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

Percentage Accurate: 95.6% → 96.8%

Time: 12.1s

Alternatives: 15

Speedup: 0.9×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -1 \cdot 10^{-128}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

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) -1e-128)
   (fma a (* 27.0 b) (fma x 2.0 (* t (* (* y z) -9.0))))
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* 9.0 (* 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) <= -1e-128) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * ((y * z) * -9.0))));
	} else {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (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) <= -1e-128)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(Float64(y * z) * -9.0))));
	else
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(y * Float64(9.0 * 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], -1e-128], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < -1.00000000000000005e-128

   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. Step-by-step derivation

      1. +-commutative 92.9%

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

      2. associate-+r- 92.9%

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

      3. *-commutative 92.9%

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

      4. cancel-sign-sub-inv 92.9%

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

      5. associate-*r* 91.8%

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

      6. distribute-lft-neg-in 91.8%

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

      7. *-commutative 91.8%

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

      8. cancel-sign-sub-inv 91.8%

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

      9. associate-+r- 91.8%

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

      10. associate-*l* 91.9%

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

      11. fma-def 93.1%

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

      12. cancel-sign-sub-inv 93.1%

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

      13. fma-def 93.1%

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

      14. distribute-lft-neg-in 93.1%

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

      15. distribute-rgt-neg-in 93.1%

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

      16. *-commutative 93.1%

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

      17. associate-*r* 94.2%

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

      18. distribute-rgt-neg-out 94.2%

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

      19. *-commutative 94.2%

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

      20. associate-*r* 94.1%

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

   3. Simplified 94.1%

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

   if -1.00000000000000005e-128 < (*.f64 (*.f64 y 9) z)

   1. Initial program 97.6%

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

      1. sub-neg 97.6%

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

      2. sub-neg 97.6%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

      1. +-commutative 95.3%

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

      2. associate-+r- 95.3%

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

      3. associate-*l* 95.4%

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

   5. Applied egg-rr 95.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -1 \cdot 10^{-128}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 2: 96.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;t_1 + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -1.3e+40)
     (+ t_1 (* z (* t (* y -9.0))))
     (+ t_1 (+ (* x 2.0) (* (* y z) (* t -9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.3e+40) {
		tmp = t_1 + (z * (t * (y * -9.0)));
	} else {
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -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) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-1.3d+40)) then
        tmp = t_1 + (z * (t * (y * (-9.0d0))))
    else
        tmp = t_1 + ((x * 2.0d0) + ((y * z) * (t * (-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 t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.3e+40) {
		tmp = t_1 + (z * (t * (y * -9.0)));
	} else {
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -1.3e+40:
		tmp = t_1 + (z * (t * (y * -9.0)))
	else:
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -9.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1.3e+40)
		tmp = Float64(t_1 + Float64(z * Float64(t * Float64(y * -9.0))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -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)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1.3e+40)
		tmp = t_1 + (z * (t * (y * -9.0)));
	else
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -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_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+40], N[(t$95$1 + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e40

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 83.0%

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

      4. associate-*l* 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in x around 0 69.9%

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

      1. sub-neg 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*r* 69.9%

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

      4. *-commutative 69.9%

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

      5. +-commutative 69.9%

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

      6. *-commutative 69.9%

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

      7. distribute-rgt-neg-in 69.9%

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

      8. *-commutative 69.9%

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

      9. associate-*r* 66.1%

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

      10. *-commutative 66.1%

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

      11. metadata-eval 66.1%

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

      12. associate-*r* 66.0%

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

      13. associate-*l* 73.6%

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

   6. Applied egg-rr 73.6%

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

   if -1.3e40 < z

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

      1. associate-*r* 97.5%

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

      2. cancel-sign-sub-inv 97.5%

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

      3. distribute-lft-neg-in 97.5%

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

      4. distribute-rgt-neg-in 97.5%

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

      5. metadata-eval 97.5%

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

      6. associate-*r* 97.4%

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

      7. *-commutative 97.4%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 97.4%

