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

Percentage Accurate: 95.5% → 96.7%

Time: 17.8s

Alternatives: 14

Speedup: 1.0×

• 28.4% 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: 95.5% 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: 96.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	return fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(-9.0 * z)))))
end

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. +-commutative 93.9%

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

   2. associate-+r- 93.9%

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

   3. cancel-sign-sub-inv 93.9%

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

   4. *-commutative 93.9%

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

   5. distribute-rgt-neg-out 93.9%

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

   6. associate-*r* 96.5%

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

   7. *-commutative 96.5%

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

   8. distribute-rgt-neg-in 96.5%

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

   9. associate-+r+ 96.5%

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

   10. sub-neg 96.5%

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

   11. associate-*l* 96.5%

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

   12. fma-def 96.9%

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

   13. fma-neg 96.9%

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

   14. associate-*l* 96.9%

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

   15. *-commutative 96.9%

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

   16. associate-*r* 96.5%

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

   17. distribute-rgt-neg-in 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+145}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t_1\\ \mathbf{elif}\;t_2 \leq 10^{-58}:\\ \;\;\;\;x \cdot 2 - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(a \cdot b\right)\right) \cdot 3 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y (* t z)))) (t_2 (* b (* a 27.0))))
   (if (<= t_2 -2e+145)
     (- (* 27.0 (* a b)) t_1)
     (if (<= t_2 1e-58) (- (* x 2.0) t_1) (- (* (* 9.0 (* a b)) 3.0) t_1)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (t * z));
	double t_2 = b * (a * 27.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = (27.0 * (a * b)) - t_1;
	} else if (t_2 <= 1e-58) {
		tmp = (x * 2.0) - t_1;
	} else {
		tmp = ((9.0 * (a * b)) * 3.0) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 = 9.0d0 * (y * (t * z))
    t_2 = b * (a * 27.0d0)
    if (t_2 <= (-2d+145)) then
        tmp = (27.0d0 * (a * b)) - t_1
    else if (t_2 <= 1d-58) then
        tmp = (x * 2.0d0) - t_1
    else
        tmp = ((9.0d0 * (a * b)) * 3.0d0) - t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (t * z));
	double t_2 = b * (a * 27.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = (27.0 * (a * b)) - t_1;
	} else if (t_2 <= 1e-58) {
		tmp = (x * 2.0) - t_1;
	} else {
		tmp = ((9.0 * (a * b)) * 3.0) - t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (y * (t * z))
	t_2 = b * (a * 27.0)
	tmp = 0
	if t_2 <= -2e+145:
		tmp = (27.0 * (a * b)) - t_1
	elif t_2 <= 1e-58:
		tmp = (x * 2.0) - t_1
	else:
		tmp = ((9.0 * (a * b)) * 3.0) - t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(y * Float64(t * z)))
	t_2 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_2 <= -2e+145)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - t_1);
	elseif (t_2 <= 1e-58)
		tmp = Float64(Float64(x * 2.0) - t_1);
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(a * b)) * 3.0) - t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (y * (t * z));
	t_2 = b * (a * 27.0);
	tmp = 0.0;
	if (t_2 <= -2e+145)
		tmp = (27.0 * (a * b)) - t_1;
	elseif (t_2 <= 1e-58)
		tmp = (x * 2.0) - t_1;
	else
		tmp = ((9.0 * (a * b)) * 3.0) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+145], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e-58], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(9.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -2e145

   1. Initial program 87.4%

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

      1. sub-neg 87.4%

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

      2. distribute-lft-neg-in 87.4%

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

      3. associate-*l* 87.4%

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

      4. *-commutative 87.4%

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

      5. *-commutative 87.4%

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

      6. cancel-sign-sub-inv 87.4%

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

      7. *-commutative 87.4%

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

      8. *-commutative 87.4%

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

      9. associate-*l* 87.4%

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

      10. associate-*l* 89.9%

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

      11. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 85.1%

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

   if -2e145 < (*.f64 (*.f64 a 27) b) < 1e-58

   1. Initial program 93.9%

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

      1. sub-neg 93.9%

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

      2. distribute-lft-neg-in 93.9%

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

      3. associate-*l* 93.9%

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

      4. *-commutative 93.9%

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

      5. *-commutative 93.9%

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

      6. cancel-sign-sub-inv 93.9%

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

      7. *-commutative 93.9%

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

      8. *-commutative 93.9%

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

      9. associate-*l* 93.9%

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

      10. associate-*l* 98.4%

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

      11. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in a around 0 85.5%

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

   if 1e-58 < (*.f64 (*.f64 a 27) b)

