113)))
		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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+143], t$95$1, If[LessEqual[t$95$2, -2e-134], t$95$3, If[LessEqual[t$95$2, -1e-298], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, 4e+20], And[N[Not[LessEqual[t$95$2, 4e+44]], $MachinePrecision], LessEqual[t$95$2, 1e+113]]], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e143 or 4e20 < (*.f64 (*.f64 j 27) k) < 4.0000000000000004e44 or 1e113 < (*.f64 (*.f64 j 27) k)

   1. Initial program 82.5%

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

   2. Taylor expanded in t around 0 76.3%

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

   3. Taylor expanded in c around 0 70.5%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-in 70.5%

         \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \left(27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 70.5%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(\left(27 \cdot k\right) \cdot j\right)} \]

      3. *-commutative 70.5%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(j \cdot \left(27 \cdot k\right)\right)} \]

      4. neg-mul-1 70.5%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(-j \cdot \left(27 \cdot k\right)\right)} \]

      5. associate-*r* 70.5%

         \[\leadsto \color{blue}{\left(-1 \cdot 4\right) \cdot \left(i \cdot x\right)} + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 70.5%

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

      7. sub-neg 70.5%

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

      8. associate-*r* 70.6%

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

      9. cancel-sign-sub-inv 70.6%

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

      10. *-commutative 70.6%

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

      11. distribute-rgt-neg-in 70.6%

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

      12. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   if -2e143 < (*.f64 (*.f64 j 27) k) < -2.00000000000000008e-134 or -9.99999999999999912e-299 < (*.f64 (*.f64 j 27) k) < 4e20 or 4.0000000000000004e44 < (*.f64 (*.f64 j 27) k) < 1e113

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 79.4%

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

      1. distribute-lft-out 79.4%

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

      2. *-commutative 79.4%

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

      3. *-commutative 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in j around 0 74.9%

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

   6. Taylor expanded in i around 0 60.9%

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

      1. *-commutative 60.9%

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

      2. *-commutative 60.9%

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

      3. associate-*l* 60.9%

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

   8. Simplified 60.9%

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

   if -2.00000000000000008e-134 < (*.f64 (*.f64 j 27) k) < -9.99999999999999912e-299

   1. Initial program 89.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around inf 74.6%

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

   5. Taylor expanded in y around inf 59.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+143}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{-134}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+20} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+44}\right) \land \left(j \cdot 27\right) \cdot k \leq 10^{+113}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 3: 48.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \cdot 27 \leq -2 \cdot 10^{+166}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;j \cdot 27 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;j \cdot 27 \leq 5 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \cdot 27 \leq 2 \cdot 10^{-88}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - j \cdot \left(27 \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (- (* b c) (* 4.0 (* x i)))))
   (if (<= (* j 27.0) -2e+166)
     (- t_1 (* (* j 27.0) k))
     (if (<= (* j 27.0) -5e+80)
       t_2
       (if (<= (* j 27.0) -1e-259)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= (* j 27.0) 5e-246)
           t_2
           (if (<= (* j 27.0) 2e-88)
             (- (* b c) (* t (* a 4.0)))
             (- t_1 (* 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) {
	double t_1 = t * (a * -4.0);
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if ((j * 27.0) <= -2e+166) {
		tmp = t_1 - ((j * 27.0) * k);
	} else if ((j * 27.0) <= -5e+80) {
		tmp = t_2;
	} else if ((j * 27.0) <= -1e-259) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if ((j * 27.0) <= 5e-246) {
		tmp = t_2;
	} else if ((j * 27.0) <= 2e-88) {
		tmp = (b * c) - (t * (a * 4.0));
	} else {
		tmp = t_1 - (j * (27.0 * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = (b * c) - (4.0d0 * (x * i))
    if ((j * 27.0d0) <= (-2d+166)) then
        tmp = t_1 - ((j * 27.0d0) * k)
    else if ((j * 27.0d0) <= (-5d+80)) then
        tmp = t_2
    else if ((j * 27.0d0) <= (-1d-259)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if ((j * 27.0d0) <= 5d-246) then
        tmp = t_2
    else if ((j * 27.0d0) <= 2d-88) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else
        tmp = t_1 - (j * (27.0d0 * 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 t_1 = t * (a * -4.0);
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if ((j * 27.0) <= -2e+166) {
		tmp = t_1 - ((j * 27.0) * k);
	} else if ((j * 27.0) <= -5e+80) {
		tmp = t_2;
	} else if ((j * 27.0) <= -1e-259) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if ((j * 27.0) <= 5e-246) {
		tmp = t_2;
	} else if ((j * 27.0) <= 2e-88) {
		tmp = (b * c) - (t * (a * 4.0));
	} else {
		tmp = t_1 - (j * (27.0 * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if (j * 27.0) <= -2e+166:
		tmp = t_1 - ((j * 27.0) * k)
	elif (j * 27.0) <= -5e+80:
		tmp = t_2
	elif (j * 27.0) <= -1e-259:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif (j * 27.0) <= 5e-246:
		tmp = t_2
	elif (j * 27.0) <= 2e-88:
		tmp = (b * c) - (t * (a * 4.0))
	else:
		tmp = t_1 - (j * (27.0 * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (Float64(j * 27.0) <= -2e+166)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	elseif (Float64(j * 27.0) <= -5e+80)
		tmp = t_2;
	elseif (Float64(j * 27.0) <= -1e-259)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (Float64(j * 27.0) <= 5e-246)
		tmp = t_2;
	elseif (Float64(j * 27.0) <= 2e-88)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	else
		tmp = Float64(t_1 - Float64(j * Float64(27.0 * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if ((j * 27.0) <= -2e+166)
		tmp = t_1 - ((j * 27.0) * k);
	elseif ((j * 27.0) <= -5e+80)
		tmp = t_2;
	elseif ((j * 27.0) <= -1e-259)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif ((j * 27.0) <= 5e-246)
		tmp = t_2;
	elseif ((j * 27.0) <= 2e-88)
		tmp = (b * c) - (t * (a * 4.0));
	else
		tmp = t_1 - (j * (27.0 * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(j * 27.0), $MachinePrecision], -2e+166], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(j * 27.0), $MachinePrecision], -5e+80], t$95$2, If[LessEqual[N[(j * 27.0), $MachinePrecision], -1e-259], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(j * 27.0), $MachinePrecision], 5e-246], t$95$2, If[LessEqual[N[(j * 27.0), $MachinePrecision], 2e-88], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 j 27) < -1.99999999999999988e166

