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

Percentage Accurate: 85.5% → 90.9%

Time: 19.5s

Alternatives: 20

Speedup: 0.5×

• 50.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double 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 = t * ((18.0 * (x * (y * z))) - (a * 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 = t * ((18.0 * (x * (y * z))) - (a * 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 = t * ((18.0 * (x * (y * z))) - (a * 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(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 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 96.6%

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

   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 23.1%

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

   4. Taylor expanded in t around inf 81.0%

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

4. Final simplification 95.0%

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

Alternative 2: 37.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1.45 \cdot 10^{+155}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.15 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x t) (* z (* 18.0 y)))))
   (if (<= (* b c) -1.45e+155)
     (* b c)
     (if (<= (* b c) -3.4e+115)
       t_1
       (if (<= (* b c) -4e+64)
         (* x (* i -4.0))
         (if (<= (* b c) -5.2e-117)
           t_1
           (if (<= (* b c) -1.15e-296)
             (* k (* j -27.0))
             (if (<= (* b c) 2.5e+83) t_1 (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * t) * (z * (18.0 * y));
	double tmp;
	if ((b * c) <= -1.45e+155) {
		tmp = b * c;
	} else if ((b * c) <= -3.4e+115) {
		tmp = t_1;
	} else if ((b * c) <= -4e+64) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= -5.2e-117) {
		tmp = t_1;
	} else if ((b * c) <= -1.15e-296) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 2.5e+83) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * t) * (z * (18.0d0 * y))
    if ((b * c) <= (-1.45d+155)) then
        tmp = b * c
    else if ((b * c) <= (-3.4d+115)) then
        tmp = t_1
    else if ((b * c) <= (-4d+64)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= (-5.2d-117)) then
        tmp = t_1
    else if ((b * c) <= (-1.15d-296)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 2.5d+83) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * t) * (z * (18.0 * y));
	double tmp;
	if ((b * c) <= -1.45e+155) {
		tmp = b * c;
	} else if ((b * c) <= -3.4e+115) {
		tmp = t_1;
	} else if ((b * c) <= -4e+64) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= -5.2e-117) {
		tmp = t_1;
	} else if ((b * c) <= -1.15e-296) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 2.5e+83) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * t) * (z * (18.0 * y))
	tmp = 0
	if (b * c) <= -1.45e+155:
		tmp = b * c
	elif (b * c) <= -3.4e+115:
		tmp = t_1
	elif (b * c) <= -4e+64:
		tmp = x * (i * -4.0)
	elif (b * c) <= -5.2e-117:
		tmp = t_1
	elif (b * c) <= -1.15e-296:
		tmp = k * (j * -27.0)
	elif (b * c) <= 2.5e+83:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * t) * Float64(z * Float64(18.0 * y)))
	tmp = 0.0
	if (Float64(b * c) <= -1.45e+155)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.4e+115)
		tmp = t_1;
	elseif (Float64(b * c) <= -4e+64)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= -5.2e-117)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.15e-296)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 2.5e+83)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * t) * (z * (18.0 * y));
	tmp = 0.0;
	if ((b * c) <= -1.45e+155)
		tmp = b * c;
	elseif ((b * c) <= -3.4e+115)
		tmp = t_1;
	elseif ((b * c) <= -4e+64)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= -5.2e-117)
		tmp = t_1;
	elseif ((b * c) <= -1.15e-296)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 2.5e+83)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.45e+155], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.4e+115], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -4e+64], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.2e-117], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.15e-296], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.5e+83], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.45e155 or 2.50000000000000014e83 < (*.f64 b c)

   1. Initial program 90.3%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in b around inf 59.2%

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

   if -1.45e155 < (*.f64 b c) < -3.4000000000000001e115 or -4.00000000000000009e64 < (*.f64 b c) < -5.19999999999999966e-117 or -1.15000000000000002e-296 < (*.f64 b c) < 2.50000000000000014e83

   1. Initial program 84.9%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 58.7%

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

      1. pow1 58.7%

         \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]

   6. Applied egg-rr 58.7%

      \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 58.7%

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

      2. *-commutative 58.7%

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

      3. associate-*l* 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in x around inf 36.4%

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

       1. *-commutative 36.4%

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

       2. associate-*r* 40.8%

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

       3. associate-*l* 40.8%

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

       4. associate-*r* 40.8%

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

       5. *-commutative 40.8%

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

       6. associate-*l* 40.8%

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

   11. Simplified 40.8%

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

   if -3.4000000000000001e115 < (*.f64 b c) < -4.00000000000000009e64

   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 78.3%

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

   4. Taylor expanded in i around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

   6. Simplified 57.1%

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

   if -5.19999999999999966e-117 < (*.f64 b c) < -1.15000000000000002e-296

   1. Initial program 86.5%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in j around inf 41.7%

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

      1. associate-*r* 41.7%

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

   6. Simplified 41.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.45 \cdot 10^{+155}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.15 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 3: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+136} \lor \neg \left(x \leq 8.4 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.56e+136) (not (<= x 8.4e+99)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* 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 ((x <= -1.56e+136) || !(x <= 8.4e+99)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((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 ((x <= (-1.56d+136)) .or. (.not. (x <= 8.4d+99))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((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 ((x <= -1.56e+136) || !(x <= 8.4e+99)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((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 (x <= -1.56e+136) or not (x <= 8.4e+99):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((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 ((x <= -1.56e+136) || !(x <= 8.4e+99))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.56e+136) || ~((x <= 8.4e+99)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((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[Or[LessEqual[x, -1.56e+136], N[Not[LessEqual[x, 8.4e+99]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.56000000000000013e136 or 8.40000000000000041e99 < x