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. distribute-lft-neg-in 97.2%

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

      3. associate-*l* 97.3%

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

      4. *-commutative 97.3%

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

      5. *-commutative 97.3%

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

      6. cancel-sign-sub-inv 97.3%

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

      7. *-commutative 97.3%

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

      8. *-commutative 97.3%

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

      9. associate-*l* 97.2%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around 0 87.6%

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

      1. add-cbrt-cube 56.0%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      2. pow3 56.0%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(27 \cdot \left(a \cdot b\right)\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      3. unpow-prod-down 56.0%

         \[\leadsto \sqrt[3]{\color{blue}{{27}^{3} \cdot {\left(a \cdot b\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      4. metadata-eval 56.0%

         \[\leadsto \sqrt[3]{\color{blue}{19683} \cdot {\left(a \cdot b\right)}^{3}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

   6. Applied egg-rr 56.0%

      \[\leadsto \color{blue}{\sqrt[3]{19683 \cdot {\left(a \cdot b\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

   8. Applied egg-rr 87.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+145}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-58}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(a \cdot b\right)\right) \cdot 3 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 3: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+145}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t_1\\ \mathbf{elif}\;t_2 \leq 10^{-58}:\\ \;\;\;\;x \cdot 2 - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y (* t z)))) (t_2 (* b (* a 27.0))))
   (if (<= t_2 -2e+145)
     (- (* 27.0 (* a b)) t_1)
     (if (<= t_2 1e-58) (- (* x 2.0) t_1) (- t_2 t_1)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (t * z));
	double t_2 = b * (a * 27.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = (27.0 * (a * b)) - t_1;
	} else if (t_2 <= 1e-58) {
		tmp = (x * 2.0) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 = 9.0d0 * (y * (t * z))
    t_2 = b * (a * 27.0d0)
    if (t_2 <= (-2d+145)) then
        tmp = (27.0d0 * (a * b)) - t_1
    else if (t_2 <= 1d-58) then
        tmp = (x * 2.0d0) - t_1
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (t * z));
	double t_2 = b * (a * 27.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = (27.0 * (a * b)) - t_1;
	} else if (t_2 <= 1e-58) {
		tmp = (x * 2.0) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (y * (t * z))
	t_2 = b * (a * 27.0)
	tmp = 0
	if t_2 <= -2e+145:
		tmp = (27.0 * (a * b)) - t_1
	elif t_2 <= 1e-58:
		tmp = (x * 2.0) - t_1
	else:
		tmp = t_2 - t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(y * Float64(t * z)))
	t_2 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_2 <= -2e+145)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - t_1);
	elseif (t_2 <= 1e-58)
		tmp = Float64(Float64(x * 2.0) - t_1);
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (y * (t * z));
	t_2 = b * (a * 27.0);
	tmp = 0.0;
	if (t_2 <= -2e+145)
		tmp = (27.0 * (a * b)) - t_1;
	elseif (t_2 <= 1e-58)
		tmp = (x * 2.0) - t_1;
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+145], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e-58], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -2e145

   1. Initial program 87.4%

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

      1. sub-neg 87.4%

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

      2. distribute-lft-neg-in 87.4%

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

      3. associate-*l* 87.4%

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

      4. *-commutative 87.4%

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

      5. *-commutative 87.4%

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

      6. cancel-sign-sub-inv 87.4%

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

      7. *-commutative 87.4%

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

      8. *-commutative 87.4%

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

      9. associate-*l* 87.4%

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

      10. associate-*l* 89.9%

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

      11. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 85.1%

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

   if -2e145 < (*.f64 (*.f64 a 27) b) < 1e-58

   1. Initial program 93.9%

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

      1. sub-neg 93.9%

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

      2. distribute-lft-neg-in 93.9%

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

      3. associate-*l* 93.9%

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

      4. *-commutative 93.9%

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

      5. *-commutative 93.9%

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

      6. cancel-sign-sub-inv 93.9%

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

      7. *-commutative 93.9%

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

      8. *-commutative 93.9%

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

      9. associate-*l* 93.9%

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

      10. associate-*l* 98.4%

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

      11. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in a around 0 85.5%

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

   if 1e-58 < (*.f64 (*.f64 a 27) b)

