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

Percentage Accurate: 95.8% → 97.4%

Time: 11.2s

Alternatives: 12

Speedup: 0.7×

• 27.3% 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: 95.8% 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: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+234}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

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 (<= (* (* y 9.0) z) 5e+234)
   (fma x 2.0 (fma t (* (* y z) -9.0) (* (* a 27.0) b)))
   (- (* x 2.0) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+234) {
		tmp = fma(x, 2.0, fma(t, ((y * z) * -9.0), ((a * 27.0) * b)));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+234)
		tmp = fma(x, 2.0, fma(t, Float64(Float64(y * z) * -9.0), Float64(Float64(a * 27.0) * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return 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[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+234], N[(x * 2.0 + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 5.0000000000000003e234

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. fma-neg 96.9%

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

      3. neg-sub0 96.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 96.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 96.9%

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

      6. *-commutative 96.9%

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

      7. distribute-rgt-neg-in 96.9%

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

      8. fma-def 97.3%

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

      9. *-commutative 97.3%

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

      10. associate-*r* 97.3%

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

      11. distribute-rgt-neg-in 97.3%

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

      12. *-commutative 97.3%

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

      13. metadata-eval 97.3%

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

   3. Simplified 97.3%

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

   if 5.0000000000000003e234 < (*.f64 (*.f64 y 9) z)

   1. Initial program 74.3%

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

   2. Taylor expanded in a around 0 91.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+234}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 2: 96.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+174}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

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 (<= (* (* y 9.0) z) 2e+174)
   (+ (* (* a 27.0) b) (- (* x 2.0) (* t (* y (* 9.0 z)))))
   (- (* x 2.0) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 2e+174) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (y * (9.0 * z))));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	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 (((y * 9.0d0) * z) <= 2d+174) then
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (t * (y * (9.0d0 * z))))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    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 (((y * 9.0) * z) <= 2e+174) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (y * (9.0 * z))));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * 9.0) * z) <= 2e+174:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (y * (9.0 * z))))
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 2e+174)
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z)))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	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 (((y * 9.0) * z) <= 2e+174)
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (y * (9.0 * z))));
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	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[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 2e+174], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 2.00000000000000014e174

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*r* 96.3%

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

   4. Simplified 96.3%

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

   if 2.00000000000000014e174 < (*.f64 (*.f64 y 9) z)

   1. Initial program 82.3%

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

   2. Taylor expanded in a around 0 91.1%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+174}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 3: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-155}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 0.00046:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* z t)))))
   (if (<= z -4.1e-92)
     t_1
     (if (<= z -1.36e-155)
       (* x 2.0)
       (if (<= z -3.7e-266)
         (* 27.0 (* a b))
         (if (<= z 1.4e-109)
           (* x 2.0)
           (if (<= z 0.00046) (* a (* 27.0 b)) 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 * (z * t));
	double tmp;
	if (z <= -4.1e-92) {
		tmp = t_1;
	} else if (z <= -1.36e-155) {
		tmp = x * 2.0;
	} else if (z <= -3.7e-266) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1.4e-109) {
		tmp = x * 2.0;
	} else if (z <= 0.00046) {
		tmp = a * (27.0 * b);
	} else {
		tmp = 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) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    if (z <= (-4.1d-92)) then
        tmp = t_1
    else if (z <= (-1.36d-155)) then
        tmp = x * 2.0d0
    else if (z <= (-3.7d-266)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 1.4d-109) then
        tmp = x * 2.0d0
    else if (z <= 0.00046d0) then
        tmp = a * (27.0d0 * b)
    else
        tmp = 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 * (z * t));
	double tmp;
	if (z <= -4.1e-92) {
		tmp = t_1;
	} else if (z <= -1.36e-155) {
		tmp = x * 2.0;
	} else if (z <= -3.7e-266) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1.4e-109) {
		tmp = x * 2.0;
	} else if (z <= 0.00046) {
		tmp = a * (27.0 * b);
	} else {
		tmp = 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 * (z * t))
	tmp = 0
	if z <= -4.1e-92:
		tmp = t_1
	elif z <= -1.36e-155:
		tmp = x * 2.0
	elif z <= -3.7e-266:
		tmp = 27.0 * (a * b)
	elif z <= 1.4e-109:
		tmp = x * 2.0
	elif z <= 0.00046:
		tmp = a * (27.0 * b)
	else:
		tmp = 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(z * t)))
	tmp = 0.0
	if (z <= -4.1e-92)
		tmp = t_1;
	elseif (z <= -1.36e-155)
		tmp = Float64(x * 2.0);
	elseif (z <= -3.7e-266)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 1.4e-109)
		tmp = Float64(x * 2.0);
	elseif (z <= 0.00046)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = 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 * (z * t));
	tmp = 0.0;
	if (z <= -4.1e-92)
		tmp = t_1;
	elseif (z <= -1.36e-155)
		tmp = x * 2.0;
	elseif (z <= -3.7e-266)
		tmp = 27.0 * (a * b);
	elseif (z <= 1.4e-109)
		tmp = x * 2.0;
	elseif (z <= 0.00046)
		tmp = a * (27.0 * b);
	else
		tmp = 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[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e-92], t$95$1, If[LessEqual[z, -1.36e-155], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -3.7e-266], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-109], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 0.00046], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1000000000000002e-92 or 4.6000000000000001e-4 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in y around 0 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*r* 90.6%

