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

Percentage Accurate: 95.6% → 98.6%

Time: 18.8s

Alternatives: 15

Speedup: 0.8×

• 27.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 5e+224)
   (fma a (* 27.0 b) (fma x 2.0 (* t (* y (* z -9.0)))))
   (+ (* a (* 27.0 b)) (+ (* y (* z (* t -9.0))) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+224) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (y * (z * -9.0)))));
	} else {
		tmp = (a * (27.0 * b)) + ((y * (z * (t * -9.0))) + (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+224)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(y * Float64(z * -9.0)))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+224], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 4.99999999999999964e224

   1. Initial program 96.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 96.9%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 96.9%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 96.9%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 96.9%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 95.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 95.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 95.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 95.6%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 95.6%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 95.6%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-def 95.6%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 95.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-def 95.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. distribute-lft-neg-in 95.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(\left(y \cdot 9\right) \cdot t\right) \cdot z}\right)\right) \]

      15. distribute-rgt-neg-in 95.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(y \cdot 9\right) \cdot t\right) \cdot \left(-z\right)}\right)\right) \]

      16. *-commutative 95.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right)} \cdot \left(-z\right)\right)\right) \]

      17. associate-*r* 96.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot \left(-z\right)\right)}\right)\right) \]

      18. associate-*l* 96.8%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(9 \cdot \left(-z\right)\right)\right)}\right)\right) \]

      19. neg-mul-1 96.8%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 96.8%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   if 4.99999999999999964e224 < (*.f64 (*.f64 y 9) z)

   1. Initial program 77.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 77.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 77.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. sub-neg 96.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

      2. *-commutative 96.3%

         \[\leadsto \left(x \cdot 2 + \left(-\color{blue}{\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      3. distribute-rgt-neg-in 96.3%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot t\right) \cdot \left(-y \cdot 9\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      4. *-commutative 96.3%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(-\color{blue}{9 \cdot y}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      5. distribute-lft-neg-in 96.3%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \color{blue}{\left(\left(-9\right) \cdot y\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      6. metadata-eval 96.3%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(\color{blue}{-9} \cdot y\right)\right) + a \cdot \left(27 \cdot b\right) \]

      7. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right) \cdot y}\right) + a \cdot \left(27 \cdot b\right) \]

      8. associate-*r* 96.4%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y\right) + a \cdot \left(27 \cdot b\right) \]

      9. *-commutative 96.4%

         \[\leadsto \left(x \cdot 2 + \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right) + a \cdot \left(27 \cdot b\right) \]

   6. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* t (* z (* y -9.0)))))
   (if (<= t -1.95e-150)
     t_2
     (if (<= t 1.05e-169)
       (* x 2.0)
       (if (<= t 7.5e-97)
         (* b (* a 27.0))
         (if (<= t 2.4e-45)
           (* x 2.0)
           (if (<= t 1.32e+39)
             t_1
             (if (<= t 6e+64) (* x 2.0) (if (<= t 8.8e+127) t_1 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = t * (z * (y * -9.0));
	double tmp;
	if (t <= -1.95e-150) {
		tmp = t_2;
	} else if (t <= 1.05e-169) {
		tmp = x * 2.0;
	} else if (t <= 7.5e-97) {
		tmp = b * (a * 27.0);
	} else if (t <= 2.4e-45) {
		tmp = x * 2.0;
	} else if (t <= 1.32e+39) {
		tmp = t_1;
	} else if (t <= 6e+64) {
		tmp = x * 2.0;
	} else if (t <= 8.8e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = t * (z * (y * (-9.0d0)))
    if (t <= (-1.95d-150)) then
        tmp = t_2
    else if (t <= 1.05d-169) then
        tmp = x * 2.0d0
    else if (t <= 7.5d-97) then
        tmp = b * (a * 27.0d0)
    else if (t <= 2.4d-45) then
        tmp = x * 2.0d0
    else if (t <= 1.32d+39) then
        tmp = t_1
    else if (t <= 6d+64) then
        tmp = x * 2.0d0
    else if (t <= 8.8d+127) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = t * (z * (y * -9.0));
	double tmp;
	if (t <= -1.95e-150) {
		tmp = t_2;
	} else if (t <= 1.05e-169) {
		tmp = x * 2.0;
	} else if (t <= 7.5e-97) {
		tmp = b * (a * 27.0);
	} else if (t <= 2.4e-45) {
		tmp = x * 2.0;
	} else if (t <= 1.32e+39) {
		tmp = t_1;
	} else if (t <= 6e+64) {
		tmp = x * 2.0;
	} else if (t <= 8.8e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = t * (z * (y * -9.0))
	tmp = 0
	if t <= -1.95e-150:
		tmp = t_2
	elif t <= 1.05e-169:
		tmp = x * 2.0
	elif t <= 7.5e-97:
		tmp = b * (a * 27.0)
	elif t <= 2.4e-45:
		tmp = x * 2.0
	elif t <= 1.32e+39:
		tmp = t_1
	elif t <= 6e+64:
		tmp = x * 2.0
	elif t <= 8.8e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(t * Float64(z * Float64(y * -9.0)))
	tmp = 0.0
	if (t <= -1.95e-150)
		tmp = t_2;
	elseif (t <= 1.05e-169)
		tmp = Float64(x * 2.0);
	elseif (t <= 7.5e-97)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (t <= 2.4e-45)
		tmp = Float64(x * 2.0);
	elseif (t <= 1.32e+39)
		tmp = t_1;
	elseif (t <= 6e+64)
		tmp = Float64(x * 2.0);
	elseif (t <= 8.8e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = t * (z * (y * -9.0));
	tmp = 0.0;
	if (t <= -1.95e-150)
		tmp = t_2;
	elseif (t <= 1.05e-169)
		tmp = x * 2.0;
	elseif (t <= 7.5e-97)
		tmp = b * (a * 27.0);
	elseif (t <= 2.4e-45)
		tmp = x * 2.0;
	elseif (t <= 1.32e+39)
		tmp = t_1;
	elseif (t <= 6e+64)
		tmp = x * 2.0;
	elseif (t <= 8.8e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e-150], t$95$2, If[LessEqual[t, 1.05e-169], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 7.5e-97], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-45], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 1.32e+39], t$95$1, If[LessEqual[t, 6e+64], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 8.8e+127], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9500000000000001e-150 or 8.8000000000000007e127 < t