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 84.3%

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

   3. Taylor expanded in a around inf 65.5%

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

      1. associate-*r* 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -1.99999999999999988e166 < (*.f64 j 27) < -4.99999999999999961e80 or -1.0000000000000001e-259 < (*.f64 j 27) < 4.9999999999999997e-246

   1. Initial program 84.1%

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

   2. Taylor expanded in t around 0 57.4%

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

   3. Taylor expanded in j around 0 55.0%

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

   if -4.99999999999999961e80 < (*.f64 j 27) < -1.0000000000000001e-259

   1. Initial program 90.0%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around inf 59.6%

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

   if 4.9999999999999997e-246 < (*.f64 j 27) < 1.99999999999999987e-88

   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. Taylor expanded in y around 0 75.4%

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

      1. distribute-lft-out 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in j around 0 72.3%

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

   6. Taylor expanded in i around 0 59.8%

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

      1. *-commutative 59.8%

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

      2. *-commutative 59.8%

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

      3. associate-*l* 59.8%

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

   8. Simplified 59.8%

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

   if 1.99999999999999987e-88 < (*.f64 j 27)

   1. Initial program 86.1%

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

   2. Taylor expanded in x around 0 91.2%

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

   3. Taylor expanded in a around inf 49.4%

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

      1. associate-*r* 49.4%

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

      2. *-commutative 49.4%

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

   5. Simplified 49.4%

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

      1. sub-neg 49.4%

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

      2. associate-*l* 49.4%

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

   7. Applied egg-rr 49.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot 27 \leq -2 \cdot 10^{+166}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;j \cdot 27 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;j \cdot 27 \leq 5 \cdot 10^{-246}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \cdot 27 \leq 2 \cdot 10^{-88}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternative 4: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-187}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2
         (-
          (+ (* b c) (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))
          (* 27.0 (* j k)))))
   (if (<= y -4.8e+187)
     t_2
     (if (<= y -1.02e+175)
       (* x (+ (* (* 18.0 y) (* z t)) (* i -4.0)))
       (if (<= y -1e+50)
         t_2
         (if (<= y 7.8e-187)
           (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
           (- (+ (* b c) (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	double tmp;
	if (y <= -4.8e+187) {
		tmp = t_2;
	} else if (y <= -1.02e+175) {
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	} else if (y <= -1e+50) {
		tmp = t_2;
	} else if (y <= 7.8e-187) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - 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 = (j * 27.0d0) * k
    t_2 = ((b * c) + (t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0))))) - (27.0d0 * (j * k))
    if (y <= (-4.8d+187)) then
        tmp = t_2
    else if (y <= (-1.02d+175)) then
        tmp = x * (((18.0d0 * y) * (z * t)) + (i * (-4.0d0)))
    else if (y <= (-1d+50)) then
        tmp = t_2
    else if (y <= 7.8d-187) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = ((b * c) + (x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i)))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	double tmp;
	if (y <= -4.8e+187) {
		tmp = t_2;
	} else if (y <= -1.02e+175) {
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	} else if (y <= -1e+50) {
		tmp = t_2;
	} else if (y <= 7.8e-187) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k))
	tmp = 0
	if y <= -4.8e+187:
		tmp = t_2
	elif y <= -1.02e+175:
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0))
	elif y <= -1e+50:
		tmp = t_2
	elif y <= 7.8e-187:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (y <= -4.8e+187)
		tmp = t_2;
	elseif (y <= -1.02e+175)
		tmp = Float64(x * Float64(Float64(Float64(18.0 * y) * Float64(z * t)) + Float64(i * -4.0)));
	elseif (y <= -1e+50)
		tmp = t_2;
	elseif (y <= 7.8e-187)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	tmp = 0.0;
	if (y <= -4.8e+187)
		tmp = t_2;
	elseif (y <= -1.02e+175)
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	elseif (y <= -1e+50)
		tmp = t_2;
	elseif (y <= 7.8e-187)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+187], t$95$2, If[LessEqual[y, -1.02e+175], N[(x * N[(N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e+50], t$95$2, If[LessEqual[y, 7.8e-187], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.79999999999999971e187 or -1.0199999999999999e175 < y < -1.0000000000000001e50

   1. Initial program 87.8%

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

      1. associate--l- 87.8%

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

      2. associate-+l- 87.8%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in i around 0 87.6%

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

   if -4.79999999999999971e187 < y < -1.0199999999999999e175

   1. Initial program 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -1.0000000000000001e50 < y < 7.7999999999999998e-187

   1. Initial program 92.8%

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

   2. Taylor expanded in y around 0 85.2%

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

      1. distribute-lft-out 85.2%

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

      2. *-commutative 85.2%

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

      3. *-commutative 85.2%

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

   4. Simplified 85.2%

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

   if 7.7999999999999998e-187 < y

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0 91.3%

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

   3. Taylor expanded in a around 0 79.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+187}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-187}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 5: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -8e+220)
   (- (+ (* b c) (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))) (* 27.0 (* j k)))
   (-
    (+ (* t (- (* (* x 18.0) (* y z)) (* a 4.0))) (* 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) {
	double tmp;
	if (y <= -8e+220) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * 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 (y <= (-8d+220)) then
        tmp = ((b * c) + (t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0))))) - (27.0d0 * (j * k))
    else
        tmp = ((t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0))) + (b * c)) - ((x * (4.0d0 * i)) + (j * (27.0d0 * 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 (y <= -8e+220) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -8e+220:
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k))
	else:
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -8e+220)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -8e+220)
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - (27.0 * (j * k));
	else
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -8e+220], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e220

   1. Initial program 78.8%

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

      1. associate--l- 78.8%

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

      2. associate-+l- 78.8%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in i around 0 86.9%