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

   4. Simplified 90.6%

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

   5. Taylor expanded in y around inf 43.5%

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

   if -4.1000000000000002e-92 < z < -1.35999999999999996e-155 or -3.7000000000000003e-266 < z < 1.39999999999999989e-109

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. fma-neg 99.9%

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

      3. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. fma-def 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-rgt-neg-in 99.9%

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

      12. *-commutative 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 58.5%

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

   if -1.35999999999999996e-155 < z < -3.7000000000000003e-266

   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. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in a around inf 48.9%

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

   if 1.39999999999999989e-109 < z < 4.6000000000000001e-4

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. neg-mul-1 99.6%

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

      4. metadata-eval 99.6%

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

      5. metadata-eval 99.6%

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

      6. cancel-sign-sub-inv 99.6%

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

      7. metadata-eval 99.6%

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

      8. *-lft-identity 99.6%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 71.9%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in a around 0 71.9%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 71.9%

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

      2. associate-*r* 72.0%

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

   9. Simplified 72.0%

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

   10. Taylor expanded in x around 0 34.1%

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

       1. *-commutative 34.1%

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

       2. associate-*r* 34.1%

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

   12. Simplified 34.1%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-92}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-155}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 0.00046:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 4: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-90}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-159}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-265}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 0.00045:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 -5.2e-90)
   (* -9.0 (* y (* z t)))
   (if (<= z -2.8e-159)
     (* x 2.0)
     (if (<= z -3.6e-265)
       (* 27.0 (* a b))
       (if (<= z 1.4e-109)
         (* x 2.0)
         (if (<= z 0.00045) (* a (* 27.0 b)) (* 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 <= -5.2e-90) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -2.8e-159) {
		tmp = x * 2.0;
	} else if (z <= -3.6e-265) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1.4e-109) {
		tmp = x * 2.0;
	} else if (z <= 0.00045) {
		tmp = a * (27.0 * b);
	} 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 <= (-5.2d-90)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-2.8d-159)) then
        tmp = x * 2.0d0
    else if (z <= (-3.6d-265)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 1.4d-109) then
        tmp = x * 2.0d0
    else if (z <= 0.00045d0) then
        tmp = a * (27.0d0 * b)
    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 <= -5.2e-90) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -2.8e-159) {
		tmp = x * 2.0;
	} else if (z <= -3.6e-265) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1.4e-109) {
		tmp = x * 2.0;
	} else if (z <= 0.00045) {
		tmp = a * (27.0 * b);
	} 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 <= -5.2e-90:
		tmp = -9.0 * (y * (z * t))
	elif z <= -2.8e-159:
		tmp = x * 2.0
	elif z <= -3.6e-265:
		tmp = 27.0 * (a * b)
	elif z <= 1.4e-109:
		tmp = x * 2.0
	elif z <= 0.00045:
		tmp = a * (27.0 * b)
	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 <= -5.2e-90)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -2.8e-159)
		tmp = Float64(x * 2.0);
	elseif (z <= -3.6e-265)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 1.4e-109)
		tmp = Float64(x * 2.0);
	elseif (z <= 0.00045)
		tmp = Float64(a * Float64(27.0 * b));
	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 <= -5.2e-90)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -2.8e-159)
		tmp = x * 2.0;
	elseif (z <= -3.6e-265)
		tmp = 27.0 * (a * b);
	elseif (z <= 1.4e-109)
		tmp = x * 2.0;
	elseif (z <= 0.00045)
		tmp = a * (27.0 * b);
	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, -5.2e-90], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-159], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -3.6e-265], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-109], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 0.00045], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.2000000000000001e-90