   1. Initial program 67.9%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in x around inf 84.2%

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

   if -1.56000000000000013e136 < x < 8.40000000000000041e99

   1. Initial program 95.8%

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

   3. Simplified 93.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+136} \lor \neg \left(x \leq 8.4 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+135} \lor \neg \left(x \leq 2.9 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -8.8e+135) (not (<= x 2.9e+38)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (-
    (+ (* b c) (* t (- (* (* x y) (* 18.0 z)) (* a 4.0))))
    (+ (* 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 ((x <= -8.8e+135) || !(x <= 2.9e+38)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((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 ((x <= (-8.8d+135)) .or. (.not. (x <= 2.9d+38))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0)))) - ((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 ((x <= -8.8e+135) || !(x <= 2.9e+38)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((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 (x <= -8.8e+135) or not (x <= 2.9e+38):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((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 ((x <= -8.8e+135) || !(x <= 2.9e+38))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)))) - 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 ((x <= -8.8e+135) || ~((x <= 2.9e+38)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((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[Or[LessEqual[x, -8.8e+135], N[Not[LessEqual[x, 2.9e+38]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999998e135 or 2.90000000000000007e38 < x

   1. Initial program 68.4%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in x around inf 82.4%

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

   if -8.7999999999999998e135 < x < 2.90000000000000007e38

   1. Initial program 96.8%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-*r* 98.7%

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

      3. associate-*l* 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+135} \lor \neg \left(x \leq 2.9 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 5: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-138}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{elif}\;t \leq 1500000000000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(t_1 + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2
         (-
          (+ (* b c) (* t (- (* (* x y) (* 18.0 z)) (* a 4.0))))
          (* x (* 4.0 i)))))
   (if (<= t -3.8e+69)
     t_2
     (if (<= t 2.6e-138)
       (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) t_1))
       (if (<= t 1500000000000.0)
         (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (+ t_1 (* 4.0 (* t a))))
         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 = 27.0 * (j * k);
	double t_2 = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i));
	double tmp;
	if (t <= -3.8e+69) {
		tmp = t_2;
	} else if (t <= 2.6e-138) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	} else if (t <= 1500000000000.0) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (t_1 + (4.0 * (t * a)));
	} 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 = 27.0d0 * (j * k)
    t_2 = ((b * c) + (t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0)))) - (x * (4.0d0 * i))
    if (t <= (-3.8d+69)) then
        tmp = t_2
    else if (t <= 2.6d-138) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + t_1)
    else if (t <= 1500000000000.0d0) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - (t_1 + (4.0d0 * (t * a)))
    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 = 27.0 * (j * k);
	double t_2 = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i));
	double tmp;
	if (t <= -3.8e+69) {
		tmp = t_2;
	} else if (t <= 2.6e-138) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	} else if (t <= 1500000000000.0) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (t_1 + (4.0 * (t * a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i))
	tmp = 0
	if t <= -3.8e+69:
		tmp = t_2
	elif t <= 2.6e-138:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1)
	elif t <= 1500000000000.0:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (t_1 + (4.0 * (t * a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (t <= -3.8e+69)
		tmp = t_2;
	elseif (t <= 2.6e-138)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	elseif (t <= 1500000000000.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(t_1 + Float64(4.0 * Float64(t * a))));
	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 = 27.0 * (j * k);
	t_2 = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i));
	tmp = 0.0;
	if (t <= -3.8e+69)
		tmp = t_2;
	elseif (t <= 2.6e-138)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	elseif (t <= 1500000000000.0)
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (t_1 + (4.0 * (t * a)));
	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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+69], t$95$2, If[LessEqual[t, 2.6e-138], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1500000000000.0], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000028e69 or 1.5e12 < t

   1. Initial program 86.0%

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

   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 x around 0 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r* 91.3%

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

      3. associate-*l* 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in x around inf 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   9. Simplified 89.4%

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

   if -3.80000000000000028e69 < t < 2.6e-138

   1. Initial program 86.9%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in y around 0 84.4%

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

   if 2.6e-138 < t < 1.5e12

   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 i around 0 92.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-138}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1500000000000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \end{array} \]

Alternative 6: 82.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+69} \lor \neg \left(t \leq 39000000000000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.5e+69) (not (<= t 39000000000000.0)))
   (- (+ (* b c) (* t (- (* (* x y) (* 18.0 z)) (* a 4.0)))) (* x (* 4.0 i)))
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.5e+69) || !(t <= 39000000000000.0)) {
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-2.5d+69)) .or. (.not. (t <= 39000000000000.0d0))) then
        tmp = ((b * c) + (t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0)))) - (x * (4.0d0 * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.5e+69) || !(t <= 39000000000000.0)) {
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -2.5e+69) or not (t <= 39000000000000.0):
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.5e+69) || !(t <= 39000000000000.0))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -2.5e+69) || ~((t <= 39000000000000.0)))
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - (x * (4.0 * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.5e+69], N[Not[LessEqual[t, 39000000000000.0]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000018e69 or 3.9e13 < t

   1. Initial program 86.0%

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

   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 x around 0 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r* 91.3%

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

      3. associate-*l* 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in x around inf 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   9. Simplified 89.4%