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

   if -8e220 < y

   1. Initial program 89.2%

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

   3. Simplified 89.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 6: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 8 \cdot 10^{+140}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= i 8e+140)
   (-
    (+ (* t (- (* (* x 18.0) (* y z)) (* a 4.0))) (* b c))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (-
    (- (+ (* b c) (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))) (* 4.0 (* t a)))
    (* (* 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) {
	double tmp;
	if (i <= 8e+140) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * 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 (i <= 8d+140) then
        tmp = ((t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0))) + (b * c)) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (((b * c) + (x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - ((j * 27.0d0) * 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 (i <= 8e+140) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if i <= 8e+140:
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= 8e+140)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (i <= 8e+140)
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + (b * c)) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[i, 8e+140], N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 8.00000000000000047e140

   1. Initial program 90.9%

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

   3. Simplified 90.6%

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

   if 8.00000000000000047e140 < i

   1. Initial program 74.9%

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

   2. Taylor expanded in x around 0 94.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 8 \cdot 10^{+140}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 7: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{if}\;a \cdot 4 \leq -4 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 4 \leq -1 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (- (* b c) (* 4.0 (* t a))) t_1)))
   (if (<= (* a 4.0) -4e+60)
     t_2
     (if (<= (* a 4.0) -1e-86)
       (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
       (if (<= (* a 4.0) 2e-9) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (t * a))) - t_1;
	double tmp;
	if ((a * 4.0) <= -4e+60) {
		tmp = t_2;
	} else if ((a * 4.0) <= -1e-86) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if ((a * 4.0) <= 2e-9) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = ((b * c) - (4.0d0 * (t * a))) - t_1
    if ((a * 4.0d0) <= (-4d+60)) then
        tmp = t_2
    else if ((a * 4.0d0) <= (-1d-86)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if ((a * 4.0d0) <= 2d-9) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (t * a))) - t_1;
	double tmp;
	if ((a * 4.0) <= -4e+60) {
		tmp = t_2;
	} else if ((a * 4.0) <= -1e-86) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if ((a * 4.0) <= 2e-9) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((b * c) - (4.0 * (t * a))) - t_1
	tmp = 0
	if (a * 4.0) <= -4e+60:
		tmp = t_2
	elif (a * 4.0) <= -1e-86:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif (a * 4.0) <= 2e-9:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1)
	tmp = 0.0
	if (Float64(a * 4.0) <= -4e+60)
		tmp = t_2;
	elseif (Float64(a * 4.0) <= -1e-86)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (Float64(a * 4.0) <= 2e-9)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((b * c) - (4.0 * (t * a))) - t_1;
	tmp = 0.0;
	if ((a * 4.0) <= -4e+60)
		tmp = t_2;
	elseif ((a * 4.0) <= -1e-86)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif ((a * 4.0) <= 2e-9)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[N[(a * 4.0), $MachinePrecision], -4e+60], t$95$2, If[LessEqual[N[(a * 4.0), $MachinePrecision], -1e-86], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 4.0), $MachinePrecision], 2e-9], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 4) < -3.9999999999999998e60 or 2.00000000000000012e-9 < (*.f64 a 4)

   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. Taylor expanded in x around 0 78.6%

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

   if -3.9999999999999998e60 < (*.f64 a 4) < -1.00000000000000008e-86

   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 84.5%

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

   4. Taylor expanded in t around inf 64.0%

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

   if -1.00000000000000008e-86 < (*.f64 a 4) < 2.00000000000000012e-9

   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. Taylor expanded in t around 0 74.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -4 \cdot 10^{+60}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;a \cdot 4 \leq -1 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 8: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;a \cdot 4 \leq -4 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 4 \leq -1 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))
   (if (<= (* a 4.0) -4e+60)
     t_1
     (if (<= (* a 4.0) -1e-86)
       (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
       (if (<= (* a 4.0) 2e-9)
         (- (+ (* b c) (* -4.0 (* x i))) (* j (* 27.0 k)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double tmp;
	if ((a * 4.0) <= -4e+60) {
		tmp = t_1;
	} else if ((a * 4.0) <= -1e-86) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if ((a * 4.0) <= 2e-9) {
		tmp = ((b * c) + (-4.0 * (x * i))) - (j * (27.0 * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    if ((a * 4.0d0) <= (-4d+60)) then
        tmp = t_1
    else if ((a * 4.0d0) <= (-1d-86)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if ((a * 4.0d0) <= 2d-9) then
        tmp = ((b * c) + ((-4.0d0) * (x * i))) - (j * (27.0d0 * k))
    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) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double tmp;
	if ((a * 4.0) <= -4e+60) {
		tmp = t_1;
	} else if ((a * 4.0) <= -1e-86) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if ((a * 4.0) <= 2e-9) {
		tmp = ((b * c) + (-4.0 * (x * i))) - (j * (27.0 * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	tmp = 0
	if (a * 4.0) <= -4e+60:
		tmp = t_1
	elif (a * 4.0) <= -1e-86:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif (a * 4.0) <= 2e-9:
		tmp = ((b * c) + (-4.0 * (x * i))) - (j * (27.0 * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (Float64(a * 4.0) <= -4e+60)
		tmp = t_1;
	elseif (Float64(a * 4.0) <= -1e-86)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (Float64(a * 4.0) <= 2e-9)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	tmp = 0.0;
	if ((a * 4.0) <= -4e+60)
		tmp = t_1;
	elseif ((a * 4.0) <= -1e-86)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif ((a * 4.0) <= 2e-9)
		tmp = ((b * c) + (-4.0 * (x * i))) - (j * (27.0 * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 4.0), $MachinePrecision], -4e+60], t$95$1, If[LessEqual[N[(a * 4.0), $MachinePrecision], -1e-86], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 4.0), $MachinePrecision], 2e-9], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 4) < -3.9999999999999998e60 or 2.00000000000000012e-9 < (*.f64 a 4)

   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. Taylor expanded in x around 0 78.6%

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

   if -3.9999999999999998e60 < (*.f64 a 4) < -1.00000000000000008e-86

   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 84.5%

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

   4. Taylor expanded in t around inf 64.0%

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

   if -1.00000000000000008e-86 < (*.f64 a 4) < 2.00000000000000012e-9

   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. Taylor expanded in t around 0 74.1%