   1. Initial program 89.9%

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

   2. Taylor expanded in y around 0 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*r* 89.9%

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

   4. Simplified 89.9%

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

   5. Taylor expanded in y around inf 33.3%

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

   if -5.2000000000000001e-90 < z < -2.8000000000000002e-159 or -3.6000000000000002e-265 < z < 1.39999999999999989e-109

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. fma-neg 99.9%

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

      3. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. fma-def 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-rgt-neg-in 99.9%

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

      12. *-commutative 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 57.6%

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

   if -2.8000000000000002e-159 < z < -3.6000000000000002e-265

   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. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in a around inf 45.0%

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

   if 1.39999999999999989e-109 < z < 4.4999999999999999e-4

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. neg-mul-1 99.6%

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

      4. metadata-eval 99.6%

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

      5. metadata-eval 99.6%

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

      6. cancel-sign-sub-inv 99.6%

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

      7. metadata-eval 99.6%

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

      8. *-lft-identity 99.6%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 71.9%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in a around 0 71.9%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 71.9%

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

      2. associate-*r* 72.0%

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

   9. Simplified 72.0%

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

   10. Taylor expanded in x around 0 34.1%

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

       1. *-commutative 34.1%

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

       2. associate-*r* 34.1%

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

   12. Simplified 34.1%

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

   if 4.4999999999999999e-4 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*r* 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*r* 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in y around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*l* 58.6%

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

   10. Simplified 58.6%

       \[\leadsto z \cdot \color{blue}{\left(t \cdot \left(y \cdot -9\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-90}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-159}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-265}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 0.00045:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 5: 80.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-87} \lor \neg \left(z \leq 3.5 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \end{array} \]

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 (or (<= z -3.5e-87) (not (<= z 3.5e-5)))
   (+ (* x 2.0) (* (* y t) (* z -9.0)))
   (- (* x 2.0) (* 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 <= -3.5e-87) || !(z <= 3.5e-5)) {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	} else {
		tmp = (x * 2.0) - (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 <= (-3.5d-87)) .or. (.not. (z <= 3.5d-5))) then
        tmp = (x * 2.0d0) + ((y * t) * (z * (-9.0d0)))
    else
        tmp = (x * 2.0d0) - (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 <= -3.5e-87) || !(z <= 3.5e-5)) {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	} else {
		tmp = (x * 2.0) - (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 <= -3.5e-87) or not (z <= 3.5e-5):
		tmp = (x * 2.0) + ((y * t) * (z * -9.0))
	else:
		tmp = (x * 2.0) - (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 <= -3.5e-87) || !(z <= 3.5e-5))
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * t) * Float64(z * -9.0)));
	else
		tmp = Float64(Float64(x * 2.0) - 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 <= -3.5e-87) || ~((z <= 3.5e-5)))
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	else
		tmp = (x * 2.0) - (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[Or[LessEqual[z, -3.5e-87], N[Not[LessEqual[z, 3.5e-5]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000012e-87 or 3.4999999999999997e-5 < z

   1. Initial program 91.2%

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

   2. Taylor expanded in a around 0 65.9%

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

      1. associate-*r* 65.9%

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

      2. *-commutative 65.9%

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

      3. *-commutative 65.9%

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

      4. associate-*l* 69.9%

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

      5. *-commutative 69.9%

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

      6. sub-neg 69.9%

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

      7. +-commutative 69.9%

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

      8. associate-*l* 65.9%

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

      9. *-commutative 65.9%

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

      10. *-commutative 65.9%

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

      11. associate-*r* 65.9%

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

      12. distribute-lft-neg-in 65.9%

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

      13. *-commutative 65.9%

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

      14. associate-*r* 73.4%

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

      15. *-commutative 73.4%

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

      16. metadata-eval 73.4%

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

   4. Applied egg-rr 73.4%

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

   5. Taylor expanded in z around 0 65.9%

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

      1. associate-*r* 73.4%

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

      2. *-commutative 73.4%

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

      3. *-commutative 73.4%

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

      4. *-commutative 73.4%

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

      5. associate-*l* 72.8%

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

   7. Simplified 72.8%

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

   if -3.50000000000000012e-87 < z < 3.4999999999999997e-5

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in a around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 83.7%