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

   if -2.50000000000000018e69 < t < 3.9e13

   1. Initial program 87.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around 0 82.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+69} \lor \neg \left(t \leq 39000000000000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 7: 31.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ t_3 := 18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0)))
        (t_2 (* x (* i -4.0)))
        (t_3 (* 18.0 (* x (* t (* y z))))))
   (if (<= y -1.6e+99)
     t_3
     (if (<= y -6e+47)
       (* b c)
       (if (<= y -5.3e-34)
         t_3
         (if (<= y -9.8e-154)
           t_1
           (if (<= y -3.1e-181)
             t_2
             (if (<= y -6.2e-296)
               t_1
               (if (<= y 6e-200) t_2 (if (<= y 1.8e-85) (* b c) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = x * (i * -4.0);
	double t_3 = 18.0 * (x * (t * (y * z)));
	double tmp;
	if (y <= -1.6e+99) {
		tmp = t_3;
	} else if (y <= -6e+47) {
		tmp = b * c;
	} else if (y <= -5.3e-34) {
		tmp = t_3;
	} else if (y <= -9.8e-154) {
		tmp = t_1;
	} else if (y <= -3.1e-181) {
		tmp = t_2;
	} else if (y <= -6.2e-296) {
		tmp = t_1;
	} else if (y <= 6e-200) {
		tmp = t_2;
	} else if (y <= 1.8e-85) {
		tmp = b * c;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = x * (i * (-4.0d0))
    t_3 = 18.0d0 * (x * (t * (y * z)))
    if (y <= (-1.6d+99)) then
        tmp = t_3
    else if (y <= (-6d+47)) then
        tmp = b * c
    else if (y <= (-5.3d-34)) then
        tmp = t_3
    else if (y <= (-9.8d-154)) then
        tmp = t_1
    else if (y <= (-3.1d-181)) then
        tmp = t_2
    else if (y <= (-6.2d-296)) then
        tmp = t_1
    else if (y <= 6d-200) then
        tmp = t_2
    else if (y <= 1.8d-85) then
        tmp = b * c
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = x * (i * -4.0);
	double t_3 = 18.0 * (x * (t * (y * z)));
	double tmp;
	if (y <= -1.6e+99) {
		tmp = t_3;
	} else if (y <= -6e+47) {
		tmp = b * c;
	} else if (y <= -5.3e-34) {
		tmp = t_3;
	} else if (y <= -9.8e-154) {
		tmp = t_1;
	} else if (y <= -3.1e-181) {
		tmp = t_2;
	} else if (y <= -6.2e-296) {
		tmp = t_1;
	} else if (y <= 6e-200) {
		tmp = t_2;
	} else if (y <= 1.8e-85) {
		tmp = b * c;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = x * (i * -4.0)
	t_3 = 18.0 * (x * (t * (y * z)))
	tmp = 0
	if y <= -1.6e+99:
		tmp = t_3
	elif y <= -6e+47:
		tmp = b * c
	elif y <= -5.3e-34:
		tmp = t_3
	elif y <= -9.8e-154:
		tmp = t_1
	elif y <= -3.1e-181:
		tmp = t_2
	elif y <= -6.2e-296:
		tmp = t_1
	elif y <= 6e-200:
		tmp = t_2
	elif y <= 1.8e-85:
		tmp = b * c
	else:
		tmp = t_3
	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(x * Float64(i * -4.0))
	t_3 = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))))
	tmp = 0.0
	if (y <= -1.6e+99)
		tmp = t_3;
	elseif (y <= -6e+47)
		tmp = Float64(b * c);
	elseif (y <= -5.3e-34)
		tmp = t_3;
	elseif (y <= -9.8e-154)
		tmp = t_1;
	elseif (y <= -3.1e-181)
		tmp = t_2;
	elseif (y <= -6.2e-296)
		tmp = t_1;
	elseif (y <= 6e-200)
		tmp = t_2;
	elseif (y <= 1.8e-85)
		tmp = Float64(b * c);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = x * (i * -4.0);
	t_3 = 18.0 * (x * (t * (y * z)));
	tmp = 0.0;
	if (y <= -1.6e+99)
		tmp = t_3;
	elseif (y <= -6e+47)
		tmp = b * c;
	elseif (y <= -5.3e-34)
		tmp = t_3;
	elseif (y <= -9.8e-154)
		tmp = t_1;
	elseif (y <= -3.1e-181)
		tmp = t_2;
	elseif (y <= -6.2e-296)
		tmp = t_1;
	elseif (y <= 6e-200)
		tmp = t_2;
	elseif (y <= 1.8e-85)
		tmp = b * c;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+99], t$95$3, If[LessEqual[y, -6e+47], N[(b * c), $MachinePrecision], If[LessEqual[y, -5.3e-34], t$95$3, If[LessEqual[y, -9.8e-154], t$95$1, If[LessEqual[y, -3.1e-181], t$95$2, If[LessEqual[y, -6.2e-296], t$95$1, If[LessEqual[y, 6e-200], t$95$2, If[LessEqual[y, 1.8e-85], N[(b * c), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e99 or -6.0000000000000003e47 < y < -5.2999999999999997e-34 or 1.7999999999999999e-85 < y

   1. Initial program 80.4%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. associate-*l* 47.2%

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

   6. Simplified 47.2%

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

   if -1.6e99 < y < -6.0000000000000003e47 or 5.99999999999999989e-200 < y < 1.7999999999999999e-85

   1. Initial program 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in b around inf 36.8%

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

   if -5.2999999999999997e-34 < y < -9.79999999999999993e-154 or -3.10000000000000021e-181 < y < -6.2000000000000004e-296

   1. Initial program 95.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around inf 32.5%

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

      1. *-commutative 32.5%

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

      2. *-commutative 32.5%

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

      3. associate-*r* 32.5%

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

   6. Simplified 32.5%

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

   if -9.79999999999999993e-154 < y < -3.10000000000000021e-181 or -6.2000000000000004e-296 < y < 5.99999999999999989e-200

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in i around inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