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

      1. sub-neg 74.1%

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

      2. cancel-sign-sub-inv 74.1%

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

      3. metadata-eval 74.1%

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

      4. associate-*l* 74.1%

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

   4. Applied egg-rr 74.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -4 \cdot 10^{+60}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;a \cdot 4 \leq -1 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 9: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -8 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+156}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= z -8e-108)
     (- (* t (- (* 18.0 (* y (* x z))) (* a 4.0))) t_1)
     (if (<= z 5.9e+156)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
       (- (+ (* b c) (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (z <= -8e-108) {
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 4.0))) - t_1;
	} else if (z <= 5.9e+156) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (z <= (-8d-108)) then
        tmp = (t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))) - t_1
    else if (z <= 5.9d+156) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = ((b * c) + (x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i)))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (z <= -8e-108) {
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 4.0))) - t_1;
	} else if (z <= 5.9e+156) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if z <= -8e-108:
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 4.0))) - t_1
	elif z <= 5.9e+156:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (z <= -8e-108)
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0))) - t_1);
	elseif (z <= 5.9e+156)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (z <= -8e-108)
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 4.0))) - t_1;
	elseif (z <= 5.9e+156)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[z, -8e-108], N[(N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 5.9e+156], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000032e-108

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 83.1%

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

   3. Taylor expanded in t around inf 73.9%

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

   if -8.00000000000000032e-108 < z < 5.8999999999999997e156

   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. Taylor expanded in y around 0 89.1%

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

      1. distribute-lft-out 89.1%

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

      2. *-commutative 89.1%

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

      3. *-commutative 89.1%

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

   4. Simplified 89.1%

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

   if 5.8999999999999997e156 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in x around 0 79.9%

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

   3. Taylor expanded in a around 0 82.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+156}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 10: 74.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+165}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;x \leq -49000 \lor \neg \left(x \leq 6.2 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.38e+240)
   (* x (+ (* (* 18.0 y) (* z t)) (* i -4.0)))
   (if (<= x -1.35e+165)
     (- (* b c) (* 4.0 (+ (* t a) (* x i))))
     (if (or (<= x -49000.0) (not (<= x 6.2e-41)))
       (+ (* b c) (* x (- (* 18.0 (* y (* z t))) (* 4.0 i))))
       (- (- (* b c) (* 4.0 (* t a))) (* 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) {
	double tmp;
	if (x <= -1.38e+240) {
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	} else if (x <= -1.35e+165) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else if ((x <= -49000.0) || !(x <= 6.2e-41)) {
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - (j * (27.0 * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-1.38d+240)) then
        tmp = x * (((18.0d0 * y) * (z * t)) + (i * (-4.0d0)))
    else if (x <= (-1.35d+165)) then
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    else if ((x <= (-49000.0d0)) .or. (.not. (x <= 6.2d-41))) then
        tmp = (b * c) + (x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i)))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - (j * (27.0d0 * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.38e+240) {
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	} else if (x <= -1.35e+165) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else if ((x <= -49000.0) || !(x <= 6.2e-41)) {
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - (j * (27.0 * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -1.38e+240:
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0))
	elif x <= -1.35e+165:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	elif (x <= -49000.0) or not (x <= 6.2e-41):
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - (j * (27.0 * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.38e+240)
		tmp = Float64(x * Float64(Float64(Float64(18.0 * y) * Float64(z * t)) + Float64(i * -4.0)));
	elseif (x <= -1.35e+165)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	elseif ((x <= -49000.0) || !(x <= 6.2e-41))
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(j * Float64(27.0 * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -1.38e+240)
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	elseif (x <= -1.35e+165)
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	elseif ((x <= -49000.0) || ~((x <= 6.2e-41)))
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - (j * (27.0 * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.38e+240], N[(x * N[(N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e+165], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -49000.0], N[Not[LessEqual[x, 6.2e-41]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.3799999999999999e240

   1. Initial program 53.7%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in x around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. cancel-sign-sub-inv 86.2%

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

      3. metadata-eval 86.2%

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

      4. associate-*r* 86.2%

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

      5. *-commutative 86.2%

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

      6. *-commutative 86.2%

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

   6. Simplified 86.2%

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

   if -1.3799999999999999e240 < x < -1.35e165

   1. Initial program 68.8%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. distribute-lft-out 87.6%

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

      2. *-commutative 87.6%

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

      3. *-commutative 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in j around 0 84.5%