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. distribute-lft-neg-in 97.2%

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

      3. associate-*l* 97.3%

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

      4. *-commutative 97.3%

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

      5. *-commutative 97.3%

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

      6. cancel-sign-sub-inv 97.3%

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

      7. *-commutative 97.3%

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

      8. *-commutative 97.3%

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

      9. associate-*l* 97.2%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around 0 87.6%

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

      1. add-cbrt-cube 56.0%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      2. pow3 56.0%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(27 \cdot \left(a \cdot b\right)\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      3. unpow-prod-down 56.0%

         \[\leadsto \sqrt[3]{\color{blue}{{27}^{3} \cdot {\left(a \cdot b\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      4. metadata-eval 56.0%

         \[\leadsto \sqrt[3]{\color{blue}{19683} \cdot {\left(a \cdot b\right)}^{3}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

   6. Applied egg-rr 56.0%

      \[\leadsto \color{blue}{\sqrt[3]{19683 \cdot {\left(a \cdot b\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

   8. Applied egg-rr 87.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+145}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-58}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+35)
   (- (* 27.0 (* a b)) (* 9.0 (* y (* t z))))
   (+ (- (* x 2.0) (* t (* 9.0 (* y z)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+35) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (t * z)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 <= (-8.5d+35)) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (t * z)))
    else
        tmp = ((x * 2.0d0) - (t * (9.0d0 * (y * z)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+35) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (t * z)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e+35:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (t * z)))
	else:
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+35)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(t * z))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e+35)
		tmp = (27.0 * (a * b)) - (9.0 * (y * (t * z)));
	else
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+35], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999995e35

   1. Initial program 87.2%

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

      1. sub-neg 87.2%

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

      2. distribute-lft-neg-in 87.2%

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

      3. associate-*l* 87.2%

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

      4. *-commutative 87.2%

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

      5. *-commutative 87.2%

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

      6. cancel-sign-sub-inv 87.2%

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

      7. *-commutative 87.2%

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

      8. *-commutative 87.2%

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

      9. associate-*l* 87.2%

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

      10. associate-*l* 94.8%

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

      11. 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. Taylor expanded in x around 0 75.7%

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

   if -8.4999999999999995e35 < z

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 96.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 5: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-87} \lor \neg \left(z \leq 6 \cdot 10^{-65}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e-87) (not (<= z 6e-65)))
   (+ (* a (* 27.0 b)) (* z (* -9.0 (* y t))))
   (+ (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-87) || !(z <= 6e-65)) {
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	} else {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 <= (-8.5d-87)) .or. (.not. (z <= 6d-65))) then
        tmp = (a * (27.0d0 * b)) + (z * ((-9.0d0) * (y * t)))
    else
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-87) || !(z <= 6e-65)) {
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	} else {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e-87) or not (z <= 6e-65):
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)))
	else:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e-87) || !(z <= 6e-65))
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(z * Float64(-9.0 * Float64(y * t))));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e-87) || ~((z <= 6e-65)))
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	else
		tmp = (27.0 * (a * b)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e-87], N[Not[LessEqual[z, 6e-65]], $MachinePrecision]], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e-87 or 5.99999999999999996e-65 < z

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. distribute-lft-neg-in 92.4%

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

      3. associate-*l* 92.4%

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

      4. *-commutative 92.4%

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

      5. *-commutative 92.4%

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

      6. cancel-sign-sub-inv 92.4%

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

      7. *-commutative 92.4%

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

      8. *-commutative 92.4%

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

      9. associate-*l* 92.4%

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

      10. associate-*l* 94.9%

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

      11. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around 0 78.2%

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

      1. add-cbrt-cube 56.2%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      2. pow3 56.2%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(27 \cdot \left(a \cdot b\right)\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      3. unpow-prod-down 56.2%

         \[\leadsto \sqrt[3]{\color{blue}{{27}^{3} \cdot {\left(a \cdot b\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      4. metadata-eval 56.2%

         \[\leadsto \sqrt[3]{\color{blue}{19683} \cdot {\left(a \cdot b\right)}^{3}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

   6. Applied egg-rr 56.2%

      \[\leadsto \color{blue}{\sqrt[3]{19683 \cdot {\left(a \cdot b\right)}^{3}}} - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