   6. Simplified 48.0%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+99}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-34}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 8: 31.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ t_3 := 18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0)))
        (t_2 (* x (* i -4.0)))
        (t_3 (* 18.0 (* x (* t (* y z))))))
   (if (<= y -2.8e+89)
     (* x (* z (* 18.0 (* y t))))
     (if (<= y -8e+47)
       (* b c)
       (if (<= y -2.55e-34)
         t_3
         (if (<= y -9.8e-154)
           t_1
           (if (<= y -1.25e-183)
             t_2
             (if (<= y -1.45e-296)
               t_1
               (if (<= y 2.4e-200) t_2 (if (<= y 9.5e-85) (* b c) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = x * (i * -4.0);
	double t_3 = 18.0 * (x * (t * (y * z)));
	double tmp;
	if (y <= -2.8e+89) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (y <= -8e+47) {
		tmp = b * c;
	} else if (y <= -2.55e-34) {
		tmp = t_3;
	} else if (y <= -9.8e-154) {
		tmp = t_1;
	} else if (y <= -1.25e-183) {
		tmp = t_2;
	} else if (y <= -1.45e-296) {
		tmp = t_1;
	} else if (y <= 2.4e-200) {
		tmp = t_2;
	} else if (y <= 9.5e-85) {
		tmp = b * c;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = x * (i * (-4.0d0))
    t_3 = 18.0d0 * (x * (t * (y * z)))
    if (y <= (-2.8d+89)) then
        tmp = x * (z * (18.0d0 * (y * t)))
    else if (y <= (-8d+47)) then
        tmp = b * c
    else if (y <= (-2.55d-34)) then
        tmp = t_3
    else if (y <= (-9.8d-154)) then
        tmp = t_1
    else if (y <= (-1.25d-183)) then
        tmp = t_2
    else if (y <= (-1.45d-296)) then
        tmp = t_1
    else if (y <= 2.4d-200) then
        tmp = t_2
    else if (y <= 9.5d-85) then
        tmp = b * c
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = x * (i * -4.0);
	double t_3 = 18.0 * (x * (t * (y * z)));
	double tmp;
	if (y <= -2.8e+89) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (y <= -8e+47) {
		tmp = b * c;
	} else if (y <= -2.55e-34) {
		tmp = t_3;
	} else if (y <= -9.8e-154) {
		tmp = t_1;
	} else if (y <= -1.25e-183) {
		tmp = t_2;
	} else if (y <= -1.45e-296) {
		tmp = t_1;
	} else if (y <= 2.4e-200) {
		tmp = t_2;
	} else if (y <= 9.5e-85) {
		tmp = b * c;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = x * (i * -4.0)
	t_3 = 18.0 * (x * (t * (y * z)))
	tmp = 0
	if y <= -2.8e+89:
		tmp = x * (z * (18.0 * (y * t)))
	elif y <= -8e+47:
		tmp = b * c
	elif y <= -2.55e-34:
		tmp = t_3
	elif y <= -9.8e-154:
		tmp = t_1
	elif y <= -1.25e-183:
		tmp = t_2
	elif y <= -1.45e-296:
		tmp = t_1
	elif y <= 2.4e-200:
		tmp = t_2
	elif y <= 9.5e-85:
		tmp = b * c
	else:
		tmp = t_3
	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(x * Float64(i * -4.0))
	t_3 = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))))
	tmp = 0.0
	if (y <= -2.8e+89)
		tmp = Float64(x * Float64(z * Float64(18.0 * Float64(y * t))));
	elseif (y <= -8e+47)
		tmp = Float64(b * c);
	elseif (y <= -2.55e-34)
		tmp = t_3;
	elseif (y <= -9.8e-154)
		tmp = t_1;
	elseif (y <= -1.25e-183)
		tmp = t_2;
	elseif (y <= -1.45e-296)
		tmp = t_1;
	elseif (y <= 2.4e-200)
		tmp = t_2;
	elseif (y <= 9.5e-85)
		tmp = Float64(b * c);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = x * (i * -4.0);
	t_3 = 18.0 * (x * (t * (y * z)));
	tmp = 0.0;
	if (y <= -2.8e+89)
		tmp = x * (z * (18.0 * (y * t)));
	elseif (y <= -8e+47)
		tmp = b * c;
	elseif (y <= -2.55e-34)
		tmp = t_3;
	elseif (y <= -9.8e-154)
		tmp = t_1;
	elseif (y <= -1.25e-183)
		tmp = t_2;
	elseif (y <= -1.45e-296)
		tmp = t_1;
	elseif (y <= 2.4e-200)
		tmp = t_2;
	elseif (y <= 9.5e-85)
		tmp = b * c;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+89], N[(x * N[(z * N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e+47], N[(b * c), $MachinePrecision], If[LessEqual[y, -2.55e-34], t$95$3, If[LessEqual[y, -9.8e-154], t$95$1, If[LessEqual[y, -1.25e-183], t$95$2, If[LessEqual[y, -1.45e-296], t$95$1, If[LessEqual[y, 2.4e-200], t$95$2, If[LessEqual[y, 9.5e-85], N[(b * c), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7999999999999998e89

   1. Initial program 81.8%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in y around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l* 56.6%

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

      3. *-commutative 56.6%

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

      4. associate-*l* 56.6%

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

      5. *-commutative 56.6%

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

      6. associate-*l* 56.6%

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

      7. associate-*r* 60.4%

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

      8. associate-*r* 60.5%

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

      9. *-commutative 60.5%

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

   6. Simplified 60.5%

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

   if -2.7999999999999998e89 < y < -8.0000000000000004e47 or 2.40000000000000002e-200 < y < 9.49999999999999964e-85

   1. Initial program 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in b around inf 36.8%

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

   if -8.0000000000000004e47 < y < -2.55e-34 or 9.49999999999999964e-85 < y

   1. Initial program 79.6%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in y around inf 40.8%

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

      1. *-commutative 40.8%

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

      2. associate-*l* 42.2%

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

   6. Simplified 42.2%

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

   if -2.55e-34 < y < -9.79999999999999993e-154 or -1.2500000000000001e-183 < y < -1.44999999999999991e-296