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

   if -1.35e165 < x < -49000 or 6.20000000000000001e-41 < x

   1. Initial program 84.1%

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

   2. Taylor expanded in x around 0 87.2%

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

   3. Taylor expanded in a around 0 81.2%

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

   4. Taylor expanded in j around 0 75.5%

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

   if -49000 < x < 6.20000000000000001e-41

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 84.7%

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

      1. sub-neg 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*l* 84.7%

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

   4. Applied egg-rr 84.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+165}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;x \leq -49000 \lor \neg \left(x \leq 6.2 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternative 11: 57.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;k \leq -9 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_1\\ \mathbf{elif}\;k \leq 7 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+92}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{+233}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (* b c) (* 4.0 (+ (* t a) (* x i))))))
   (if (<= k -9e-78)
     (- (* t (* a -4.0)) t_1)
     (if (<= k 7e+25)
       t_2
       (if (<= k 2.3e+92)
         (+ (* -4.0 (* x i)) (* k (* j -27.0)))
         (if (<= k 4.6e+150)
           t_2
           (if (<= k 3.1e+233)
             (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
             (- (* b c) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double tmp;
	if (k <= -9e-78) {
		tmp = (t * (a * -4.0)) - t_1;
	} else if (k <= 7e+25) {
		tmp = t_2;
	} else if (k <= 2.3e+92) {
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	} else if (k <= 4.6e+150) {
		tmp = t_2;
	} else if (k <= 3.1e+233) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    if (k <= (-9d-78)) then
        tmp = (t * (a * (-4.0d0))) - t_1
    else if (k <= 7d+25) then
        tmp = t_2
    else if (k <= 2.3d+92) then
        tmp = ((-4.0d0) * (x * i)) + (k * (j * (-27.0d0)))
    else if (k <= 4.6d+150) then
        tmp = t_2
    else if (k <= 3.1d+233) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else
        tmp = (b * c) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double tmp;
	if (k <= -9e-78) {
		tmp = (t * (a * -4.0)) - t_1;
	} else if (k <= 7e+25) {
		tmp = t_2;
	} else if (k <= 2.3e+92) {
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	} else if (k <= 4.6e+150) {
		tmp = t_2;
	} else if (k <= 3.1e+233) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)))
	tmp = 0
	if k <= -9e-78:
		tmp = (t * (a * -4.0)) - t_1
	elif k <= 7e+25:
		tmp = t_2
	elif k <= 2.3e+92:
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0))
	elif k <= 4.6e+150:
		tmp = t_2
	elif k <= 3.1e+233:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	else:
		tmp = (b * c) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))))
	tmp = 0.0
	if (k <= -9e-78)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - t_1);
	elseif (k <= 7e+25)
		tmp = t_2;
	elseif (k <= 2.3e+92)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(k * Float64(j * -27.0)));
	elseif (k <= 4.6e+150)
		tmp = t_2;
	elseif (k <= 3.1e+233)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	tmp = 0.0;
	if (k <= -9e-78)
		tmp = (t * (a * -4.0)) - t_1;
	elseif (k <= 7e+25)
		tmp = t_2;
	elseif (k <= 2.3e+92)
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	elseif (k <= 4.6e+150)
		tmp = t_2;
	elseif (k <= 3.1e+233)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	else
		tmp = (b * c) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -9e-78], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[k, 7e+25], t$95$2, If[LessEqual[k, 2.3e+92], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.6e+150], t$95$2, If[LessEqual[k, 3.1e+233], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -9e-78

   1. Initial program 89.2%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in a around inf 52.7%

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

      1. associate-*r* 52.7%

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

      2. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   if -9e-78 < k < 6.99999999999999999e25 or 2.29999999999999998e92 < k < 4.60000000000000002e150

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 77.3%

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

      1. distribute-lft-out 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in j around 0 69.6%

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

   if 6.99999999999999999e25 < k < 2.29999999999999998e92

   1. Initial program 88.5%

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

   2. Taylor expanded in t around 0 78.7%

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

   3. Taylor expanded in c around 0 70.9%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-in 70.9%

         \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \left(27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 71.1%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(\left(27 \cdot k\right) \cdot j\right)} \]

      3. *-commutative 71.1%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(j \cdot \left(27 \cdot k\right)\right)} \]

      4. neg-mul-1 71.1%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(-j \cdot \left(27 \cdot k\right)\right)} \]

      5. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(-1 \cdot 4\right) \cdot \left(i \cdot x\right)} + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 71.1%

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

      7. sub-neg 71.1%

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

      8. associate-*r* 71.1%

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

      9. cancel-sign-sub-inv 71.1%

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

      10. *-commutative 71.1%

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

      11. distribute-rgt-neg-in 71.1%

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

      12. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   if 4.60000000000000002e150 < k < 3.10000000000000016e233

   1. Initial program 64.1%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in t around inf 82.3%

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

   if 3.10000000000000016e233 < k

   1. Initial program 91.7%

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

   2. Taylor expanded in x around 0 91.7%

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

   3. Taylor expanded in c around inf 83.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;k \leq 7 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+92}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{+233}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 12: 78.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq 9.6 \cdot 10^{+148}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t 9.6e+148)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
     (- (* t (- (* 18.0 (* y (* x z))) (* a 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 = (j * 27.0) * k;
	double tmp;
	if (t <= 9.6e+148) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 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 = (j * 27.0d0) * k
    if (t <= 9.6d+148) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = (t * ((18.0d0 * (y * (x * z))) - (a * 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 = (j * 27.0) * k;
	double tmp;
	if (t <= 9.6e+148) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 4.0))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t <= 9.6e+148:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 4.0))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t <= 9.6e+148)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 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 = (j * 27.0) * k;
	tmp = 0.0;
	if (t <= 9.6e+148)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = (t * ((18.0 * (y * (x * z))) - (a * 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[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t, 9.6e+148], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 9.59999999999999979e148

   1. Initial program 89.0%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. distribute-lft-out 81.5%

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

      2. *-commutative 81.5%

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

      3. *-commutative 81.5%

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

   4. Simplified 81.5%

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

   if 9.59999999999999979e148 < t

   1. Initial program 86.8%

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

   2. Taylor expanded in x around 0 79.3%

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

   3. Taylor expanded in t around inf 89.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 9.6 \cdot 10^{+148}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 13: 50.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-248}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;c \leq 10^{-51}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -1.12e+14)
   (- (* b c) (* 4.0 (* x i)))
   (if (<= c -5.3e-248)
     (* -4.0 (+ (* t a) (* x i)))
     (if (<= c 1e-51)
       (- (* t (* a -4.0)) (* (* j 27.0) k))
       (if (<= c 2.1e+133)
         (+ (* -4.0 (* x i)) (* k (* j -27.0)))
         (- (* b c) (* t (* a 4.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= -1.12e+14) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (c <= -5.3e-248) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (c <= 1e-51) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else if (c <= 2.1e+133) {
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	} else {
		tmp = (b * c) - (t * (a * 4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (c <= (-1.12d+14)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (c <= (-5.3d-248)) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if (c <= 1d-51) then
        tmp = (t * (a * (-4.0d0))) - ((j * 27.0d0) * k)
    else if (c <= 2.1d+133) then
        tmp = ((-4.0d0) * (x * i)) + (k * (j * (-27.0d0)))
    else
        tmp = (b * c) - (t * (a * 4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= -1.12e+14) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (c <= -5.3e-248) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (c <= 1e-51) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else if (c <= 2.1e+133) {
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	} else {
		tmp = (b * c) - (t * (a * 4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= -1.12e+14:
		tmp = (b * c) - (4.0 * (x * i))
	elif c <= -5.3e-248:
		tmp = -4.0 * ((t * a) + (x * i))
	elif c <= 1e-51:
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k)
	elif c <= 2.1e+133:
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0))
	else:
		tmp = (b * c) - (t * (a * 4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (c <= -1.12e+14)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (c <= -5.3e-248)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (c <= 1e-51)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - Float64(Float64(j * 27.0) * k));
	elseif (c <= 2.1e+133)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (c <= -1.12e+14)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (c <= -5.3e-248)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif (c <= 1e-51)
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	elseif (c <= 2.1e+133)
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	else
		tmp = (b * c) - (t * (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, -1.12e+14], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.3e-248], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e-51], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+133], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.12e14