   1. Initial program 96.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 96.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 91.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 91.7%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 49.2%

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

      1. *-commutative 49.2%

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} \]

      2. associate-*l* 49.2%

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      3. *-commutative 49.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(z \cdot y\right)} \cdot -9\right) \]

      4. associate-*l* 49.2%

         \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(y \cdot -9\right)\right)} \]

   7. Simplified 49.2%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(y \cdot -9\right)\right)} \]

   if -1.9500000000000001e-150 < t < 1.05e-169 or 7.5e-97 < t < 2.3999999999999999e-45 or 1.32e39 < t < 6.0000000000000004e64

   1. Initial program 92.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 92.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 92.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 1.05e-169 < t < 7.5e-97

   1. Initial program 90.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.4%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 90.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 90.4%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 90.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 90.3%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   6. Step-by-step derivation

      1. +-commutative 90.3%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right)} \]

      2. associate-+r- 90.3%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t} \]

      3. associate-*l* 90.5%

         \[\leadsto \left(\color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t \]

      4. associate-*l* 99.8%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

      5. *-commutative 99.8%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(\color{blue}{\left(z \cdot 9\right)} \cdot t\right) \]

      6. associate-*l* 99.8%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(z \cdot \left(9 \cdot t\right)\right)} \]

   7. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)} \]

   8. Taylor expanded in a around inf 54.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} \]

      2. *-commutative 54.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot 27 \]

      3. associate-*l* 54.1%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot 27\right)} \]

      4. *-commutative 54.1%

         \[\leadsto b \cdot \color{blue}{\left(27 \cdot a\right)} \]

   10. Simplified 54.1%

       \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   if 2.3999999999999999e-45 < t < 1.32e39 or 6.0000000000000004e64 < t < 8.8000000000000007e127

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 85.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 85.9%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 42.0%

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

      1. associate-*r* 42.0%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

      2. *-commutative 42.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      3. associate-*r* 42.0%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   7. Simplified 42.0%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := \left(t \cdot -9\right) \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-95}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* (* t -9.0) (* y z))))
   (if (<= t -1.95e-150)
     t_2
     (if (<= t 1.05e-169)
       (* x 2.0)
       (if (<= t 1.05e-95)
         (* b (* a 27.0))
         (if (<= t 1.18e-45)
           (* x 2.0)
           (if (<= t 2.2e+40)
             t_1
             (if (<= t 1.52e+63) (* x 2.0) (if (<= t 8.8e+127) t_1 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = (t * -9.0) * (y * z);
	double tmp;
	if (t <= -1.95e-150) {
		tmp = t_2;
	} else if (t <= 1.05e-169) {
		tmp = x * 2.0;
	} else if (t <= 1.05e-95) {
		tmp = b * (a * 27.0);
	} else if (t <= 1.18e-45) {
		tmp = x * 2.0;
	} else if (t <= 2.2e+40) {
		tmp = t_1;
	} else if (t <= 1.52e+63) {
		tmp = x * 2.0;
	} else if (t <= 8.8e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = (t * (-9.0d0)) * (y * z)
    if (t <= (-1.95d-150)) then
        tmp = t_2
    else if (t <= 1.05d-169) then
        tmp = x * 2.0d0
    else if (t <= 1.05d-95) then
        tmp = b * (a * 27.0d0)
    else if (t <= 1.18d-45) then
        tmp = x * 2.0d0
    else if (t <= 2.2d+40) then
        tmp = t_1
    else if (t <= 1.52d+63) then
        tmp = x * 2.0d0
    else if (t <= 8.8d+127) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = (t * -9.0) * (y * z);
	double tmp;
	if (t <= -1.95e-150) {
		tmp = t_2;
	} else if (t <= 1.05e-169) {
		tmp = x * 2.0;
	} else if (t <= 1.05e-95) {
		tmp = b * (a * 27.0);
	} else if (t <= 1.18e-45) {
		tmp = x * 2.0;
	} else if (t <= 2.2e+40) {
		tmp = t_1;
	} else if (t <= 1.52e+63) {
		tmp = x * 2.0;
	} else if (t <= 8.8e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = (t * -9.0) * (y * z)
	tmp = 0
	if t <= -1.95e-150:
		tmp = t_2
	elif t <= 1.05e-169:
		tmp = x * 2.0
	elif t <= 1.05e-95:
		tmp = b * (a * 27.0)
	elif t <= 1.18e-45:
		tmp = x * 2.0
	elif t <= 2.2e+40:
		tmp = t_1
	elif t <= 1.52e+63:
		tmp = x * 2.0
	elif t <= 8.8e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(Float64(t * -9.0) * Float64(y * z))
	tmp = 0.0
	if (t <= -1.95e-150)
		tmp = t_2;
	elseif (t <= 1.05e-169)
		tmp = Float64(x * 2.0);
	elseif (t <= 1.05e-95)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (t <= 1.18e-45)
		tmp = Float64(x * 2.0);
	elseif (t <= 2.2e+40)
		tmp = t_1;
	elseif (t <= 1.52e+63)
		tmp = Float64(x * 2.0);
	elseif (t <= 8.8e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = (t * -9.0) * (y * z);
	tmp = 0.0;
	if (t <= -1.95e-150)
		tmp = t_2;
	elseif (t <= 1.05e-169)
		tmp = x * 2.0;
	elseif (t <= 1.05e-95)
		tmp = b * (a * 27.0);
	elseif (t <= 1.18e-45)
		tmp = x * 2.0;
	elseif (t <= 2.2e+40)
		tmp = t_1;
	elseif (t <= 1.52e+63)
		tmp = x * 2.0;
	elseif (t <= 8.8e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e-150], t$95$2, If[LessEqual[t, 1.05e-169], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 1.05e-95], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e-45], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 2.2e+40], t$95$1, If[LessEqual[t, 1.52e+63], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 8.8e+127], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9500000000000001e-150 or 8.8000000000000007e127 < t