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

      2. associate-*r* 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in a around 0 83.7%

       \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 83.7%

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

       2. *-commutative 83.7%

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

   12. Simplified 83.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-87} \lor \neg \left(z \leq 3.5 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \]

Alternative 6: 80.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-83}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

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 -1.35e-83)
   (+ (* x 2.0) (* (* y t) (* z -9.0)))
   (if (<= z 3.2e-5)
     (- (* x 2.0) (* b (* a -27.0)))
     (+ (* x 2.0) (* -9.0 (* z (* y t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e-83) {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	} else if (z <= 3.2e-5) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	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 <= (-1.35d-83)) then
        tmp = (x * 2.0d0) + ((y * t) * (z * (-9.0d0)))
    else if (z <= 3.2d-5) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((-9.0d0) * (z * (y * t)))
    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 <= -1.35e-83) {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	} else if (z <= 3.2e-5) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.35e-83:
		tmp = (x * 2.0) + ((y * t) * (z * -9.0))
	elif z <= 3.2e-5:
		tmp = (x * 2.0) - (b * (a * -27.0))
	else:
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.35e-83)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * t) * Float64(z * -9.0)));
	elseif (z <= 3.2e-5)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(z * Float64(y * t))));
	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 <= -1.35e-83)
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	elseif (z <= 3.2e-5)
		tmp = (x * 2.0) - (b * (a * -27.0));
	else
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	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, -1.35e-83], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-5], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999996e-83

   1. Initial program 89.8%

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

   2. Taylor expanded in a around 0 54.5%

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

      1. associate-*r* 54.5%

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

      2. *-commutative 54.5%

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

      3. *-commutative 54.5%

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

      4. associate-*l* 61.6%

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

      5. *-commutative 61.6%

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

      6. sub-neg 61.6%

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

      7. +-commutative 61.6%

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

      8. associate-*l* 54.5%

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

      9. *-commutative 54.5%

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

      10. *-commutative 54.5%

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

      11. associate-*r* 54.5%

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

      12. distribute-lft-neg-in 54.5%

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

      13. *-commutative 54.5%

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

      14. associate-*r* 63.4%

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

      15. *-commutative 63.4%

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

      16. metadata-eval 63.4%

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

   4. Applied egg-rr 63.4%

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

   5. Taylor expanded in z around 0 54.5%

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

      1. associate-*r* 63.4%

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

      2. *-commutative 63.4%

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

      3. *-commutative 63.4%

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

      4. *-commutative 63.4%

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

      5. associate-*l* 63.4%

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

   7. Simplified 63.4%

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

   if -1.34999999999999996e-83 < z < 3.19999999999999986e-5

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in a around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 83.7%

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

      2. associate-*r* 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in a around 0 83.7%

       \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 83.7%

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

       2. *-commutative 83.7%

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

   12. Simplified 83.7%

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

   if 3.19999999999999986e-5 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in a around 0 79.5%

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

      1. associate-*r* 79.5%

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

      2. *-commutative 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*l* 80.0%

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

      5. *-commutative 80.0%

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

      6. sub-neg 80.0%

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

      7. +-commutative 80.0%

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

      8. associate-*l* 79.5%

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

      9. *-commutative 79.5%

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

      10. *-commutative 79.5%

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

      11. associate-*r* 79.5%

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

      12. distribute-lft-neg-in 79.5%

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

      13. *-commutative 79.5%

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

      14. associate-*r* 85.4%

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

      15. *-commutative 85.4%

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

      16. metadata-eval 85.4%

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

   4. Applied egg-rr 85.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-83}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

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 -6e-87)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= z 3.5e-5)
     (- (* x 2.0) (* b (* a -27.0)))
     (+ (* x 2.0) (* -9.0 (* z (* y t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e-87) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 3.5e-5) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	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 <= (-6d-87)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (z <= 3.5d-5) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((-9.0d0) * (z * (y * t)))
    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 <= -6e-87) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 3.5e-5) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6e-87:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif z <= 3.5e-5:
		tmp = (x * 2.0) - (b * (a * -27.0))
	else:
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e-87)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 3.5e-5)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(z * Float64(y * t))));
	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 <= -6e-87)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (z <= 3.5e-5)
		tmp = (x * 2.0) - (b * (a * -27.0));
	else
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	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, -6e-87], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-5], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.00000000000000033e-87