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

   5. Applied egg-rr 97.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 3: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+40}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -1e+40)
     (+ t_1 (- (* x 2.0) (* 9.0 (* z (* y t)))))
     (+ t_1 (+ (* x 2.0) (* (* y z) (* t -9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1e+40) {
		tmp = t_1 + ((x * 2.0) - (9.0 * (z * (y * t))));
	} else {
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -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) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-1d+40)) then
        tmp = t_1 + ((x * 2.0d0) - (9.0d0 * (z * (y * t))))
    else
        tmp = t_1 + ((x * 2.0d0) + ((y * z) * (t * (-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 t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1e+40) {
		tmp = t_1 + ((x * 2.0) - (9.0 * (z * (y * t))));
	} else {
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -1e+40:
		tmp = t_1 + ((x * 2.0) - (9.0 * (z * (y * t))))
	else:
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -9.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1e+40)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t)))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -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)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1e+40)
		tmp = t_1 + ((x * 2.0) - (9.0 * (z * (y * t))));
	else
		tmp = t_1 + ((x * 2.0) + ((y * z) * (t * -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_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+40], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000003e40

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 83.0%

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

      4. associate-*l* 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in y around 0 90.5%

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

      1. associate-*r* 94.3%

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

   6. Simplified 94.3%

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

   if -1.00000000000000003e40 < z

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

      1. associate-*r* 97.5%

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

      2. cancel-sign-sub-inv 97.5%

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

      3. distribute-lft-neg-in 97.5%

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

      4. distribute-rgt-neg-in 97.5%

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

      5. metadata-eval 97.5%

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

      6. associate-*r* 97.4%

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

      7. *-commutative 97.4%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 97.4%

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

   5. Applied egg-rr 97.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 4: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 6e+102)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* z t))))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

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+102) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 6d+102) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6e+102) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 6e+102:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 6e+102)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	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+102)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 6e+102], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.9999999999999996e102

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. sub-neg 96.6%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   if 5.9999999999999996e102 < z

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. sub-neg 93.2%

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

      3. associate-*l* 88.5%

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

      4. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around 0 73.2%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 5: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+102}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 6e+102)
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* 9.0 (* z t))))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

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+102) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 6d+102) then
        tmp = ((a * (27.0d0 * b)) + (x * 2.0d0)) - (y * (9.0d0 * (z * t)))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6e+102) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 6e+102:
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 6e+102)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(y * Float64(9.0 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	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+102)
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 6e+102], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.9999999999999996e102

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. sub-neg 96.6%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

      1. +-commutative 95.3%

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

      2. associate-+r- 95.3%

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

      3. associate-*l* 95.3%

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

   5. Applied egg-rr 95.3%

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

   if 5.9999999999999996e102 < z

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. sub-neg 93.2%

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

      3. associate-*l* 88.5%

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

      4. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around 0 73.2%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+102}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 6: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+100}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 (<= x -1.05e+100)
   (- (* x 2.0) (* 9.0 (* t (* y z))))
   (if (<= x 1.15e-104)
     (+ (* a (* 27.0 b)) (* z (* t (* y -9.0))))
     (+ (* 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 (x <= -1.05e+100) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else if (x <= 1.15e-104) {
		tmp = (a * (27.0 * b)) + (z * (t * (y * -9.0)));
	} else {
		tmp = (x * 2.0) + (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 (x <= (-1.05d+100)) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else if (x <= 1.15d-104) then
        tmp = (a * (27.0d0 * b)) + (z * (t * (y * (-9.0d0))))
    else
        tmp = (x * 2.0d0) + (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 (x <= -1.05e+100) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else if (x <= 1.15e-104) {
		tmp = (a * (27.0 * b)) + (z * (t * (y * -9.0)));
	} else {
		tmp = (x * 2.0) + (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 x <= -1.05e+100:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	elif x <= 1.15e-104:
		tmp = (a * (27.0 * b)) + (z * (t * (y * -9.0)))
	else:
		tmp = (x * 2.0) + (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 (x <= -1.05e+100)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	elseif (x <= 1.15e-104)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(z * Float64(t * Float64(y * -9.0))));
	else
		tmp = Float64(Float64(x * 2.0) + 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 (x <= -1.05e+100)
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	elseif (x <= 1.15e-104)
		tmp = (a * (27.0 * b)) + (z * (t * (y * -9.0)));
	else
		tmp = (x * 2.0) + (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[x, -1.05e+100], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-104], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0499999999999999e100

   1. Initial program 97.6%

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

      1. sub-neg 97.6%

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

      2. sub-neg 97.6%

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

      3. associate-*l* 84.6%

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

      4. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in a around 0 92.6%

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

   if -1.0499999999999999e100 < x < 1.15e-104

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around 0 87.8%

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

      1. sub-neg 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-*r* 87.7%

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

      4. *-commutative 87.7%

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

      5. +-commutative 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-rgt-neg-in 87.7%