   1. Initial program 96.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 96.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 91.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 91.7%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 49.2%

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

      1. associate-*r* 49.1%

         \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} \]

      2. *-commutative 49.1%

         \[\leadsto \color{blue}{\left(t \cdot -9\right)} \cdot \left(y \cdot z\right) \]

   7. Simplified 49.1%

      \[\leadsto \color{blue}{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)} \]

   if -1.9500000000000001e-150 < t < 1.05e-169 or 1.05e-95 < t < 1.18e-45 or 2.1999999999999999e40 < t < 1.51999999999999993e63

   1. Initial program 92.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 92.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 92.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 48.4%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 1.05e-169 < t < 1.05e-95

   1. Initial program 90.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.4%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 90.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 90.4%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 90.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 90.3%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   6. Step-by-step derivation

      1. +-commutative 90.3%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right)} \]

      2. associate-+r- 90.3%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t} \]

      3. associate-*l* 90.5%

         \[\leadsto \left(\color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t \]

      4. associate-*l* 99.8%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

      5. *-commutative 99.8%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(\color{blue}{\left(z \cdot 9\right)} \cdot t\right) \]

      6. associate-*l* 99.8%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(z \cdot \left(9 \cdot t\right)\right)} \]

   7. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)} \]

   8. Taylor expanded in a around inf 54.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} \]

      2. *-commutative 54.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot 27 \]

      3. associate-*l* 54.1%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot 27\right)} \]

      4. *-commutative 54.1%

         \[\leadsto b \cdot \color{blue}{\left(27 \cdot a\right)} \]

   10. Simplified 54.1%

       \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   if 1.18e-45 < t < 2.1999999999999999e40 or 1.51999999999999993e63 < t < 8.8000000000000007e127

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 86.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 86.6%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.7%

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

      1. associate-*r* 44.7%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

      2. *-commutative 44.7%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      3. associate-*r* 44.7%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   7. Simplified 44.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-95}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+52} \lor \neg \left(a \leq -8.1 \cdot 10^{-112} \lor \neg \left(a \leq -2.2 \cdot 10^{-174}\right) \land a \leq 8.8 \cdot 10^{+39}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.8e+52)
         (not
          (or (<= a -8.1e-112) (and (not (<= a -2.2e-174)) (<= a 8.8e+39)))))
   (* 27.0 (* a b))
   (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.8e+52) || !((a <= -8.1e-112) || (!(a <= -2.2e-174) && (a <= 8.8e+39)))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((a <= (-6.8d+52)) .or. (.not. (a <= (-8.1d-112)) .or. (.not. (a <= (-2.2d-174))) .and. (a <= 8.8d+39))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.8e+52) || !((a <= -8.1e-112) || (!(a <= -2.2e-174) && (a <= 8.8e+39)))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.8e+52) or not ((a <= -8.1e-112) or (not (a <= -2.2e-174) and (a <= 8.8e+39))):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.8e+52) || !((a <= -8.1e-112) || (!(a <= -2.2e-174) && (a <= 8.8e+39))))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.8e+52) || ~(((a <= -8.1e-112) || (~((a <= -2.2e-174)) && (a <= 8.8e+39)))))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.8e+52], N[Not[Or[LessEqual[a, -8.1e-112], And[N[Not[LessEqual[a, -2.2e-174]], $MachinePrecision], LessEqual[a, 8.8e+39]]]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.8e52 or -8.10000000000000022e-112 < a < -2.20000000000000022e-174 or 8.8000000000000006e39 < a

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 91.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 91.3%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 56.4%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -6.8e52 < a < -8.10000000000000022e-112 or -2.20000000000000022e-174 < a < 8.8000000000000006e39

   1. Initial program 94.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.7%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.2%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+52} \lor \neg \left(a \leq -8.1 \cdot 10^{-112} \lor \neg \left(a \leq -2.2 \cdot 10^{-174}\right) \land a \leq 8.8 \cdot 10^{+39}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-111} \lor \neg \left(a \leq -2.2 \cdot 10^{-174}\right) \land a \leq 4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.4e+52)
   (* a (* 27.0 b))
   (if (or (<= a -2.55e-111) (and (not (<= a -2.2e-174)) (<= a 4e+39)))
     (* x 2.0)
     (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.4e+52) {
		tmp = a * (27.0 * b);
	} else if ((a <= -2.55e-111) || (!(a <= -2.2e-174) && (a <= 4e+39))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= (-1.4d+52)) then
        tmp = a * (27.0d0 * b)
    else if ((a <= (-2.55d-111)) .or. (.not. (a <= (-2.2d-174))) .and. (a <= 4d+39)) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.4e+52) {
		tmp = a * (27.0 * b);
	} else if ((a <= -2.55e-111) || (!(a <= -2.2e-174) && (a <= 4e+39))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.4e+52:
		tmp = a * (27.0 * b)
	elif (a <= -2.55e-111) or (not (a <= -2.2e-174) and (a <= 4e+39)):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.4e+52)
		tmp = Float64(a * Float64(27.0 * b));
	elseif ((a <= -2.55e-111) || (!(a <= -2.2e-174) && (a <= 4e+39)))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.4e+52)
		tmp = a * (27.0 * b);
	elseif ((a <= -2.55e-111) || (~((a <= -2.2e-174)) && (a <= 4e+39)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.4e+52], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -2.55e-111], And[N[Not[LessEqual[a, -2.2e-174]], $MachinePrecision], LessEqual[a, 4e+39]]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4e52

   1. Initial program 93.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 93.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 93.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 86.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 87.0%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 61.8%

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

      1. associate-*r* 61.9%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

      2. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      3. associate-*r* 61.9%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   if -1.4e52 < a < -2.55000000000000016e-111 or -2.20000000000000022e-174 < a < 3.99999999999999976e39