   1. Initial program 89.8%

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

   2. Taylor expanded in a around 0 54.5%

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

   if -6.00000000000000033e-87 < z < 3.4999999999999997e-5

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in a around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 83.7%

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

      2. associate-*r* 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in a around 0 83.7%

       \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 83.7%

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

       2. *-commutative 83.7%

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

   12. Simplified 83.7%

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

   if 3.4999999999999997e-5 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in a around 0 79.5%

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

      1. associate-*r* 79.5%

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

      2. *-commutative 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*l* 80.0%

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

      5. *-commutative 80.0%

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

      6. sub-neg 80.0%

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

      7. +-commutative 80.0%

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

      8. associate-*l* 79.5%

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

      9. *-commutative 79.5%

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

      10. *-commutative 79.5%

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

      11. associate-*r* 79.5%

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

      12. distribute-lft-neg-in 79.5%

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

      13. *-commutative 79.5%

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

      14. associate-*r* 85.4%

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

      15. *-commutative 85.4%

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

      16. metadata-eval 85.4%

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

   4. Applied egg-rr 85.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 8: 74.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 0.046:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 -2.5e-83)
   (* -9.0 (* y (* z t)))
   (if (<= z 0.046) (- (* x 2.0) (* a (* b -27.0))) (* 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 <= -2.5e-83) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 0.046) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} 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 <= (-2.5d-83)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 0.046d0) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    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 <= -2.5e-83) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 0.046) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} 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 <= -2.5e-83:
		tmp = -9.0 * (y * (z * t))
	elif z <= 0.046:
		tmp = (x * 2.0) - (a * (b * -27.0))
	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 <= -2.5e-83)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 0.046)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	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 <= -2.5e-83)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 0.046)
		tmp = (x * 2.0) - (a * (b * -27.0));
	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, -2.5e-83], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.046], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e-83

   1. Initial program 89.8%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r* 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in y around inf 33.7%

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

   if -2.5e-83 < z < 0.045999999999999999

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in a around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 83.7%

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

      2. associate-*r* 83.6%

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

   9. Simplified 83.6%

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

   if 0.045999999999999999 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*r* 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*r* 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in y around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*l* 58.6%

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

   10. Simplified 58.6%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 0.046:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 9: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 0.0052:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 -2.5e-83)
   (* -9.0 (* y (* z t)))
   (if (<= z 0.0052) (- (* x 2.0) (* b (* a -27.0))) (* 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 <= -2.5e-83) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 0.0052) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} 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 <= (-2.5d-83)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 0.0052d0) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    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 <= -2.5e-83) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 0.0052) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} 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 <= -2.5e-83:
		tmp = -9.0 * (y * (z * t))
	elif z <= 0.0052:
		tmp = (x * 2.0) - (b * (a * -27.0))
	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 <= -2.5e-83)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 0.0052)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	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 <= -2.5e-83)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 0.0052)
		tmp = (x * 2.0) - (b * (a * -27.0));
	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, -2.5e-83], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0052], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e-83

   1. Initial program 89.8%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r* 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in y around inf 33.7%

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

   if -2.5e-83 < z < 0.0051999999999999998

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in a around 0 83.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 83.7%

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

      2. associate-*r* 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in a around 0 83.7%

       \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 83.7%

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

       2. *-commutative 83.7%

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

   12. Simplified 83.7%

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

   if 0.0051999999999999998 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*r* 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*r* 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in y around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*l* 58.6%

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

   10. Simplified 58.6%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 0.0052:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 10: 46.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-59} \lor \neg \left(b \leq 2.1 \cdot 10^{+114}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 (or (<= b -6.2e-59) (not (<= b 2.1e+114))) (* 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 ((b <= -6.2e-59) || !(b <= 2.1e+114)) {
		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 ((b <= (-6.2d-59)) .or. (.not. (b <= 2.1d+114))) 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 ((b <= -6.2e-59) || !(b <= 2.1e+114)) {
		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 (b <= -6.2e-59) or not (b <= 2.1e+114):
		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 ((b <= -6.2e-59) || !(b <= 2.1e+114))
		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 ((b <= -6.2e-59) || ~((b <= 2.1e+114)))
		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[Or[LessEqual[b, -6.2e-59], N[Not[LessEqual[b, 2.1e+114]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.19999999999999998e-59 or 2.1e114 < b