   8. Applied egg-rr 81.4%

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

   if -8.5000000000000001e-87 < z < 5.99999999999999996e-65

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. distribute-lft-neg-in 97.4%

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

      3. associate-*l* 97.4%

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

      4. *-commutative 97.4%

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

      5. *-commutative 97.4%

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

      6. cancel-sign-sub-inv 97.4%

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

      7. *-commutative 97.4%

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

      8. *-commutative 97.4%

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

      9. associate-*l* 97.4%

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

      10. associate-*l* 98.6%

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

      11. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 84.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-87} \lor \neg \left(z \leq 6 \cdot 10^{-65}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]

Alternative 6: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+82}:\\ \;\;\;\;t_2 + x \cdot 2\\ \mathbf{elif}\;x \leq 5.8:\\ \;\;\;\;t_2 - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y (* t z)))) (t_2 (* 27.0 (* a b))))
   (if (<= x -4e+82)
     (+ t_2 (* x 2.0))
     (if (<= x 5.8) (- t_2 t_1) (- (* x 2.0) t_1)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (t * z));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -4e+82) {
		tmp = t_2 + (x * 2.0);
	} else if (x <= 5.8) {
		tmp = t_2 - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 = 9.0d0 * (y * (t * z))
    t_2 = 27.0d0 * (a * b)
    if (x <= (-4d+82)) then
        tmp = t_2 + (x * 2.0d0)
    else if (x <= 5.8d0) then
        tmp = t_2 - t_1
    else
        tmp = (x * 2.0d0) - t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (t * z));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -4e+82) {
		tmp = t_2 + (x * 2.0);
	} else if (x <= 5.8) {
		tmp = t_2 - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (y * (t * z))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if x <= -4e+82:
		tmp = t_2 + (x * 2.0)
	elif x <= 5.8:
		tmp = t_2 - t_1
	else:
		tmp = (x * 2.0) - t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(y * Float64(t * z)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -4e+82)
		tmp = Float64(t_2 + Float64(x * 2.0));
	elseif (x <= 5.8)
		tmp = Float64(t_2 - t_1);
	else
		tmp = Float64(Float64(x * 2.0) - t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (y * (t * z));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -4e+82)
		tmp = t_2 + (x * 2.0);
	elseif (x <= 5.8)
		tmp = t_2 - t_1;
	else
		tmp = (x * 2.0) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+82], N[(t$95$2 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8], N[(t$95$2 - t$95$1), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999999e82

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. distribute-lft-neg-in 95.7%

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

      3. associate-*l* 95.7%

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

      4. *-commutative 95.7%

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

      5. *-commutative 95.7%

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

      6. cancel-sign-sub-inv 95.7%

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

      7. *-commutative 95.7%

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

      8. *-commutative 95.7%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 91.4%

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

      11. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around 0 81.2%

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

   if -3.9999999999999999e82 < x < 5.79999999999999982

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. distribute-lft-neg-in 92.6%

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

      3. associate-*l* 92.6%

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

      4. *-commutative 92.6%

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

      5. *-commutative 92.6%

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

      6. cancel-sign-sub-inv 92.6%

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

      7. *-commutative 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-*l* 92.6%

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

      10. associate-*l* 96.1%

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

      11. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 87.0%

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

   if 5.79999999999999982 < x

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. distribute-lft-neg-in 96.2%

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

      3. associate-*l* 96.2%

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

      4. *-commutative 96.2%

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

      5. *-commutative 96.2%

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

      6. cancel-sign-sub-inv 96.2%

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

      7. *-commutative 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 99.9%

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

      11. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 83.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+82}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;x \leq 5.8:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 7: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y, z, and t 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) - ((y * 9.0d0) * (t * z))) + (a * (27.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - ((y * 9.0) * (t * z))) + (a * (27.0 * b));
end