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

      8. *-commutative 87.7%

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

      9. associate-*r* 88.4%

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

      10. *-commutative 88.4%

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

      11. metadata-eval 88.4%

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

      12. associate-*r* 88.4%

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

      13. associate-*l* 85.6%

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

   6. Applied egg-rr 85.6%

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

   if 1.15e-104 < x

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 94.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around 0 78.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+100}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;x \cdot 2 - t_2\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+71}:\\ \;\;\;\;t_1 - t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* 9.0 (* t (* y z)))))
   (if (<= x -5.6e+42)
     (- (* x 2.0) t_2)
     (if (<= x 8.6e+71) (- t_1 t_2) (+ (* x 2.0) t_1)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double tmp;
	if (x <= -5.6e+42) {
		tmp = (x * 2.0) - t_2;
	} else if (x <= 8.6e+71) {
		tmp = t_1 - t_2;
	} else {
		tmp = (x * 2.0) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = 9.0d0 * (t * (y * z))
    if (x <= (-5.6d+42)) then
        tmp = (x * 2.0d0) - t_2
    else if (x <= 8.6d+71) then
        tmp = t_1 - t_2
    else
        tmp = (x * 2.0d0) + t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double tmp;
	if (x <= -5.6e+42) {
		tmp = (x * 2.0) - t_2;
	} else if (x <= 8.6e+71) {
		tmp = t_1 - t_2;
	} else {
		tmp = (x * 2.0) + t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = 9.0 * (t * (y * z))
	tmp = 0
	if x <= -5.6e+42:
		tmp = (x * 2.0) - t_2
	elif x <= 8.6e+71:
		tmp = t_1 - t_2
	else:
		tmp = (x * 2.0) + t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (x <= -5.6e+42)
		tmp = Float64(Float64(x * 2.0) - t_2);
	elseif (x <= 8.6e+71)
		tmp = Float64(t_1 - t_2);
	else
		tmp = Float64(Float64(x * 2.0) + t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = 9.0 * (t * (y * z));
	tmp = 0.0;
	if (x <= -5.6e+42)
		tmp = (x * 2.0) - t_2;
	elseif (x <= 8.6e+71)
		tmp = t_1 - t_2;
	else
		tmp = (x * 2.0) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+42], N[(N[(x * 2.0), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, 8.6e+71], N[(t$95$1 - t$95$2), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5999999999999999e42

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. sub-neg 98.2%

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

      3. associate-*l* 88.1%

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

      4. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in a around 0 89.1%

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

   if -5.5999999999999999e42 < x < 8.59999999999999967e71

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 95.6%

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

      4. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around 0 86.0%

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

   if 8.59999999999999967e71 < x

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 87.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+71}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \left(z \cdot \left(9 \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= x -1.2e+78)
     (* x 2.0)
     (if (<= x -1.75e-86)
       (* y (* z (* 9.0 (- t))))
       (if (<= x -2.5e-175)
         t_1
         (if (<= x 5.5e-242)
           (* z (* t (* y -9.0)))
           (if (<= x 5.1e-5) t_1 (* x 2.0))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -1.2e+78) {
		tmp = x * 2.0;
	} else if (x <= -1.75e-86) {
		tmp = y * (z * (9.0 * -t));
	} else if (x <= -2.5e-175) {
		tmp = t_1;
	} else if (x <= 5.5e-242) {
		tmp = z * (t * (y * -9.0));
	} else if (x <= 5.1e-5) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (x <= (-1.2d+78)) then
        tmp = x * 2.0d0
    else if (x <= (-1.75d-86)) then
        tmp = y * (z * (9.0d0 * -t))
    else if (x <= (-2.5d-175)) then
        tmp = t_1
    else if (x <= 5.5d-242) then
        tmp = z * (t * (y * (-9.0d0)))
    else if (x <= 5.1d-5) then
        tmp = t_1
    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 t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -1.2e+78) {
		tmp = x * 2.0;
	} else if (x <= -1.75e-86) {
		tmp = y * (z * (9.0 * -t));
	} else if (x <= -2.5e-175) {
		tmp = t_1;
	} else if (x <= 5.5e-242) {
		tmp = z * (t * (y * -9.0));
	} else if (x <= 5.1e-5) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if x <= -1.2e+78:
		tmp = x * 2.0
	elif x <= -1.75e-86:
		tmp = y * (z * (9.0 * -t))
	elif x <= -2.5e-175:
		tmp = t_1
	elif x <= 5.5e-242:
		tmp = z * (t * (y * -9.0))
	elif x <= 5.1e-5:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -1.2e+78)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.75e-86)
		tmp = Float64(y * Float64(z * Float64(9.0 * Float64(-t))));
	elseif (x <= -2.5e-175)
		tmp = t_1;
	elseif (x <= 5.5e-242)
		tmp = Float64(z * Float64(t * Float64(y * -9.0)));
	elseif (x <= 5.1e-5)
		tmp = t_1;
	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)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -1.2e+78)
		tmp = x * 2.0;
	elseif (x <= -1.75e-86)
		tmp = y * (z * (9.0 * -t));
	elseif (x <= -2.5e-175)
		tmp = t_1;
	elseif (x <= 5.5e-242)
		tmp = z * (t * (y * -9.0));
	elseif (x <= 5.1e-5)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+78], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.75e-86], N[(y * N[(z * N[(9.0 * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-175], t$95$1, If[LessEqual[x, 5.5e-242], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-5], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1999999999999999e78 or 5.09999999999999996e-5 < x