   1. Initial program 95.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around inf 32.5%

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

      1. *-commutative 32.5%

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

      2. *-commutative 32.5%

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

      3. associate-*r* 32.5%

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

   6. Simplified 32.5%

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

   if -9.79999999999999993e-154 < y < -1.2500000000000001e-183 or -1.44999999999999991e-296 < y < 2.40000000000000002e-200

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in i around inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

   6. Simplified 48.0%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-34}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 9: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+167}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{+66}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.5e+167)
   (* b c)
   (if (<= (* b c) -1.95e+86)
     (* x (* i -4.0))
     (if (<= (* b c) -2.25e+66)
       (* b c)
       (if (<= (* b c) -1e-240)
         (* j (* k -27.0))
         (if (<= (* b c) 2.5e+86) (* t (* a -4.0)) (* 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 ((b * c) <= -1.5e+167) {
		tmp = b * c;
	} else if ((b * c) <= -1.95e+86) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= -2.25e+66) {
		tmp = b * c;
	} else if ((b * c) <= -1e-240) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.5e+86) {
		tmp = t * (a * -4.0);
	} 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 ((b * c) <= (-1.5d+167)) then
        tmp = b * c
    else if ((b * c) <= (-1.95d+86)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= (-2.25d+66)) then
        tmp = b * c
    else if ((b * c) <= (-1d-240)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2.5d+86) then
        tmp = t * (a * (-4.0d0))
    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 ((b * c) <= -1.5e+167) {
		tmp = b * c;
	} else if ((b * c) <= -1.95e+86) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= -2.25e+66) {
		tmp = b * c;
	} else if ((b * c) <= -1e-240) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.5e+86) {
		tmp = t * (a * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.5e+167:
		tmp = b * c
	elif (b * c) <= -1.95e+86:
		tmp = x * (i * -4.0)
	elif (b * c) <= -2.25e+66:
		tmp = b * c
	elif (b * c) <= -1e-240:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2.5e+86:
		tmp = t * (a * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.5e+167)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.95e+86)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= -2.25e+66)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e-240)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2.5e+86)
		tmp = Float64(t * Float64(a * -4.0));
	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 ((b * c) <= -1.5e+167)
		tmp = b * c;
	elseif ((b * c) <= -1.95e+86)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= -2.25e+66)
		tmp = b * c;
	elseif ((b * c) <= -1e-240)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2.5e+86)
		tmp = t * (a * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.5e+167], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+86], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.25e+66], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-240], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.5e+86], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.50000000000000006e167 or -1.9500000000000001e86 < (*.f64 b c) < -2.2499999999999999e66 or 2.4999999999999999e86 < (*.f64 b c)

   1. Initial program 90.4%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in b around inf 62.5%

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

   if -1.50000000000000006e167 < (*.f64 b c) < -1.9500000000000001e86

   1. Initial program 79.3%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in i around inf 44.1%

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

      1. associate-*r* 44.1%

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

      2. *-commutative 44.1%

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

   6. Simplified 44.1%

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

   if -2.2499999999999999e66 < (*.f64 b c) < -9.9999999999999997e-241

   1. Initial program 87.0%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in j around inf 38.7%

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

      1. *-commutative 38.7%

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

      2. associate-*l* 38.8%

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

   6. Simplified 38.8%

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

   if -9.9999999999999997e-241 < (*.f64 b c) < 2.4999999999999999e86

   1. Initial program 85.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in a around inf 36.4%

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

      1. *-commutative 36.4%

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

      2. *-commutative 36.4%

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

      3. associate-*r* 36.4%

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

   6. Simplified 36.4%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+167}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{+66}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 10: 77.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+135} \lor \neg \left(x \leq 4.2 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.1e+135) (not (<= x 4.2e+37)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.1e+135) || !(x <= 4.2e+37)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2.1d+135)) .or. (.not. (x <= 4.2d+37))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.1e+135) || !(x <= 4.2e+37)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2.1e+135) or not (x <= 4.2e+37):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.1e+135) || !(x <= 4.2e+37))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2.1e+135) || ~((x <= 4.2e+37)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.1e+135], N[Not[LessEqual[x, 4.2e+37]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e135 or 4.2000000000000002e37 < x

   1. Initial program 68.4%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in x around inf 82.4%

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

   if -2.1000000000000001e135 < x < 4.2000000000000002e37

   1. Initial program 96.8%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 84.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+135} \lor \neg \left(x \leq 4.2 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 11: 72.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+168}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+224} \lor \neg \left(t \leq 1.35 \cdot 10^{+227}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -2.25e+73)
     t_1
     (if (<= t 0.001)
       (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
       (if (<= t 1.1e+168)
         (+ (* -4.0 (+ (* t a) (* x i))) (* k (* j -27.0)))
         (if (or (<= t 5.4e+224) (not (<= t 1.35e+227)))
           t_1
           (* (* x t) (* z (* 18.0 y)))))))))