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. sub-neg 93.9%

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

   2. distribute-lft-neg-in 93.9%

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

   3. associate-*l* 93.9%

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

   4. *-commutative 93.9%

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

   5. *-commutative 93.9%

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

   6. cancel-sign-sub-inv 93.9%

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

   7. *-commutative 93.9%

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

   8. *-commutative 93.9%

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

   9. associate-*l* 93.9%

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

   10. associate-*l* 96.0%

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

   11. associate-*l* 96.0%

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

3. Simplified 96.0%

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

4. Final simplification 96.0%

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

Alternative 8: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t 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))) (t_2 (* -9.0 (* y (* t z)))))
   (if (<= z -4.3e-68)
     t_2
     (if (<= z -5.8e-147)
       t_1
       (if (<= z -3.3e-283) (* x 2.0) (if (<= z 1.4e-19) t_1 t_2))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (t * z));
	double tmp;
	if (z <= -4.3e-68) {
		tmp = t_2;
	} else if (z <= -5.8e-147) {
		tmp = t_1;
	} else if (z <= -3.3e-283) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (y * (t * z))
    if (z <= (-4.3d-68)) then
        tmp = t_2
    else if (z <= (-5.8d-147)) then
        tmp = t_1
    else if (z <= (-3.3d-283)) then
        tmp = x * 2.0d0
    else if (z <= 1.4d-19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (t * z));
	double tmp;
	if (z <= -4.3e-68) {
		tmp = t_2;
	} else if (z <= -5.8e-147) {
		tmp = t_1;
	} else if (z <= -3.3e-283) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (y * (t * z))
	tmp = 0
	if z <= -4.3e-68:
		tmp = t_2
	elif z <= -5.8e-147:
		tmp = t_1
	elif z <= -3.3e-283:
		tmp = x * 2.0
	elif z <= 1.4e-19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(y * Float64(t * z)))
	tmp = 0.0
	if (z <= -4.3e-68)
		tmp = t_2;
	elseif (z <= -5.8e-147)
		tmp = t_1;
	elseif (z <= -3.3e-283)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.4e-19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (y * (t * z));
	tmp = 0.0;
	if (z <= -4.3e-68)
		tmp = t_2;
	elseif (z <= -5.8e-147)
		tmp = t_1;
	elseif (z <= -3.3e-283)
		tmp = x * 2.0;
	elseif (z <= 1.4e-19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t 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]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e-68], t$95$2, If[LessEqual[z, -5.8e-147], t$95$1, If[LessEqual[z, -3.3e-283], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.4e-19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3000000000000001e-68 or 1.40000000000000001e-19 < z

   1. Initial program 91.9%

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

      1. sub-neg 91.9%

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

      2. distribute-lft-neg-in 91.9%

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

      3. associate-*l* 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

      6. cancel-sign-sub-inv 91.9%

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

      7. *-commutative 91.9%

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

      8. *-commutative 91.9%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 50.2%

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

   if -4.3000000000000001e-68 < z < -5.8000000000000002e-147 or -3.30000000000000019e-283 < z < 1.40000000000000001e-19

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. distribute-lft-neg-in 97.1%

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

      3. associate-*l* 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. cancel-sign-sub-inv 97.1%

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

      7. *-commutative 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 98.3%

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

      11. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 65.7%

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

   5. Taylor expanded in a around inf 47.2%

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

   if -5.8000000000000002e-147 < z < -3.30000000000000019e-283

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-neg-in 99.7%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.7%

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

      10. associate-*l* 99.6%

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

      11. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 38.7%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-68}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-147}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 9: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -8.3 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t 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 -8.3e-66)
     (* y (* t (* -9.0 z)))
     (if (<= z -2.2e-147)
       t_1
       (if (<= z -3.3e-283)
         (* x 2.0)
         (if (<= z 8.5e-21) t_1 (* -9.0 (* y (* t z)))))))))