   1. Initial program 94.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.7%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.2%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2.55000000000000016e-111 < a < -2.20000000000000022e-174 or 3.99999999999999976e39 < a

   1. Initial program 95.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 95.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 93.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 93.9%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 53.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-111} \lor \neg \left(a \leq -2.2 \cdot 10^{-174}\right) \land a \leq 4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-112} \lor \neg \left(a \leq -2.2 \cdot 10^{-174}\right) \land a \leq 1.9 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.95e+51)
   (* a (* 27.0 b))
   (if (or (<= a -6.5e-112) (and (not (<= a -2.2e-174)) (<= a 1.9e+40)))
     (* x 2.0)
     (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.95e+51) {
		tmp = a * (27.0 * b);
	} else if ((a <= -6.5e-112) || (!(a <= -2.2e-174) && (a <= 1.9e+40))) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= (-2.95d+51)) then
        tmp = a * (27.0d0 * b)
    else if ((a <= (-6.5d-112)) .or. (.not. (a <= (-2.2d-174))) .and. (a <= 1.9d+40)) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.95e+51) {
		tmp = a * (27.0 * b);
	} else if ((a <= -6.5e-112) || (!(a <= -2.2e-174) && (a <= 1.9e+40))) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.95e+51:
		tmp = a * (27.0 * b)
	elif (a <= -6.5e-112) or (not (a <= -2.2e-174) and (a <= 1.9e+40)):
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.95e+51)
		tmp = Float64(a * Float64(27.0 * b));
	elseif ((a <= -6.5e-112) || (!(a <= -2.2e-174) && (a <= 1.9e+40)))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.95e+51)
		tmp = a * (27.0 * b);
	elseif ((a <= -6.5e-112) || (~((a <= -2.2e-174)) && (a <= 1.9e+40)))
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.95e+51], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -6.5e-112], And[N[Not[LessEqual[a, -2.2e-174]], $MachinePrecision], LessEqual[a, 1.9e+40]]], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.94999999999999991e51

   1. Initial program 93.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 93.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 93.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 86.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 87.0%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 61.8%

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

      1. associate-*r* 61.9%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

      2. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      3. associate-*r* 61.9%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   if -2.94999999999999991e51 < a < -6.49999999999999956e-112 or -2.20000000000000022e-174 < a < 1.90000000000000002e40

   1. Initial program 94.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.7%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.2%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -6.49999999999999956e-112 < a < -2.20000000000000022e-174 or 1.90000000000000002e40 < a

   1. Initial program 95.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 95.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 95.0%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 95.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 95.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   6. Step-by-step derivation

      1. +-commutative 95.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right)} \]

      2. associate-+r- 95.0%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t} \]

      3. associate-*l* 95.1%

         \[\leadsto \left(\color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t \]

      4. associate-*l* 92.7%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

      5. *-commutative 92.7%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(\color{blue}{\left(z \cdot 9\right)} \cdot t\right) \]

      6. associate-*l* 92.7%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(z \cdot \left(9 \cdot t\right)\right)} \]

   7. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)} \]

   8. Taylor expanded in a around inf 53.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. *-commutative 53.3%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} \]

      2. *-commutative 53.3%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot 27 \]

      3. associate-*l* 53.3%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot 27\right)} \]

      4. *-commutative 53.3%

         \[\leadsto b \cdot \color{blue}{\left(27 \cdot a\right)} \]

   10. Simplified 53.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-112} \lor \neg \left(a \leq -2.2 \cdot 10^{-174}\right) \land a \leq 1.9 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -1.32e-87)
     (+ (* y (* z (* t -9.0))) (* a (* 27.0 b)))
     (if (<= z 8e-6) (+ (* x 2.0) t_1) (- t_1 (* 9.0 (* t (* y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -1.32e-87) {
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	} else if (z <= 8e-6) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_1 - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (z <= (-1.32d-87)) then
        tmp = (y * (z * (t * (-9.0d0)))) + (a * (27.0d0 * b))
    else if (z <= 8d-6) then
        tmp = (x * 2.0d0) + t_1
    else
        tmp = t_1 - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -1.32e-87) {
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	} else if (z <= 8e-6) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_1 - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if z <= -1.32e-87:
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b))
	elif z <= 8e-6:
		tmp = (x * 2.0) + t_1
	else:
		tmp = t_1 - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -1.32e-87)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(a * Float64(27.0 * b)));
	elseif (z <= 8e-6)
		tmp = Float64(Float64(x * 2.0) + t_1);
	else
		tmp = Float64(t_1 - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -1.32e-87)
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	elseif (z <= 8e-6)
		tmp = (x * 2.0) + t_1;
	else
		tmp = t_1 - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e-87], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-6], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999997e-87

   1. Initial program 88.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 88.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 88.7%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 88.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 88.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Taylor expanded in x around 0 67.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. *-commutative 67.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 67.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

   8. Simplified 67.1%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 40.5%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 40.0%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 40.0%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. associate-*l* 40.9%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(z \cdot t\right)}\right)} - 1\right) \]

   10. Applied egg-rr 40.9%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 41.4%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

       2. expm1-log1p 71.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

       3. *-commutative 71.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \]

       4. associate-*l* 74.7%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   12. Simplified 74.7%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]
   13. Step-by-step derivation

       1. sub-neg 74.7%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]

       2. associate-*r* 74.7%

          \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       3. *-commutative 74.7%

          \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       4. associate-*r* 74.6%

          \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       5. +-commutative 74.6%

          \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

       6. distribute-lft-neg-in 74.6%

          \[\leadsto \color{blue}{\left(-9\right) \cdot \left(z \cdot \left(t \cdot y\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

       7. metadata-eval 74.6%

          \[\leadsto \color{blue}{-9} \cdot \left(z \cdot \left(t \cdot y\right)\right) + 27 \cdot \left(a \cdot b\right) \]

       8. associate-*r* 71.0%

          \[\leadsto -9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} + 27 \cdot \left(a \cdot b\right) \]