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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.25e+73) {
		tmp = t_1;
	} else if (t <= 0.001) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if (t <= 1.1e+168) {
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0));
	} else if ((t <= 5.4e+224) || !(t <= 1.35e+227)) {
		tmp = t_1;
	} else {
		tmp = (x * t) * (z * (18.0 * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-2.25d+73)) then
        tmp = t_1
    else if (t <= 0.001d0) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else if (t <= 1.1d+168) then
        tmp = ((-4.0d0) * ((t * a) + (x * i))) + (k * (j * (-27.0d0)))
    else if ((t <= 5.4d+224) .or. (.not. (t <= 1.35d+227))) then
        tmp = t_1
    else
        tmp = (x * t) * (z * (18.0d0 * y))
    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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.25e+73) {
		tmp = t_1;
	} else if (t <= 0.001) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if (t <= 1.1e+168) {
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0));
	} else if ((t <= 5.4e+224) || !(t <= 1.35e+227)) {
		tmp = t_1;
	} else {
		tmp = (x * t) * (z * (18.0 * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -2.25e+73:
		tmp = t_1
	elif t <= 0.001:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	elif t <= 1.1e+168:
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0))
	elif (t <= 5.4e+224) or not (t <= 1.35e+227):
		tmp = t_1
	else:
		tmp = (x * t) * (z * (18.0 * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.25e+73)
		tmp = t_1;
	elseif (t <= 0.001)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	elseif (t <= 1.1e+168)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) + Float64(k * Float64(j * -27.0)));
	elseif ((t <= 5.4e+224) || !(t <= 1.35e+227))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * t) * Float64(z * Float64(18.0 * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.25e+73)
		tmp = t_1;
	elseif (t <= 0.001)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	elseif (t <= 1.1e+168)
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0));
	elseif ((t <= 5.4e+224) || ~((t <= 1.35e+227)))
		tmp = t_1;
	else
		tmp = (x * t) * (z * (18.0 * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+73], t$95$1, If[LessEqual[t, 0.001], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+168], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5.4e+224], N[Not[LessEqual[t, 1.35e+227]], $MachinePrecision]], t$95$1, N[(N[(x * t), $MachinePrecision] * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.24999999999999992e73 or 1.1000000000000001e168 < t < 5.3999999999999997e224 or 1.3499999999999999e227 < t

   1. Initial program 82.7%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 84.4%

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

   if -2.24999999999999992e73 < t < 1e-3

   1. Initial program 87.6%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in t around 0 75.0%

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

   if 1e-3 < t < 1.1000000000000001e168

   1. Initial program 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around 0 79.9%

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

   5. Taylor expanded in b around 0 74.2%

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

      1. associate--r+ 74.2%

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

      2. cancel-sign-sub-inv 74.2%

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

      3. sub-neg 74.2%

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

      4. metadata-eval 74.2%

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

      5. *-commutative 74.2%

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

      6. distribute-lft-neg-in 74.2%

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

      7. metadata-eval 74.2%

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

      8. distribute-lft-out 74.2%

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

      9. *-commutative 74.2%

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

      10. associate-*l* 74.3%

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

   7. Simplified 74.3%

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

   if 5.3999999999999997e224 < t < 1.3499999999999999e227

   1. Initial program 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in t around inf 70.3%

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

      1. pow1 70.3%

         \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]

   6. Applied egg-rr 70.3%

      \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*l* 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in x around inf 70.3%

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

       1. *-commutative 70.3%

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

       2. associate-*r* 100.0%

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

       3. associate-*l* 100.0%

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

       4. associate-*r* 100.0%

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

       5. *-commutative 100.0%

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

       6. associate-*l* 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+168}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+224} \lor \neg \left(t \leq 1.35 \cdot 10^{+227}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \end{array} \]

Alternative 12: 57.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-100}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -2.9e+121)
     t_1
     (if (<= x -6.8e-201)
       (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
       (if (<= x 6.2e-100)
         (- (* b c) (* 27.0 (* j k)))
         (if (<= x 1.7) (+ (* b c) (* -4.0 (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -2.9e+121) {
		tmp = t_1;
	} else if (x <= -6.8e-201) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 6.2e-100) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 1.7) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-2.9d+121)) then
        tmp = t_1
    else if (x <= (-6.8d-201)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (x <= 6.2d-100) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 1.7d0) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -2.9e+121) {
		tmp = t_1;
	} else if (x <= -6.8e-201) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 6.2e-100) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 1.7) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -2.9e+121:
		tmp = t_1
	elif x <= -6.8e-201:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif x <= 6.2e-100:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 1.7:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -2.9e+121)
		tmp = t_1;
	elseif (x <= -6.8e-201)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (x <= 6.2e-100)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 1.7)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -2.9e+121)
		tmp = t_1;
	elseif (x <= -6.8e-201)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (x <= 6.2e-100)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 1.7)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+121], t$95$1, If[LessEqual[x, -6.8e-201], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-100], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8999999999999999e121 or 1.69999999999999996 < x

   1. Initial program 72.7%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in x around inf 79.7%

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

   if -2.8999999999999999e121 < x < -6.7999999999999997e-201

   1. Initial program 93.0%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 61.3%

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

   if -6.7999999999999997e-201 < x < 6.1999999999999997e-100

   1. Initial program 98.4%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 85.4%

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

   5. Taylor expanded in a around 0 64.8%

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

   if 6.1999999999999997e-100 < x < 1.69999999999999996

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.2%

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

   5. Taylor expanded in j around 0 76.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-100}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 13: 61.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 10.6:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -1.8e+134)
     t_1
     (if (<= x -4.4e-237)
       (+ (* -4.0 (+ (* t a) (* x i))) (* k (* j -27.0)))
       (if (<= x 2e-99)
         (- (* b c) (* 27.0 (* j k)))
         (if (<= x 10.6) (+ (* b c) (* -4.0 (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -1.8e+134) {
		tmp = t_1;
	} else if (x <= -4.4e-237) {
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0));
	} else if (x <= 2e-99) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 10.6) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-1.8d+134)) then
        tmp = t_1
    else if (x <= (-4.4d-237)) then
        tmp = ((-4.0d0) * ((t * a) + (x * i))) + (k * (j * (-27.0d0)))
    else if (x <= 2d-99) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 10.6d0) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -1.8e+134) {
		tmp = t_1;
	} else if (x <= -4.4e-237) {
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0));
	} else if (x <= 2e-99) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 10.6) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -1.8e+134:
		tmp = t_1
	elif x <= -4.4e-237:
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0))
	elif x <= 2e-99:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 10.6:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -1.8e+134)
		tmp = t_1;
	elseif (x <= -4.4e-237)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) + Float64(k * Float64(j * -27.0)));
	elseif (x <= 2e-99)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 10.6)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -1.8e+134)
		tmp = t_1;
	elseif (x <= -4.4e-237)
		tmp = (-4.0 * ((t * a) + (x * i))) + (k * (j * -27.0));
	elseif (x <= 2e-99)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 10.6)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+134], t$95$1, If[LessEqual[x, -4.4e-237], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-99], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 10.6], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.79999999999999994e134 or 10.5999999999999996 < x