   1. Initial program 84.2%

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

   2. Taylor expanded in t around 0 57.6%

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

   3. Taylor expanded in j around 0 48.7%

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

   if -1.12e14 < c < -5.3e-248

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 80.9%

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

      1. distribute-lft-out 80.9%

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

      2. *-commutative 80.9%

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

      3. *-commutative 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in j around 0 64.1%

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

   6. Taylor expanded in c around 0 57.4%

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

   if -5.3e-248 < c < 1e-51

   1. Initial program 87.3%

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

   2. Taylor expanded in x around 0 81.5%

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

   3. Taylor expanded in a around inf 64.1%

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

      1. associate-*r* 64.1%

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

      2. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if 1e-51 < c < 2.1e133

   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. Taylor expanded in t around 0 71.7%

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

   3. Taylor expanded in c around 0 48.1%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-in 48.1%

         \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \left(27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 48.2%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(\left(27 \cdot k\right) \cdot j\right)} \]

      3. *-commutative 48.2%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(j \cdot \left(27 \cdot k\right)\right)} \]

      4. neg-mul-1 48.2%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(-j \cdot \left(27 \cdot k\right)\right)} \]

      5. associate-*r* 48.2%

         \[\leadsto \color{blue}{\left(-1 \cdot 4\right) \cdot \left(i \cdot x\right)} + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 48.2%

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

      7. sub-neg 48.2%

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

      8. associate-*r* 48.1%

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

      9. cancel-sign-sub-inv 48.1%

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

      10. *-commutative 48.1%

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

      11. distribute-rgt-neg-in 48.1%

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

      12. metadata-eval 48.1%

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

   5. Simplified 48.1%

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

   if 2.1e133 < c

   1. Initial program 83.5%

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

   2. Taylor expanded in y around 0 75.8%

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

      1. distribute-lft-out 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in j around 0 68.9%

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

   6. Taylor expanded in i around 0 60.0%

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

      1. *-commutative 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*l* 60.0%

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

   8. Simplified 60.0%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-248}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;c \leq 10^{-51}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \]

Alternative 14: 64.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+213}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= i -1e+213)
   (+ (* -4.0 (* x i)) (* k (* j -27.0)))
   (if (<= i 3.2e+146)
     (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
     (* x (+ (* (* 18.0 y) (* z t)) (* i -4.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (i <= -1e+213) {
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	} else if (i <= 3.2e+146) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (i <= (-1d+213)) then
        tmp = ((-4.0d0) * (x * i)) + (k * (j * (-27.0d0)))
    else if (i <= 3.2d+146) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else
        tmp = x * (((18.0d0 * y) * (z * t)) + (i * (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (i <= -1e+213) {
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	} else if (i <= 3.2e+146) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if i <= -1e+213:
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0))
	elif i <= 3.2e+146:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	else:
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= -1e+213)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(k * Float64(j * -27.0)));
	elseif (i <= 3.2e+146)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(x * Float64(Float64(Float64(18.0 * y) * Float64(z * t)) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (i <= -1e+213)
		tmp = (-4.0 * (x * i)) + (k * (j * -27.0));
	elseif (i <= 3.2e+146)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	else
		tmp = x * (((18.0 * y) * (z * t)) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[i, -1e+213], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+146], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.99999999999999984e212

   1. Initial program 96.0%

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

   2. Taylor expanded in t around 0 87.3%

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

   3. Taylor expanded in c around 0 76.2%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-in 76.2%

         \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \left(27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 76.2%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(\left(27 \cdot k\right) \cdot j\right)} \]

      3. *-commutative 76.2%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \color{blue}{\left(j \cdot \left(27 \cdot k\right)\right)} \]

      4. neg-mul-1 76.2%

         \[\leadsto -1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(-j \cdot \left(27 \cdot k\right)\right)} \]

      5. associate-*r* 76.2%

         \[\leadsto \color{blue}{\left(-1 \cdot 4\right) \cdot \left(i \cdot x\right)} + \left(-j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 76.2%