       9. associate-*r* 71.0%

          \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot t\right)\right) \cdot y} + 27 \cdot \left(a \cdot b\right) \]

       10. *-commutative 71.0%

           \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right)} \cdot y + 27 \cdot \left(a \cdot b\right) \]

       11. associate-*r* 71.0%

           \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y + 27 \cdot \left(a \cdot b\right) \]

       12. *-commutative 71.0%

           \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

       13. associate-*r* 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{\left(27 \cdot a\right) \cdot b} \]

       14. *-commutative 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

       15. associate-*r* 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   14. Applied egg-rr 71.1%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)} \]

   if -1.31999999999999997e-87 < z < 7.99999999999999964e-6

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 7.99999999999999964e-6 < z

   1. Initial program 95.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 95.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 86.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 86.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -1.32e-87)
     (+ (* y (* z (* t -9.0))) t_1)
     (if (<= z 2.3e-6)
       (+ (* x 2.0) (* 27.0 (* a b)))
       (- t_1 (* t (* y (* 9.0 z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.32e-87) {
		tmp = (y * (z * (t * -9.0))) + t_1;
	} else if (z <= 2.3e-6) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t_1 - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-1.32d-87)) then
        tmp = (y * (z * (t * (-9.0d0)))) + t_1
    else if (z <= 2.3d-6) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t_1 - (t * (y * (9.0d0 * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.32e-87) {
		tmp = (y * (z * (t * -9.0))) + t_1;
	} else if (z <= 2.3e-6) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t_1 - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -1.32e-87:
		tmp = (y * (z * (t * -9.0))) + t_1
	elif z <= 2.3e-6:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t_1 - (t * (y * (9.0 * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1.32e-87)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + t_1);
	elseif (z <= 2.3e-6)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(t_1 - Float64(t * Float64(y * Float64(9.0 * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1.32e-87)
		tmp = (y * (z * (t * -9.0))) + t_1;
	elseif (z <= 2.3e-6)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = t_1 - (t * (y * (9.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e-87], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 2.3e-6], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999997e-87

   1. Initial program 88.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 88.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 88.7%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 88.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 88.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Taylor expanded in x around 0 67.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. *-commutative 67.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 67.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

   8. Simplified 67.1%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 40.5%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 40.0%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 40.0%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. associate-*l* 40.9%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(z \cdot t\right)}\right)} - 1\right) \]

   10. Applied egg-rr 40.9%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 41.4%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

       2. expm1-log1p 71.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

       3. *-commutative 71.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \]

       4. associate-*l* 74.7%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   12. Simplified 74.7%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]
   13. Step-by-step derivation

       1. sub-neg 74.7%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]

       2. associate-*r* 74.7%

          \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       3. *-commutative 74.7%

          \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       4. associate-*r* 74.6%

          \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       5. +-commutative 74.6%

          \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

       6. distribute-lft-neg-in 74.6%

          \[\leadsto \color{blue}{\left(-9\right) \cdot \left(z \cdot \left(t \cdot y\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

       7. metadata-eval 74.6%

          \[\leadsto \color{blue}{-9} \cdot \left(z \cdot \left(t \cdot y\right)\right) + 27 \cdot \left(a \cdot b\right) \]

       8. associate-*r* 71.0%

          \[\leadsto -9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} + 27 \cdot \left(a \cdot b\right) \]

       9. associate-*r* 71.0%

          \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot t\right)\right) \cdot y} + 27 \cdot \left(a \cdot b\right) \]

       10. *-commutative 71.0%

           \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right)} \cdot y + 27 \cdot \left(a \cdot b\right) \]

       11. associate-*r* 71.0%

           \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y + 27 \cdot \left(a \cdot b\right) \]

       12. *-commutative 71.0%

           \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

       13. associate-*r* 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{\left(27 \cdot a\right) \cdot b} \]

       14. *-commutative 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

       15. associate-*r* 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   14. Applied egg-rr 71.1%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)} \]

   if -1.31999999999999997e-87 < z < 2.3e-6

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 2.3e-6 < z

   1. Initial program 95.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 95.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 95.0%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 95.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 95.1%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 84.1%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. *-commutative 84.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 84.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

   8. Simplified 84.1%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 58.7%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 57.1%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 57.1%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. associate-*l* 52.8%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(z \cdot t\right)}\right)} - 1\right) \]

   10. Applied egg-rr 52.8%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 54.4%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

       2. expm1-log1p 75.8%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

       3. *-commutative 75.8%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \]

       4. associate-*l* 87.2%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   12. Simplified 87.2%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   13. Taylor expanded in z around 0 84.1%

       \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 84.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 9} \]

       2. associate-*l* 84.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 9\right)} \]

       3. associate-*r* 84.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - t \cdot \color{blue}{\left(y \cdot \left(z \cdot 9\right)\right)} \]

   15. Simplified 84.1%

       \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{t \cdot \left(y \cdot \left(z \cdot 9\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq 6 \cdot 10^{+62}:\\ \;\;\;\;t_1 + \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z 6e+62)
     (+ t_1 (+ (* y (* z (* t -9.0))) (* x 2.0)))
     (- t_1 (* t (* y (* 9.0 z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= 6e+62) {
		tmp = t_1 + ((y * (z * (t * -9.0))) + (x * 2.0));
	} else {
		tmp = t_1 - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= 6d+62) then
        tmp = t_1 + ((y * (z * (t * (-9.0d0)))) + (x * 2.0d0))
    else
        tmp = t_1 - (t * (y * (9.0d0 * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= 6e+62) {
		tmp = t_1 + ((y * (z * (t * -9.0))) + (x * 2.0));
	} else {
		tmp = t_1 - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= 6e+62:
		tmp = t_1 + ((y * (z * (t * -9.0))) + (x * 2.0))
	else:
		tmp = t_1 - (t * (y * (9.0 * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= 6e+62)
		tmp = Float64(t_1 + Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0)));
	else
		tmp = Float64(t_1 - Float64(t * Float64(y * Float64(9.0 * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= 6e+62)
		tmp = t_1 + ((y * (z * (t * -9.0))) + (x * 2.0));
	else
		tmp = t_1 - (t * (y * (9.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 6e+62], N[(t$95$1 + N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 6e62