   1. Initial program 71.9%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around inf 80.1%

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

   if -1.79999999999999994e134 < x < -4.39999999999999996e-237

   1. Initial program 93.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 83.5%

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

   5. Taylor expanded in b around 0 68.3%

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

      1. associate--r+ 68.3%

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

      2. cancel-sign-sub-inv 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

      5. *-commutative 68.3%

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

      6. distribute-lft-neg-in 68.3%

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

      7. metadata-eval 68.3%

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

      8. distribute-lft-out 68.3%

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

      9. *-commutative 68.3%

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

      10. associate-*l* 68.3%

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

   7. Simplified 68.3%

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

   if -4.39999999999999996e-237 < x < 2e-99

   1. Initial program 98.3%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around 0 84.4%

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

   5. Taylor expanded in a around 0 65.3%

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

   if 2e-99 < x < 10.5999999999999996

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.2%

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

   5. Taylor expanded in j around 0 76.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 10.6:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 14: 71.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+133} \lor \neg \left(x \leq 22\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -4e+133) (not (<= x 22.0)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -4e+133) || !(x <= 22.0)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-4d+133)) .or. (.not. (x <= 22.0d0))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -4e+133) || !(x <= 22.0)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -4e+133) or not (x <= 22.0):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -4e+133) || !(x <= 22.0))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -4e+133) || ~((x <= 22.0)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -4e+133], N[Not[LessEqual[x, 22.0]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000001e133 or 22 < x

   1. Initial program 72.1%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in x around inf 80.3%

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

   if -4.0000000000000001e133 < x < 22

   1. Initial program 96.6%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around 0 80.9%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+133} \lor \neg \left(x \leq 22\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 15: 47.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* (* x t) (* z (* 18.0 y)))))
   (if (<= x -2.7e+133)
     t_2
     (if (<= x -4e-140)
       t_1
       (if (<= x 1.3e-99)
         (- (* b c) (* 27.0 (* j k)))
         (if (<= x 7.2e+34) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (x * t) * (z * (18.0 * y));
	double tmp;
	if (x <= -2.7e+133) {
		tmp = t_2;
	} else if (x <= -4e-140) {
		tmp = t_1;
	} else if (x <= 1.3e-99) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 7.2e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (x * t) * (z * (18.0d0 * y))
    if (x <= (-2.7d+133)) then
        tmp = t_2
    else if (x <= (-4d-140)) then
        tmp = t_1
    else if (x <= 1.3d-99) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 7.2d+34) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (x * t) * (z * (18.0 * y));
	double tmp;
	if (x <= -2.7e+133) {
		tmp = t_2;
	} else if (x <= -4e-140) {
		tmp = t_1;
	} else if (x <= 1.3e-99) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 7.2e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = (x * t) * (z * (18.0 * y))
	tmp = 0
	if x <= -2.7e+133:
		tmp = t_2
	elif x <= -4e-140:
		tmp = t_1
	elif x <= 1.3e-99:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 7.2e+34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(Float64(x * t) * Float64(z * Float64(18.0 * y)))
	tmp = 0.0
	if (x <= -2.7e+133)
		tmp = t_2;
	elseif (x <= -4e-140)
		tmp = t_1;
	elseif (x <= 1.3e-99)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 7.2e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = (x * t) * (z * (18.0 * y));
	tmp = 0.0;
	if (x <= -2.7e+133)
		tmp = t_2;
	elseif (x <= -4e-140)
		tmp = t_1;
	elseif (x <= 1.3e-99)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 7.2e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+133], t$95$2, If[LessEqual[x, -4e-140], t$95$1, If[LessEqual[x, 1.3e-99], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7000000000000002e133 or 7.2000000000000001e34 < x

   1. Initial program 69.1%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. pow1 49.0%

         \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]

   6. Applied egg-rr 49.0%

      \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-*l* 49.0%

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

   8. Simplified 49.0%

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

   9. Taylor expanded in x around inf 45.6%

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

       1. *-commutative 45.6%

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

       2. associate-*r* 51.5%

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

       3. associate-*l* 51.5%

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

       4. associate-*r* 51.5%

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

       5. *-commutative 51.5%

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

       6. associate-*l* 51.5%

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

   11. Simplified 51.5%

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

   if -2.7000000000000002e133 < x < -3.9999999999999999e-140 or 1.30000000000000003e-99 < x < 7.2000000000000001e34

   1. Initial program 94.7%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around 0 72.1%

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

   5. Taylor expanded in j around 0 59.4%

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

   if -3.9999999999999999e-140 < x < 1.30000000000000003e-99

   1. Initial program 98.7%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around 0 83.6%

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

   5. Taylor expanded in a around 0 63.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+133}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-140}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \end{array} \]

Alternative 16: 36.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.6 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -7.6e+67)
   (* b c)
   (if (<= (* b c) -1.25e-239)
     (* j (* k -27.0))
     (if (<= (* b c) 2.6e+93) (* t (* a -4.0)) (* 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 ((b * c) <= -7.6e+67) {
		tmp = b * c;
	} else if ((b * c) <= -1.25e-239) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.6e+93) {
		tmp = t * (a * -4.0);
	} 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 ((b * c) <= (-7.6d+67)) then
        tmp = b * c
    else if ((b * c) <= (-1.25d-239)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2.6d+93) then
        tmp = t * (a * (-4.0d0))
    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 ((b * c) <= -7.6e+67) {
		tmp = b * c;
	} else if ((b * c) <= -1.25e-239) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.6e+93) {
		tmp = t * (a * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -7.6e+67:
		tmp = b * c
	elif (b * c) <= -1.25e-239:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2.6e+93:
		tmp = t * (a * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -7.6e+67)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.25e-239)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2.6e+93)
		tmp = Float64(t * Float64(a * -4.0));
	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 ((b * c) <= -7.6e+67)
		tmp = b * c;
	elseif ((b * c) <= -1.25e-239)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2.6e+93)
		tmp = t * (a * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -7.6e+67], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.25e-239], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.6e+93], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -7.60000000000000041e67 or 2.6e93 < (*.f64 b c)