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 90.3%

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

      4. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 64.1%

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

   if -1.1999999999999999e78 < x < -1.7500000000000001e-86

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. sub-neg 97.0%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. associate-*l* 47.7%

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

      3. associate-*r* 47.5%

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

      4. *-commutative 47.5%

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

      5. associate-*l* 47.7%

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

      6. *-commutative 47.7%

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

   6. Simplified 47.7%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. associate-*r* 47.7%

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

      4. *-commutative 47.7%

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

      5. metadata-eval 47.7%

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

      6. distribute-lft-neg-in 47.7%

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

      7. *-commutative 47.7%

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

      8. *-commutative 47.7%

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

      9. associate-*l* 47.6%

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

      10. associate-*r* 47.6%

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

      11. associate-*l* 47.5%

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

      12. *-commutative 47.5%

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

   8. Applied egg-rr 47.5%

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

   if -1.7500000000000001e-86 < x < -2.5e-175 or 5.4999999999999998e-242 < x < 5.09999999999999996e-5

   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. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 95.4%

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

      4. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-+r- 95.5%

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

      3. associate-*l* 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in a around inf 59.2%

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

   if -2.5e-175 < x < 5.4999999999999998e-242

   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. Step-by-step derivation

      1. sub-neg 92.9%

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

      2. sub-neg 92.9%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 55.5%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-*r* 53.3%

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

      3. *-commutative 53.3%

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

      4. associate-*r* 53.4%

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

      5. *-commutative 53.4%

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

      6. associate-*l* 55.0%

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

      7. *-commutative 55.0%

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

   7. Simplified 55.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \left(z \cdot \left(9 \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-175}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-5}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 9: 75.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-73} \lor \neg \left(a \leq 1.8 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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 (<= a -2.9e-73) (not (<= a 1.8e-152)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.9e-73) || !(a <= 1.8e-152)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.9d-73)) .or. (.not. (a <= 1.8d-152))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.9e-73) || !(a <= 1.8e-152)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.9e-73) or not (a <= 1.8e-152):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.9e-73) || !(a <= 1.8e-152))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.9e-73) || ~((a <= 1.8e-152)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.9e-73], N[Not[LessEqual[a, 1.8e-152]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9e-73 or 1.8e-152 < a