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

      7. sub-neg 76.2%

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

      8. associate-*r* 76.2%

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

      9. cancel-sign-sub-inv 76.2%

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

      10. *-commutative 76.2%

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

      11. distribute-rgt-neg-in 76.2%

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

      12. metadata-eval 76.2%

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

   5. Simplified 76.2%

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

   if -9.99999999999999984e212 < i < 3.2e146

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 71.2%

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

   if 3.2e146 < i

   1. Initial program 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. cancel-sign-sub-inv 80.7%

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

      3. metadata-eval 80.7%

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

      4. associate-*r* 80.7%

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

      5. *-commutative 80.7%

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

      6. *-commutative 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+213}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 15: 48.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+64}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+220}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= t -1.6e-67)
     t_1
     (if (<= t 2.3e-152)
       (- (* b c) (* (* j 27.0) k))
       (if (<= t 1.3e+64)
         (- (* b c) (* t (* a 4.0)))
         (if (<= t 3.7e+220) t_1 (* (* 18.0 y) (* t (* x 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 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (t <= -1.6e-67) {
		tmp = t_1;
	} else if (t <= 2.3e-152) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 1.3e+64) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (t <= 3.7e+220) {
		tmp = t_1;
	} else {
		tmp = (18.0 * y) * (t * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) + (x * i))
    if (t <= (-1.6d-67)) then
        tmp = t_1
    else if (t <= 2.3d-152) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (t <= 1.3d+64) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else if (t <= 3.7d+220) then
        tmp = t_1
    else
        tmp = (18.0d0 * y) * (t * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (t <= -1.6e-67) {
		tmp = t_1;
	} else if (t <= 2.3e-152) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 1.3e+64) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (t <= 3.7e+220) {
		tmp = t_1;
	} else {
		tmp = (18.0 * y) * (t * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if t <= -1.6e-67:
		tmp = t_1
	elif t <= 2.3e-152:
		tmp = (b * c) - ((j * 27.0) * k)
	elif t <= 1.3e+64:
		tmp = (b * c) - (t * (a * 4.0))
	elif t <= 3.7e+220:
		tmp = t_1
	else:
		tmp = (18.0 * y) * (t * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (t <= -1.6e-67)
		tmp = t_1;
	elseif (t <= 2.3e-152)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.3e+64)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	elseif (t <= 3.7e+220)
		tmp = t_1;
	else
		tmp = Float64(Float64(18.0 * y) * Float64(t * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if (t <= -1.6e-67)
		tmp = t_1;
	elseif (t <= 2.3e-152)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (t <= 1.3e+64)
		tmp = (b * c) - (t * (a * 4.0));
	elseif (t <= 3.7e+220)
		tmp = t_1;
	else
		tmp = (18.0 * y) * (t * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-67], t$95$1, If[LessEqual[t, 2.3e-152], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+64], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+220], t$95$1, N[(N[(18.0 * y), $MachinePrecision] * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.60000000000000011e-67 or 1.29999999999999998e64 < t < 3.7e220

   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. Taylor expanded in y around 0 77.7%

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

      1. distribute-lft-out 77.7%

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

      2. *-commutative 77.7%

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

      3. *-commutative 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in j around 0 65.1%

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

   6. Taylor expanded in c around 0 54.8%

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

   if -1.60000000000000011e-67 < t < 2.3000000000000001e-152

   1. Initial program 87.4%

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

   2. Taylor expanded in x around 0 94.8%

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

   3. Taylor expanded in c around inf 71.1%

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

   if 2.3000000000000001e-152 < t < 1.29999999999999998e64

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 80.7%

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

      1. distribute-lft-out 80.7%

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

      2. *-commutative 80.7%

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

      3. *-commutative 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in j around 0 69.5%

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

   6. Taylor expanded in i around 0 54.0%

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

      1. *-commutative 54.0%

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

      2. *-commutative 54.0%

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

      3. associate-*l* 54.0%

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

   8. Simplified 54.0%

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

   if 3.7e220 < t

   1. Initial program 83.9%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around inf 65.0%

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

      1. associate-*r* 65.0%

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

      2. *-commutative 65.0%

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

   6. Simplified 65.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+64}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+220}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ \end{array} \]

Alternative 16: 32.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;c \leq -3200000000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (* k (* j -27.0))))
   (if (<= c -3200000000000.0)
     (* b c)
     (if (<= c -7.5e-253)
       t_1
       (if (<= c 4e-126)
         t_2
         (if (<= c 1.45e-50) t_1 (if (<= c 2.1e+133) t_2 (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = k * (j * -27.0);
	double tmp;
	if (c <= -3200000000000.0) {
		tmp = b * c;
	} else if (c <= -7.5e-253) {
		tmp = t_1;
	} else if (c <= 4e-126) {
		tmp = t_2;
	} else if (c <= 1.45e-50) {
		tmp = t_1;
	} else if (c <= 2.1e+133) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = k * (j * (-27.0d0))
    if (c <= (-3200000000000.0d0)) then
        tmp = b * c
    else if (c <= (-7.5d-253)) then
        tmp = t_1
    else if (c <= 4d-126) then
        tmp = t_2
    else if (c <= 1.45d-50) then
        tmp = t_1
    else if (c <= 2.1d+133) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = k * (j * -27.0);
	double tmp;
	if (c <= -3200000000000.0) {
		tmp = b * c;
	} else if (c <= -7.5e-253) {
		tmp = t_1;
	} else if (c <= 4e-126) {
		tmp = t_2;
	} else if (c <= 1.45e-50) {
		tmp = t_1;
	} else if (c <= 2.1e+133) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = k * (j * -27.0)
	tmp = 0
	if c <= -3200000000000.0:
		tmp = b * c
	elif c <= -7.5e-253:
		tmp = t_1
	elif c <= 4e-126:
		tmp = t_2
	elif c <= 1.45e-50:
		tmp = t_1
	elif c <= 2.1e+133:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (c <= -3200000000000.0)
		tmp = Float64(b * c);
	elseif (c <= -7.5e-253)
		tmp = t_1;
	elseif (c <= 4e-126)
		tmp = t_2;
	elseif (c <= 1.45e-50)
		tmp = t_1;
	elseif (c <= 2.1e+133)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = k * (j * -27.0);
	tmp = 0.0;
	if (c <= -3200000000000.0)
		tmp = b * c;
	elseif (c <= -7.5e-253)
		tmp = t_1;
	elseif (c <= 4e-126)
		tmp = t_2;
	elseif (c <= 1.45e-50)
		tmp = t_1;
	elseif (c <= 2.1e+133)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3200000000000.0], N[(b * c), $MachinePrecision], If[LessEqual[c, -7.5e-253], t$95$1, If[LessEqual[c, 4e-126], t$95$2, If[LessEqual[c, 1.45e-50], t$95$1, If[LessEqual[c, 2.1e+133], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.2e12 or 2.1e133 < c

   1. Initial program 84.0%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around inf 41.6%

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

   if -3.2e12 < c < -7.49999999999999987e-253 or 3.9999999999999998e-126 < c < 1.45000000000000004e-50

   1. Initial program 94.6%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around inf 38.7%

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

      1. *-commutative 38.7%

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

      2. *-commutative 38.7%

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

      3. associate-*r* 38.7%

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

   6. Simplified 38.7%

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

   if -7.49999999999999987e-253 < c < 3.9999999999999998e-126 or 1.45000000000000004e-50 < c < 2.1e133