   1. Initial program 88.6%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in b around inf 52.9%

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

   if -7.60000000000000041e67 < (*.f64 b c) < -1.25e-239

   1. Initial program 87.0%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in j around inf 38.7%

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

      1. *-commutative 38.7%

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

      2. associate-*l* 38.8%

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

   6. Simplified 38.8%

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

   if -1.25e-239 < (*.f64 b c) < 2.6e93

   1. Initial program 85.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in a around inf 36.4%

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

      1. *-commutative 36.4%

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

      2. *-commutative 36.4%

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

      3. associate-*r* 36.4%

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

   6. Simplified 36.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.6 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17: 59.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+54} \lor \neg \left(t \leq 4.3 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -8.5e+54) (not (<= t 4.3e+18)))
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (- (* b c) (* 27.0 (* j k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -8.5e+54) || !(t <= 4.3e+18)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-8.5d+54)) .or. (.not. (t <= 4.3d+18))) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -8.5e+54) || !(t <= 4.3e+18)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -8.5e+54) or not (t <= 4.3e+18):
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -8.5e+54) || !(t <= 4.3e+18))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -8.5e+54) || ~((t <= 4.3e+18)))
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -8.5e+54], N[Not[LessEqual[t, 4.3e+18]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.4999999999999995e54 or 4.3e18 < t

   1. Initial program 86.2%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 74.3%

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

   if -8.4999999999999995e54 < t < 4.3e18

   1. Initial program 87.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around 0 63.0%

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

   5. Taylor expanded in a around 0 56.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+54} \lor \neg \left(t \leq 4.3 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 18: 46.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+132} \lor \neg \left(x \leq 2.65 \cdot 10^{+38}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -4e+132) (not (<= x 2.65e+38)))
   (* (* x t) (* z (* 18.0 y)))
   (+ (* b c) (* -4.0 (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -4e+132) || !(x <= 2.65e+38)) {
		tmp = (x * t) * (z * (18.0 * y));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-4d+132)) .or. (.not. (x <= 2.65d+38))) then
        tmp = (x * t) * (z * (18.0d0 * y))
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -4e+132) || !(x <= 2.65e+38)) {
		tmp = (x * t) * (z * (18.0 * y));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -4e+132) or not (x <= 2.65e+38):
		tmp = (x * t) * (z * (18.0 * y))
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -4e+132) || !(x <= 2.65e+38))
		tmp = Float64(Float64(x * t) * Float64(z * Float64(18.0 * y)));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -4e+132) || ~((x <= 2.65e+38)))
		tmp = (x * t) * (z * (18.0 * y));
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -4e+132], N[Not[LessEqual[x, 2.65e+38]], $MachinePrecision]], N[(N[(x * t), $MachinePrecision] * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999996e132 or 2.65000000000000012e38 < x

   1. Initial program 69.1%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. pow1 49.0%

         \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]

   6. Applied egg-rr 49.0%

      \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-*l* 49.0%

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

   8. Simplified 49.0%

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

   9. Taylor expanded in x around inf 45.6%

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

       1. *-commutative 45.6%

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

       2. associate-*r* 51.5%

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

       3. associate-*l* 51.5%

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

       4. associate-*r* 51.5%

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

       5. *-commutative 51.5%

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

       6. associate-*l* 51.5%

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

   11. Simplified 51.5%

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

   if -3.99999999999999996e132 < x < 2.65000000000000012e38

   1. Initial program 96.8%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 78.2%

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

   5. Taylor expanded in j around 0 55.2%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+132} \lor \neg \left(x \leq 2.65 \cdot 10^{+38}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(z \cdot \left(18 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 19: 37.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+114}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5.8e+66)
   (* b c)
   (if (<= (* b c) 1.55e+114) (* (* j k) -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 ((b * c) <= -5.8e+66) {
		tmp = b * c;
	} else if ((b * c) <= 1.55e+114) {
		tmp = (j * k) * -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 ((b * c) <= (-5.8d+66)) then
        tmp = b * c
    else if ((b * c) <= 1.55d+114) then
        tmp = (j * k) * (-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 ((b * c) <= -5.8e+66) {
		tmp = b * c;
	} else if ((b * c) <= 1.55e+114) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5.8e+66:
		tmp = b * c
	elif (b * c) <= 1.55e+114:
		tmp = (j * k) * -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 (Float64(b * c) <= -5.8e+66)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.55e+114)
		tmp = Float64(Float64(j * k) * -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 ((b * c) <= -5.8e+66)
		tmp = b * c;
	elseif ((b * c) <= 1.55e+114)
		tmp = (j * k) * -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[N[(b * c), $MachinePrecision], -5.8e+66], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.55e+114], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.79999999999999972e66 or 1.55e114 < (*.f64 b c)

   1. Initial program 88.2%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in b around inf 53.6%

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

   if -5.79999999999999972e66 < (*.f64 b c) < 1.55e114

   1. Initial program 86.0%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in j around inf 27.8%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+114}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20: 24.0% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

3. Simplified 87.2%

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

4. Taylor expanded in b around inf 20.1%

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

5. Final simplification 20.1%

   \[\leadsto b \cdot c \]

Developer target: 89.5% 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 2023291 
(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)))