   1. Initial program 91.4%

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

   2. Taylor expanded in y around 0 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*r* 90.6%

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

   4. Simplified 90.6%

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

   5. Taylor expanded in a around inf 47.4%

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

   if -6.19999999999999998e-59 < b < 2.1e114

   1. Initial program 97.8%

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

      1. associate-+l- 97.8%

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

      2. fma-neg 97.8%

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

      3. neg-sub0 97.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 97.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 97.8%

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

      6. *-commutative 97.8%

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

      7. distribute-rgt-neg-in 97.8%

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

      8. fma-def 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*r* 97.8%

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

      11. distribute-rgt-neg-in 97.8%

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

      12. *-commutative 97.8%

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

      13. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 45.3%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-59} \lor \neg \left(b \leq 2.1 \cdot 10^{+114}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 11: 46.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+114}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 (<= b -1.35e-58)
   (* a (* 27.0 b))
   (if (<= b 2.15e+114) (* x 2.0) (* 27.0 (* a b)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e-58) {
		tmp = a * (27.0 * b);
	} else if (b <= 2.15e+114) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	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 (b <= (-1.35d-58)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 2.15d+114) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    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 (b <= -1.35e-58) {
		tmp = a * (27.0 * b);
	} else if (b <= 2.15e+114) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.35e-58:
		tmp = a * (27.0 * b)
	elif b <= 2.15e+114:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.35e-58)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 2.15e+114)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	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 (b <= -1.35e-58)
		tmp = a * (27.0 * b);
	elseif (b <= 2.15e+114)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	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[b, -1.35e-58], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+114], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3499999999999999e-58

   1. Initial program 95.2%

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

      1. associate-+l- 95.2%

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

      2. sub-neg 95.2%

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

      3. neg-mul-1 95.2%

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

      4. metadata-eval 95.2%

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

      5. metadata-eval 95.2%

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

      6. cancel-sign-sub-inv 95.2%

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

      7. metadata-eval 95.2%

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

      8. *-lft-identity 95.2%

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

      9. associate-*l* 93.9%

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

      10. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 70.2%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in a around 0 70.2%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 70.2%

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

      2. associate-*r* 70.2%

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

   9. Simplified 70.2%

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

   10. Taylor expanded in x around 0 38.1%

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

       1. *-commutative 38.1%

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

       2. associate-*r* 38.1%

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

   12. Simplified 38.1%

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

   if -1.3499999999999999e-58 < b < 2.15e114

   1. Initial program 97.8%

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

      1. associate-+l- 97.8%

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

      2. fma-neg 97.8%

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

      3. neg-sub0 97.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 97.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 97.8%

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

      6. *-commutative 97.8%

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

      7. distribute-rgt-neg-in 97.8%

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

      8. fma-def 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*r* 97.8%

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

      11. distribute-rgt-neg-in 97.8%

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

      12. *-commutative 97.8%

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

      13. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 45.3%

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

   if 2.15e114 < b

   1. Initial program 82.2%

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

   2. Taylor expanded in y around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r* 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in a around inf 70.3%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+114}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 12: 31.2% 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 94.9%

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

   1. associate-+l- 94.9%

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

   2. fma-neg 94.9%

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

   3. neg-sub0 94.9%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

   4. associate-+l- 94.9%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

   5. neg-sub0 94.9%

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

   6. *-commutative 94.9%

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

   7. distribute-rgt-neg-in 94.9%

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

   8. fma-def 95.3%

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

   9. *-commutative 95.3%

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

   10. associate-*r* 95.4%

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

   11. distribute-rgt-neg-in 95.4%

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

   12. *-commutative 95.4%

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

   13. metadata-eval 95.4%

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

3. Simplified 95.4%

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

4. Taylor expanded in x around inf 36.8%

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

5. Final simplification 36.8%

   \[\leadsto x \cdot 2 \]

Developer target: 95.3% 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 2023238 
(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)))