   1. Initial program 88.9%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in j around inf 39.0%

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

      1. *-commutative 39.0%

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

      2. associate-*l* 39.0%

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

   6. Simplified 39.0%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3200000000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-126}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17: 43.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+91} \lor \neg \left(b \leq 2.8 \cdot 10^{-40}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= b -7.5e+91) (not (<= b 2.8e-40)))
   (* b c)
   (* -4.0 (+ (* t a) (* x i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -7.5e+91) || !(b <= 2.8e-40)) {
		tmp = b * c;
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b <= (-7.5d+91)) .or. (.not. (b <= 2.8d-40))) then
        tmp = b * c
    else
        tmp = (-4.0d0) * ((t * a) + (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -7.5e+91) || !(b <= 2.8e-40)) {
		tmp = b * c;
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b <= -7.5e+91) or not (b <= 2.8e-40):
		tmp = b * c
	else:
		tmp = -4.0 * ((t * a) + (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((b <= -7.5e+91) || !(b <= 2.8e-40))
		tmp = Float64(b * c);
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b <= -7.5e+91) || ~((b <= 2.8e-40)))
		tmp = b * c;
	else
		tmp = -4.0 * ((t * a) + (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[b, -7.5e+91], N[Not[LessEqual[b, 2.8e-40]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.50000000000000033e91 or 2.8e-40 < b

   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 89.1%

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

   4. Taylor expanded in b around inf 35.9%

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

   if -7.50000000000000033e91 < b < 2.8e-40

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 75.4%

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

      1. distribute-lft-out 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in j around 0 52.8%

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

   6. Taylor expanded in c around 0 44.3%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+91} \lor \neg \left(b \leq 2.8 \cdot 10^{-40}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 18: 48.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+52} \lor \neg \left(b \leq 1.6 \cdot 10^{-105}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= b -5e+52) (not (<= b 1.6e-105)))
   (- (* b c) (* 4.0 (* x i)))
   (* -4.0 (+ (* t a) (* x i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -5e+52) || !(b <= 1.6e-105)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b <= (-5d+52)) .or. (.not. (b <= 1.6d-105))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (-4.0d0) * ((t * a) + (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -5e+52) || !(b <= 1.6e-105)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b <= -5e+52) or not (b <= 1.6e-105):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = -4.0 * ((t * a) + (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((b <= -5e+52) || !(b <= 1.6e-105))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b <= -5e+52) || ~((b <= 1.6e-105)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = -4.0 * ((t * a) + (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[b, -5e+52], N[Not[LessEqual[b, 1.6e-105]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5e52 or 1.59999999999999991e-105 < b

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 65.0%

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

   3. Taylor expanded in j around 0 49.6%

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

   if -5e52 < b < 1.59999999999999991e-105

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 75.0%

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

      1. distribute-lft-out 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in j around 0 51.5%

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

   6. Taylor expanded in c around 0 45.7%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+52} \lor \neg \left(b \leq 1.6 \cdot 10^{-105}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 19: 49.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= i -2.3e+168)
   (- (* b c) (* 4.0 (* x i)))
   (if (<= i 1.75e+27)
     (- (* b c) (* t (* a 4.0)))
     (* -4.0 (+ (* t a) (* x i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (i <= -2.3e+168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (i <= 1.75e+27) {
		tmp = (b * c) - (t * (a * 4.0));
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (i <= (-2.3d+168)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (i <= 1.75d+27) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else
        tmp = (-4.0d0) * ((t * a) + (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (i <= -2.3e+168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (i <= 1.75e+27) {
		tmp = (b * c) - (t * (a * 4.0));
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if i <= -2.3e+168:
		tmp = (b * c) - (4.0 * (x * i))
	elif i <= 1.75e+27:
		tmp = (b * c) - (t * (a * 4.0))
	else:
		tmp = -4.0 * ((t * a) + (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= -2.3e+168)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (i <= 1.75e+27)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (i <= -2.3e+168)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (i <= 1.75e+27)
		tmp = (b * c) - (t * (a * 4.0));
	else
		tmp = -4.0 * ((t * a) + (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[i, -2.3e+168], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e+27], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.2999999999999999e168

   1. Initial program 93.4%

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

   2. Taylor expanded in t around 0 83.3%

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

   3. Taylor expanded in j around 0 61.5%

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

   if -2.2999999999999999e168 < i < 1.7500000000000001e27

   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. Taylor expanded in y around 0 78.7%

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

      1. distribute-lft-out 78.7%

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

      2. *-commutative 78.7%

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

      3. *-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in j around 0 58.4%

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

   6. Taylor expanded in i around 0 53.7%

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

      1. *-commutative 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*l* 53.7%

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

   8. Simplified 53.7%

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

   if 1.7500000000000001e27 < i

   1. Initial program 79.9%

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

   2. Taylor expanded in y around 0 73.5%

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

      1. distribute-lft-out 73.5%

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

      2. *-commutative 73.5%

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

      3. *-commutative 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in j around 0 64.9%

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

   6. Taylor expanded in c around 0 56.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 20: 31.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -4.6e-179) (* b c) (if (<= c 2.2e+133) (* k (* j -27.0)) (* 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 (c <= -4.6e-179) {
		tmp = b * c;
	} else if (c <= 2.2e+133) {
		tmp = k * (j * -27.0);
	} 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 (c <= (-4.6d-179)) then
        tmp = b * c
    else if (c <= 2.2d+133) then
        tmp = k * (j * (-27.0d0))
    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 (c <= -4.6e-179) {
		tmp = b * c;
	} else if (c <= 2.2e+133) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= -4.6e-179:
		tmp = b * c
	elif c <= 2.2e+133:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (c <= -4.6e-179)
		tmp = Float64(b * c);
	elseif (c <= 2.2e+133)
		tmp = Float64(k * Float64(j * -27.0));
	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 (c <= -4.6e-179)
		tmp = b * c;
	elseif (c <= 2.2e+133)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, -4.6e-179], N[(b * c), $MachinePrecision], If[LessEqual[c, 2.2e+133], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -4.59999999999999975e-179 or 2.2e133 < c

   1. Initial program 87.9%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in b around inf 32.5%

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

   if -4.59999999999999975e-179 < c < 2.2e133

   1. Initial program 89.5%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in j around inf 33.5%

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

      1. *-commutative 33.5%

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

      2. associate-*l* 33.5%

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

   6. Simplified 33.5%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21: 24.5% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

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

3. Simplified 88.4%

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

4. Taylor expanded in b around inf 23.2%

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

5. Final simplification 23.2%

   \[\leadsto b \cdot c \]

Developer target: 89.1% accurate, 0.9× 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 2023268 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (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)))