   1. Initial program 94.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.0%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. sub-neg 97.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

      2. *-commutative 97.0%

         \[\leadsto \left(x \cdot 2 + \left(-\color{blue}{\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      3. distribute-rgt-neg-in 97.0%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot t\right) \cdot \left(-y \cdot 9\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      4. *-commutative 97.0%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(-\color{blue}{9 \cdot y}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      5. distribute-lft-neg-in 97.0%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \color{blue}{\left(\left(-9\right) \cdot y\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      6. metadata-eval 97.0%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(\color{blue}{-9} \cdot y\right)\right) + a \cdot \left(27 \cdot b\right) \]

      7. associate-*l* 97.0%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right) \cdot y}\right) + a \cdot \left(27 \cdot b\right) \]

      8. associate-*r* 97.0%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y\right) + a \cdot \left(27 \cdot b\right) \]

      9. *-commutative 97.0%

         \[\leadsto \left(x \cdot 2 + \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right) + a \cdot \left(27 \cdot b\right) \]

   6. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\left(x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

   if 6e62 < z

   1. Initial program 94.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 94.1%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 94.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 94.1%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 94.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 94.1%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Taylor expanded in x around 0 85.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 85.0%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. *-commutative 85.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 85.0%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

   8. Simplified 85.0%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 56.7%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 54.7%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 54.7%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. associate-*l* 49.5%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(z \cdot t\right)}\right)} - 1\right) \]

   10. Applied egg-rr 49.5%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 51.5%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

       2. expm1-log1p 75.0%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

       3. *-commutative 75.0%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \]

       4. associate-*l* 88.7%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   12. Simplified 88.7%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   13. Taylor expanded in z around 0 85.0%

       \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 85.0%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 9} \]

       2. associate-*l* 85.0%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 9\right)} \]

       3. associate-*r* 85.0%

          \[\leadsto a \cdot \left(27 \cdot b\right) - t \cdot \color{blue}{\left(y \cdot \left(z \cdot 9\right)\right)} \]

   15. Simplified 85.0%

       \[\leadsto a \cdot \left(27 \cdot b\right) - \color{blue}{t \cdot \left(y \cdot \left(z \cdot 9\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e-209)
   (+ (* a (* 27.0 b)) (+ (* y (* z (* t -9.0))) (* x 2.0)))
   (+ (- (* x 2.0) (* t (* y (* 9.0 z)))) (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e-209) {
		tmp = (a * (27.0 * b)) + ((y * (z * (t * -9.0))) + (x * 2.0));
	} else {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-2d-209)) then
        tmp = (a * (27.0d0 * b)) + ((y * (z * (t * (-9.0d0)))) + (x * 2.0d0))
    else
        tmp = ((x * 2.0d0) - (t * (y * (9.0d0 * z)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e-209) {
		tmp = (a * (27.0 * b)) + ((y * (z * (t * -9.0))) + (x * 2.0));
	} else {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2e-209:
		tmp = (a * (27.0 * b)) + ((y * (z * (t * -9.0))) + (x * 2.0))
	else:
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e-209)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2e-209)
		tmp = (a * (27.0 * b)) + ((y * (z * (t * -9.0))) + (x * 2.0));
	else
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2e-209], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-209

   1. Initial program 90.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 90.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 90.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 94.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 94.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. sub-neg 94.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

      2. *-commutative 94.8%

         \[\leadsto \left(x \cdot 2 + \left(-\color{blue}{\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      3. distribute-rgt-neg-in 94.8%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot t\right) \cdot \left(-y \cdot 9\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      4. *-commutative 94.8%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(-\color{blue}{9 \cdot y}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      5. distribute-lft-neg-in 94.8%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \color{blue}{\left(\left(-9\right) \cdot y\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      6. metadata-eval 94.8%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(\color{blue}{-9} \cdot y\right)\right) + a \cdot \left(27 \cdot b\right) \]

      7. associate-*l* 94.8%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right) \cdot y}\right) + a \cdot \left(27 \cdot b\right) \]

      8. associate-*r* 94.8%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y\right) + a \cdot \left(27 \cdot b\right) \]

      9. *-commutative 94.8%

         \[\leadsto \left(x \cdot 2 + \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right) + a \cdot \left(27 \cdot b\right) \]

   6. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

   if -2.0000000000000001e-209 < z

   1. Initial program 97.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.8%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 97.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 97.8%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 97.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 97.8%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.5e+24)
   (+ (* y (* z (* t -9.0))) (* x 2.0))
   (if (<= z 1.75e-44)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (- (* x 2.0) (* 9.0 (* t (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+24) {
		tmp = (y * (z * (t * -9.0))) + (x * 2.0);
	} else if (z <= 1.75e-44) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-2.5d+24)) then
        tmp = (y * (z * (t * (-9.0d0)))) + (x * 2.0d0)
    else if (z <= 1.75d-44) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+24) {
		tmp = (y * (z * (t * -9.0))) + (x * 2.0);
	} else if (z <= 1.75e-44) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.5e+24:
		tmp = (y * (z * (t * -9.0))) + (x * 2.0)
	elif z <= 1.75e-44:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.5e+24)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0));
	elseif (z <= 1.75e-44)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.5e+24)
		tmp = (y * (z * (t * -9.0))) + (x * 2.0);
	elseif (z <= 1.75e-44)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.5e+24], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-44], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000023e24

   1. Initial program 84.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 84.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 84.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 91.2%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 91.3%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 64.8%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto \color{blue}{x \cdot 2} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. sub-neg 64.8%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      3. +-commutative 64.8%

         \[\leadsto \color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + x \cdot 2} \]

      4. *-commutative 64.8%

         \[\leadsto \left(-\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 9}\right) + x \cdot 2 \]

      5. distribute-rgt-neg-in 64.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot \left(-9\right)} + x \cdot 2 \]

      6. *-commutative 64.8%

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot \left(-9\right) + x \cdot 2 \]