C

assert(y < z && z < t);
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 <= -8.3e-66) {
		tmp = y * (t * (-9.0 * z));
	} else if (z <= -2.2e-147) {
		tmp = t_1;
	} else if (z <= -3.3e-283) {
		tmp = x * 2.0;
	} else if (z <= 8.5e-21) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (y * (t * z));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 <= (-8.3d-66)) then
        tmp = y * (t * ((-9.0d0) * z))
    else if (z <= (-2.2d-147)) then
        tmp = t_1
    else if (z <= (-3.3d-283)) then
        tmp = x * 2.0d0
    else if (z <= 8.5d-21) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (y * (t * z))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
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 <= -8.3e-66) {
		tmp = y * (t * (-9.0 * z));
	} else if (z <= -2.2e-147) {
		tmp = t_1;
	} else if (z <= -3.3e-283) {
		tmp = x * 2.0;
	} else if (z <= 8.5e-21) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (y * (t * z));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if z <= -8.3e-66:
		tmp = y * (t * (-9.0 * z))
	elif z <= -2.2e-147:
		tmp = t_1
	elif z <= -3.3e-283:
		tmp = x * 2.0
	elif z <= 8.5e-21:
		tmp = t_1
	else:
		tmp = -9.0 * (y * (t * z))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -8.3e-66)
		tmp = Float64(y * Float64(t * Float64(-9.0 * z)));
	elseif (z <= -2.2e-147)
		tmp = t_1;
	elseif (z <= -3.3e-283)
		tmp = Float64(x * 2.0);
	elseif (z <= 8.5e-21)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(y * Float64(t * z)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -8.3e-66)
		tmp = y * (t * (-9.0 * z));
	elseif (z <= -2.2e-147)
		tmp = t_1;
	elseif (z <= -3.3e-283)
		tmp = x * 2.0;
	elseif (z <= 8.5e-21)
		tmp = t_1;
	else
		tmp = -9.0 * (y * (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t 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, -8.3e-66], N[(y * N[(t * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-147], t$95$1, If[LessEqual[z, -3.3e-283], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 8.5e-21], t$95$1, N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2999999999999995e-66

   1. Initial program 89.4%

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

      1. sub-neg 89.4%

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

      2. distribute-lft-neg-in 89.4%

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

      3. associate-*l* 89.4%

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

      4. *-commutative 89.4%

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

      5. *-commutative 89.4%

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

      6. cancel-sign-sub-inv 89.4%

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

      7. *-commutative 89.4%

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

      8. *-commutative 89.4%

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

      9. associate-*l* 89.4%

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

      10. associate-*l* 95.7%

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

      11. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 53.0%

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

      3. associate-*r* 53.1%

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

      4. associate-*l* 53.1%

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

   6. Simplified 53.1%

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

   if -8.2999999999999995e-66 < z < -2.2000000000000001e-147 or -3.30000000000000019e-283 < z < 8.4999999999999993e-21

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. distribute-lft-neg-in 97.1%

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

      3. associate-*l* 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. cancel-sign-sub-inv 97.1%

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

      7. *-commutative 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 98.3%

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

      11. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 65.7%

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

   5. Taylor expanded in a around inf 47.2%

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

   if -2.2000000000000001e-147 < z < -3.30000000000000019e-283

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-neg-in 99.7%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.7%

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

      10. associate-*l* 99.6%

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

      11. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 38.7%

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

   if 8.4999999999999993e-21 < z

   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. distribute-lft-neg-in 94.8%

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

      3. associate-*l* 94.8%

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

      4. *-commutative 94.8%

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

      5. *-commutative 94.8%

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

      6. cancel-sign-sub-inv 94.8%

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

      7. *-commutative 94.8%

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

      8. *-commutative 94.8%

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

      9. associate-*l* 94.8%

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

      10. associate-*l* 93.5%

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

      11. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 46.8%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-147}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 10: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t 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))) (t_2 (* z (* t (* y -9.0)))))
   (if (<= z -2.2e-63)
     t_2
     (if (<= z -3.1e-147)
       t_1
       (if (<= z -3.3e-283) (* x 2.0) (if (<= z 1.45e-20) t_1 t_2))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = z * (t * (y * -9.0));
	double tmp;
	if (z <= -2.2e-63) {
		tmp = t_2;
	} else if (z <= -3.1e-147) {
		tmp = t_1;
	} else if (z <= -3.3e-283) {
		tmp = x * 2.0;
	} else if (z <= 1.45e-20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 = 27.0d0 * (a * b)
    t_2 = z * (t * (y * (-9.0d0)))
    if (z <= (-2.2d-63)) then
        tmp = t_2
    else if (z <= (-3.1d-147)) then
        tmp = t_1
    else if (z <= (-3.3d-283)) then
        tmp = x * 2.0d0
    else if (z <= 1.45d-20) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = z * (t * (y * -9.0));
	double tmp;
	if (z <= -2.2e-63) {
		tmp = t_2;
	} else if (z <= -3.1e-147) {
		tmp = t_1;
	} else if (z <= -3.3e-283) {
		tmp = x * 2.0;
	} else if (z <= 1.45e-20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = z * (t * (y * -9.0))
	tmp = 0
	if z <= -2.2e-63:
		tmp = t_2
	elif z <= -3.1e-147:
		tmp = t_1
	elif z <= -3.3e-283:
		tmp = x * 2.0
	elif z <= 1.45e-20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(z * Float64(t * Float64(y * -9.0)))
	tmp = 0.0
	if (z <= -2.2e-63)
		tmp = t_2;
	elseif (z <= -3.1e-147)
		tmp = t_1;
	elseif (z <= -3.3e-283)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.45e-20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = z * (t * (y * -9.0));
	tmp = 0.0;
	if (z <= -2.2e-63)
		tmp = t_2;
	elseif (z <= -3.1e-147)
		tmp = t_1;
	elseif (z <= -3.3e-283)
		tmp = x * 2.0;
	elseif (z <= 1.45e-20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t 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]}, Block[{t$95$2 = N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-63], t$95$2, If[LessEqual[z, -3.1e-147], t$95$1, If[LessEqual[z, -3.3e-283], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.45e-20], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e-63 or 1.45e-20 < z