      7. metadata-eval 64.8%

         \[\leadsto \left(\left(y \cdot z\right) \cdot t\right) \cdot \color{blue}{-9} + x \cdot 2 \]

      8. associate-*r* 64.8%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)} + x \cdot 2 \]

      9. associate-*l* 72.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} + x \cdot 2 \]

   7. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2} \]

   if -2.50000000000000023e24 < z < 1.7499999999999999e-44

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.8%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 1.7499999999999999e-44 < z

   1. Initial program 95.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 95.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 88.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 88.9%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 58.2%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e-88)
   (+ (* y (* z (* t -9.0))) (* a (* 27.0 b)))
   (if (<= z 1.9e-44)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (- (* x 2.0) (* 9.0 (* t (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e-88) {
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	} else if (z <= 1.9e-44) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-4.2d-88)) then
        tmp = (y * (z * (t * (-9.0d0)))) + (a * (27.0d0 * b))
    else if (z <= 1.9d-44) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e-88) {
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	} else if (z <= 1.9e-44) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.2e-88:
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b))
	elif z <= 1.9e-44:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e-88)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(a * Float64(27.0 * b)));
	elseif (z <= 1.9e-44)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.2e-88)
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	elseif (z <= 1.9e-44)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e-88], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-44], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1999999999999999e-88

   1. Initial program 88.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 88.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 88.7%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 88.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 88.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Taylor expanded in x around 0 67.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. *-commutative 67.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 67.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

   8. Simplified 67.1%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 40.5%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 40.0%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 40.0%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. associate-*l* 40.9%

         \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(z \cdot t\right)}\right)} - 1\right) \]

   10. Applied egg-rr 40.9%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 41.4%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

       2. expm1-log1p 71.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

       3. *-commutative 71.1%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \]

       4. associate-*l* 74.7%

          \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   12. Simplified 74.7%

       \[\leadsto a \cdot \left(27 \cdot b\right) - 9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]
   13. Step-by-step derivation

       1. sub-neg 74.7%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]

       2. associate-*r* 74.7%

          \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       3. *-commutative 74.7%

          \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       4. associate-*r* 74.6%

          \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \]

       5. +-commutative 74.6%

          \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

       6. distribute-lft-neg-in 74.6%

          \[\leadsto \color{blue}{\left(-9\right) \cdot \left(z \cdot \left(t \cdot y\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

       7. metadata-eval 74.6%

          \[\leadsto \color{blue}{-9} \cdot \left(z \cdot \left(t \cdot y\right)\right) + 27 \cdot \left(a \cdot b\right) \]

       8. associate-*r* 71.0%

          \[\leadsto -9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} + 27 \cdot \left(a \cdot b\right) \]

       9. associate-*r* 71.0%

          \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot t\right)\right) \cdot y} + 27 \cdot \left(a \cdot b\right) \]

       10. *-commutative 71.0%

           \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right)} \cdot y + 27 \cdot \left(a \cdot b\right) \]

       11. associate-*r* 71.0%

           \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y + 27 \cdot \left(a \cdot b\right) \]

       12. *-commutative 71.0%

           \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

       13. associate-*r* 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{\left(27 \cdot a\right) \cdot b} \]

       14. *-commutative 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

       15. associate-*r* 71.1%

           \[\leadsto y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   14. Applied egg-rr 71.1%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)} \]

   if -4.1999999999999999e-88 < z < 1.9e-44

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 86.3%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 1.9e-44 < z

   1. Initial program 95.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 95.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 88.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 88.9%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 58.2%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 10^{+63}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e+30)
   (* y (* -9.0 (* z t)))
   (if (<= z 1e+63) (+ (* x 2.0) (* 27.0 (* a b))) (* (* z -9.0) (* y t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+30) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1e+63) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-6.5d+30)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= 1d+63) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+30) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1e+63) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e+30:
		tmp = y * (-9.0 * (z * t))
	elif z <= 1e+63:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e+30)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= 1e+63)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.5e+30)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= 1e+63)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e+30], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+63], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e30

   1. Initial program 84.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.1%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. associate-*r* 84.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 84.1%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 84.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Simplified 84.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   6. Step-by-step derivation

      1. +-commutative 84.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right)} \]

      2. associate-+r- 84.0%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t} \]

      3. associate-*l* 84.0%

         \[\leadsto \left(\color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t \]

      4. associate-*l* 91.1%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

      5. *-commutative 91.1%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(\color{blue}{\left(z \cdot 9\right)} \cdot t\right) \]

      6. associate-*l* 91.1%

         \[\leadsto \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(z \cdot \left(9 \cdot t\right)\right)} \]

   7. Applied egg-rr 91.1%

      \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)} \]

   8. Taylor expanded in y around inf 47.1%

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

      1. associate-*r* 47.1%

         \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} \]

      2. metadata-eval 47.1%

         \[\leadsto \left(\color{blue}{\left(-9\right)} \cdot t\right) \cdot \left(y \cdot z\right) \]

      3. distribute-lft-neg-in 47.1%

         \[\leadsto \color{blue}{\left(-9 \cdot t\right)} \cdot \left(y \cdot z\right) \]

      4. *-commutative 47.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(-9 \cdot t\right)} \]

      5. associate-*r* 53.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)} \]

      6. *-commutative 53.9%

         \[\leadsto y \cdot \left(z \cdot \left(-\color{blue}{t \cdot 9}\right)\right) \]

      7. distribute-rgt-neg-in 53.9%

         \[\leadsto y \cdot \left(z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right) \]

      8. metadata-eval 53.9%

         \[\leadsto y \cdot \left(z \cdot \left(t \cdot \color{blue}{-9}\right)\right) \]

   10. Simplified 53.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

   11. Taylor expanded in z around 0 53.9%

       \[\leadsto y \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right)\right)} \]

   if -6.5e30 < z < 1.00000000000000006e63

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.9%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 1.00000000000000006e63 < z

   1. Initial program 94.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 84.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 84.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 46.7%