   1. Initial program 91.9%

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

      1. sub-neg 91.9%

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

      2. distribute-lft-neg-in 91.9%

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

      3. associate-*l* 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

      6. cancel-sign-sub-inv 91.9%

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

      7. *-commutative 91.9%

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

      8. *-commutative 91.9%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. *-commutative 50.2%

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

      3. *-commutative 50.2%

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

      4. *-commutative 50.2%

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

      5. associate-*l* 51.3%

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

   6. Simplified 51.3%

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

   if -2.2e-63 < z < -3.1000000000000003e-147 or -3.30000000000000019e-283 < z < 1.45e-20

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. distribute-lft-neg-in 97.1%

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

      3. associate-*l* 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. cancel-sign-sub-inv 97.1%

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

      7. *-commutative 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 98.3%

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

      11. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 65.7%

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

   5. Taylor expanded in a around inf 47.2%

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

   if -3.1000000000000003e-147 < z < -3.30000000000000019e-283

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-neg-in 99.7%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.7%

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

      10. associate-*l* 99.6%

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

      11. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 38.7%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-147}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 11: 78.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-69} \lor \neg \left(z \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.05e-69) (not (<= z 2e-18)))
   (- (* x 2.0) (* 9.0 (* y (* t z))))
   (+ (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.05e-69) || !(z <= 2e-18)) {
		tmp = (x * 2.0) - (9.0 * (y * (t * z)));
	} else {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 <= (-2.05d-69)) .or. (.not. (z <= 2d-18))) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (t * z)))
    else
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.05e-69) || !(z <= 2e-18)) {
		tmp = (x * 2.0) - (9.0 * (y * (t * z)));
	} else {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.05e-69) or not (z <= 2e-18):
		tmp = (x * 2.0) - (9.0 * (y * (t * z)))
	else:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.05e-69) || !(z <= 2e-18))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z))));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.05e-69) || ~((z <= 2e-18)))
		tmp = (x * 2.0) - (9.0 * (y * (t * z)));
	else
		tmp = (27.0 * (a * b)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.05e-69], N[Not[LessEqual[z, 2e-18]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.04999999999999995e-69 or 2.0000000000000001e-18 < z

   1. Initial program 91.9%

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

      1. sub-neg 91.9%

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

      2. distribute-lft-neg-in 91.9%

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

      3. associate-*l* 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

      6. cancel-sign-sub-inv 91.9%

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

      7. *-commutative 91.9%

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

      8. *-commutative 91.9%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around 0 67.2%

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

   if -2.04999999999999995e-69 < z < 2.0000000000000001e-18

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. distribute-lft-neg-in 97.7%

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

      3. associate-*l* 97.7%

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

      4. *-commutative 97.7%

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

      5. *-commutative 97.7%

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

      6. cancel-sign-sub-inv 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.6%

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

      11. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 80.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-69} \lor \neg \left(z \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]

Alternative 12: 75.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.06e+49)
   (* z (* y (* t -9.0)))
   (if (<= z 2.3e-19) (+ (* 27.0 (* a b)) (* x 2.0)) (* z (* t (* y -9.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.06e+49) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= 2.3e-19) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 <= (-1.06d+49)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= 2.3d-19) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = z * (t * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.06e+49) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= 2.3e-19) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.06e+49:
		tmp = z * (y * (t * -9.0))
	elif z <= 2.3e-19:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = z * (t * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.06e+49)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= 2.3e-19)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(z * Float64(t * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.06e+49)
		tmp = z * (y * (t * -9.0));
	elseif (z <= 2.3e-19)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = z * (t * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.06e+49], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-19], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06e49