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

      1. associate-*r* 46.7%

         \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} \]

      2. *-commutative 46.7%

         \[\leadsto \color{blue}{\left(t \cdot -9\right)} \cdot \left(y \cdot z\right) \]

   7. Simplified 46.7%

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

      1. add-sqr-sqrt 25.6%

         \[\leadsto \color{blue}{\sqrt{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)} \cdot \sqrt{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)}} \]

      2. pow2 25.6%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)}\right)}^{2}} \]

      3. *-commutative 25.6%

         \[\leadsto {\left(\sqrt{\color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)}}\right)}^{2} \]

      4. associate-*l* 25.5%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}}\right)}^{2} \]

   9. Applied egg-rr 25.5%

      \[\leadsto \color{blue}{{\left(\sqrt{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right)}^{2}} \]
   10. Step-by-step derivation

       1. unpow2 25.5%

          \[\leadsto \color{blue}{\sqrt{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \cdot \sqrt{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}} \]

       2. add-sqr-sqrt 42.7%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

       3. associate-*r* 42.7%

          \[\leadsto y \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right)} \]

       4. associate-*r* 42.6%

          \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot t\right)\right) \cdot -9} \]

       5. *-commutative 42.6%

          \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \cdot -9 \]

       6. associate-*r* 50.4%

          \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \cdot -9 \]

       7. *-commutative 50.4%

          \[\leadsto \color{blue}{-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)} \]

       8. associate-*r* 50.4%

          \[\leadsto \color{blue}{\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)} \]

       9. *-commutative 50.4%

          \[\leadsto \left(-9 \cdot z\right) \cdot \color{blue}{\left(y \cdot t\right)} \]

   11. Applied egg-rr 50.4%

       \[\leadsto \color{blue}{\left(-9 \cdot z\right) \cdot \left(y \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 10^{+63}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.8e+27)
   (+ (* y (* z (* t -9.0))) (* x 2.0))
   (if (<= z 1.7e+63) (+ (* x 2.0) (* 27.0 (* a b))) (* (* z -9.0) (* y t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e+27) {
		tmp = (y * (z * (t * -9.0))) + (x * 2.0);
	} else if (z <= 1.7e+63) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-5.8d+27)) then
        tmp = (y * (z * (t * (-9.0d0)))) + (x * 2.0d0)
    else if (z <= 1.7d+63) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e+27) {
		tmp = (y * (z * (t * -9.0))) + (x * 2.0);
	} else if (z <= 1.7e+63) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.8e+27:
		tmp = (y * (z * (t * -9.0))) + (x * 2.0)
	elif z <= 1.7e+63:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.8e+27)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0));
	elseif (z <= 1.7e+63)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.8e+27)
		tmp = (y * (z * (t * -9.0))) + (x * 2.0);
	elseif (z <= 1.7e+63)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.8e+27], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+63], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000002e27

   1. Initial program 84.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 84.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 84.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 91.2%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 91.3%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 64.8%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto \color{blue}{x \cdot 2} - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      2. sub-neg 64.8%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      3. +-commutative 64.8%

         \[\leadsto \color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + x \cdot 2} \]

      4. *-commutative 64.8%

         \[\leadsto \left(-\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 9}\right) + x \cdot 2 \]

      5. distribute-rgt-neg-in 64.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot \left(-9\right)} + x \cdot 2 \]

      6. *-commutative 64.8%

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot \left(-9\right) + x \cdot 2 \]

      7. metadata-eval 64.8%

         \[\leadsto \left(\left(y \cdot z\right) \cdot t\right) \cdot \color{blue}{-9} + x \cdot 2 \]

      8. associate-*r* 64.8%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)} + x \cdot 2 \]

      9. associate-*l* 72.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} + x \cdot 2 \]

   7. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2} \]

   if -5.8000000000000002e27 < z < 1.6999999999999999e63

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 1.6999999999999999e63 < z

   1. Initial program 94.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 84.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 84.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 46.7%

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

      1. associate-*r* 46.7%

         \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} \]

      2. *-commutative 46.7%

         \[\leadsto \color{blue}{\left(t \cdot -9\right)} \cdot \left(y \cdot z\right) \]

   7. Simplified 46.7%

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

      1. add-sqr-sqrt 25.6%

         \[\leadsto \color{blue}{\sqrt{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)} \cdot \sqrt{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)}} \]

      2. pow2 25.6%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)}\right)}^{2}} \]

      3. *-commutative 25.6%

         \[\leadsto {\left(\sqrt{\color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)}}\right)}^{2} \]

      4. associate-*l* 25.5%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}}\right)}^{2} \]

   9. Applied egg-rr 25.5%

      \[\leadsto \color{blue}{{\left(\sqrt{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right)}^{2}} \]
   10. Step-by-step derivation

       1. unpow2 25.5%

          \[\leadsto \color{blue}{\sqrt{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \cdot \sqrt{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}} \]

       2. add-sqr-sqrt 42.7%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

       3. associate-*r* 42.7%

          \[\leadsto y \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right)} \]

       4. associate-*r* 42.6%

          \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot t\right)\right) \cdot -9} \]

       5. *-commutative 42.6%

          \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot y\right)} \cdot -9 \]

       6. associate-*r* 50.4%

          \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \cdot -9 \]

       7. *-commutative 50.4%

          \[\leadsto \color{blue}{-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)} \]

       8. associate-*r* 50.4%

          \[\leadsto \color{blue}{\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)} \]

       9. *-commutative 50.4%

          \[\leadsto \left(-9 \cdot z\right) \cdot \color{blue}{\left(y \cdot t\right)} \]

   11. Applied egg-rr 50.4%

       \[\leadsto \color{blue}{\left(-9 \cdot z\right) \cdot \left(y \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.4% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg 94.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

   2. sub-neg 94.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

   3. associate-*l* 94.5%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   4. associate-*l* 94.5%

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

3. Simplified 94.5%

   \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 30.8%

   \[\leadsto \color{blue}{2 \cdot x} \]

6. Final simplification 30.8%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer target: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024011 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))