   1. Initial program 87.0%

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

      1. sub-neg 87.0%

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

      2. distribute-lft-neg-in 87.0%

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

      3. associate-*l* 87.0%

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

      4. *-commutative 87.0%

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

      5. *-commutative 87.0%

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

      6. cancel-sign-sub-inv 87.0%

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

      7. *-commutative 87.0%

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

      8. *-commutative 87.0%

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

      9. associate-*l* 87.0%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 60.6%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

      3. *-commutative 60.7%

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

      4. *-commutative 60.7%

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

      5. associate-*l* 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in t around 0 60.6%

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

      1. associate-*r* 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-*l* 60.6%

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

   9. Simplified 60.6%

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

   if -1.06e49 < z < 2.2999999999999998e-19

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. distribute-lft-neg-in 98.0%

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

      3. associate-*l* 98.0%

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

      4. *-commutative 98.0%

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

      5. *-commutative 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. *-commutative 98.0%

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

      8. *-commutative 98.0%

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

      9. associate-*l* 98.0%

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

      10. associate-*l* 98.8%

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

      11. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 81.0%

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

   if 2.2999999999999998e-19 < z

   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. distribute-lft-neg-in 94.8%

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

      3. associate-*l* 94.8%

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

      4. *-commutative 94.8%

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

      5. *-commutative 94.8%

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

      6. cancel-sign-sub-inv 94.8%

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

      7. *-commutative 94.8%

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

      8. *-commutative 94.8%

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

      9. associate-*l* 94.8%

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

      10. associate-*l* 93.5%

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

      11. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 46.8%

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

      1. associate-*r* 46.8%

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

      2. *-commutative 46.8%

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

      3. *-commutative 46.8%

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

      4. *-commutative 46.8%

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

      5. associate-*l* 49.2%

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

   6. Simplified 49.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 13: 48.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+82}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 8:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.6e+82) (* x 2.0) (if (<= x 8.0) (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.6e+82) {
		tmp = x * 2.0;
	} else if (x <= 8.0) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 (x <= (-7.6d+82)) then
        tmp = x * 2.0d0
    else if (x <= 8.0d0) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.6e+82) {
		tmp = x * 2.0;
	} else if (x <= 8.0) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.6e+82:
		tmp = x * 2.0
	elif x <= 8.0:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.6e+82)
		tmp = Float64(x * 2.0);
	elseif (x <= 8.0)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.6e+82)
		tmp = x * 2.0;
	elseif (x <= 8.0)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.6e+82], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 8.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.60000000000000067e82 or 8 < x

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. distribute-lft-neg-in 96.0%

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

      3. associate-*l* 96.0%

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

      4. *-commutative 96.0%

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

      5. *-commutative 96.0%

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

      6. cancel-sign-sub-inv 96.0%

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

      7. *-commutative 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-*l* 96.0%

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

      10. associate-*l* 95.9%

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

      11. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 48.7%

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

   if -7.60000000000000067e82 < x < 8

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. distribute-lft-neg-in 92.6%

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

      3. associate-*l* 92.6%

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

      4. *-commutative 92.6%

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

      5. *-commutative 92.6%

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

      6. cancel-sign-sub-inv 92.6%

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

      7. *-commutative 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-*l* 92.6%

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

      10. associate-*l* 96.1%

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

      11. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 87.0%

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

   5. Taylor expanded in a around inf 48.3%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+82}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 8:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14: 31.0% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y, z, and t 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 93.9%

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

   1. sub-neg 93.9%

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

   2. distribute-lft-neg-in 93.9%

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

   3. associate-*l* 93.9%

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

   4. *-commutative 93.9%

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

   5. *-commutative 93.9%

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

   6. cancel-sign-sub-inv 93.9%

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

   7. *-commutative 93.9%

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

   8. *-commutative 93.9%

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

   9. associate-*l* 93.9%

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

   10. associate-*l* 96.0%

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

   11. associate-*l* 96.0%

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

3. Simplified 96.0%

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

4. Taylor expanded in x around inf 25.0%

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

5. Final simplification 25.0%

   \[\leadsto x \cdot 2 \]

Developer target: 95.1% accurate, 0.9× 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 2023274 
(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)))