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 94.0%

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

      4. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 73.1%

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

   if -2.9e-73 < a < 1.8e-152

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. sub-neg 96.6%

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

      3. associate-*l* 94.4%

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

      4. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in a around 0 91.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-73} \lor \neg \left(a \leq 1.8 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 10: 47.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.28 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 0.00014:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= x -1.28e+73)
     (* x 2.0)
     (if (<= x -4.3e-175)
       t_1
       (if (<= x 9e-243)
         (* z (* t (* y -9.0)))
         (if (<= x 0.00014) t_1 (* x 2.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -1.28e+73) {
		tmp = x * 2.0;
	} else if (x <= -4.3e-175) {
		tmp = t_1;
	} else if (x <= 9e-243) {
		tmp = z * (t * (y * -9.0));
	} else if (x <= 0.00014) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (x <= (-1.28d+73)) then
        tmp = x * 2.0d0
    else if (x <= (-4.3d-175)) then
        tmp = t_1
    else if (x <= 9d-243) then
        tmp = z * (t * (y * (-9.0d0)))
    else if (x <= 0.00014d0) then
        tmp = t_1
    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 t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -1.28e+73) {
		tmp = x * 2.0;
	} else if (x <= -4.3e-175) {
		tmp = t_1;
	} else if (x <= 9e-243) {
		tmp = z * (t * (y * -9.0));
	} else if (x <= 0.00014) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if x <= -1.28e+73:
		tmp = x * 2.0
	elif x <= -4.3e-175:
		tmp = t_1
	elif x <= 9e-243:
		tmp = z * (t * (y * -9.0))
	elif x <= 0.00014:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -1.28e+73)
		tmp = Float64(x * 2.0);
	elseif (x <= -4.3e-175)
		tmp = t_1;
	elseif (x <= 9e-243)
		tmp = Float64(z * Float64(t * Float64(y * -9.0)));
	elseif (x <= 0.00014)
		tmp = t_1;
	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)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -1.28e+73)
		tmp = x * 2.0;
	elseif (x <= -4.3e-175)
		tmp = t_1;
	elseif (x <= 9e-243)
		tmp = z * (t * (y * -9.0));
	elseif (x <= 0.00014)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.28e+73], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -4.3e-175], t$95$1, If[LessEqual[x, 9e-243], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00014], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2800000000000001e73 or 1.3999999999999999e-4 < x

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. sub-neg 94.8%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 63.0%

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

   if -1.2800000000000001e73 < x < -4.29999999999999998e-175 or 9.00000000000000035e-243 < x < 1.3999999999999999e-4

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-+r- 95.9%

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

      3. associate-*l* 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in a around inf 52.9%

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

   if -4.29999999999999998e-175 < x < 9.00000000000000035e-243

   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. Step-by-step derivation

      1. sub-neg 92.9%

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

      2. sub-neg 92.9%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 55.5%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-*r* 53.3%

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

      3. *-commutative 53.3%

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

      4. associate-*r* 53.4%

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

      5. *-commutative 53.4%

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

      6. associate-*l* 55.0%

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

      7. *-commutative 55.0%

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

   7. Simplified 55.0%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-175}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 0.00014:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 11: 75.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 1.7 \cdot 10^{+90}\right):\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 (or (<= z -9.8e+33) (not (<= z 1.7e+90)))
   (* -9.0 (* z (* y t)))
   (+ (* 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 ((z <= -9.8e+33) || !(z <= 1.7e+90)) {
		tmp = -9.0 * (z * (y * t));
	} else {
		tmp = (x * 2.0) + (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 ((z <= (-9.8d+33)) .or. (.not. (z <= 1.7d+90))) then
        tmp = (-9.0d0) * (z * (y * t))
    else
        tmp = (x * 2.0d0) + (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 ((z <= -9.8e+33) || !(z <= 1.7e+90)) {
		tmp = -9.0 * (z * (y * t));
	} else {
		tmp = (x * 2.0) + (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 (z <= -9.8e+33) or not (z <= 1.7e+90):
		tmp = -9.0 * (z * (y * t))
	else:
		tmp = (x * 2.0) + (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 ((z <= -9.8e+33) || !(z <= 1.7e+90))
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	else
		tmp = Float64(Float64(x * 2.0) + 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 ((z <= -9.8e+33) || ~((z <= 1.7e+90)))
		tmp = -9.0 * (z * (y * t));
	else
		tmp = (x * 2.0) + (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[Or[LessEqual[z, -9.8e+33], N[Not[LessEqual[z, 1.7e+90]], $MachinePrecision]], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000027e33 or 1.70000000000000009e90 < z

   1. Initial program 92.0%

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

      1. sub-neg 92.0%

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

      2. sub-neg 92.0%

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

      3. associate-*l* 85.9%

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

      4. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-*r* 55.5%

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

   6. Simplified 55.5%

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

   if -9.80000000000000027e33 < z < 1.70000000000000009e90

   1. Initial program 98.5%

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

      1. sub-neg 98.5%

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

      2. sub-neg 98.5%

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

      3. associate-*l* 99.1%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 80.7%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 1.7 \cdot 10^{+90}\right):\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 12: 47.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-243}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+77)
   (* x 2.0)
   (if (<= x 6.5e-243)
     (* -9.0 (* t (* y z)))
     (if (<= x 1.3e-5) (* 27.0 (* a b)) (* x 2.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+77) {
		tmp = x * 2.0;
	} else if (x <= 6.5e-243) {
		tmp = -9.0 * (t * (y * z));
	} else if (x <= 1.3e-5) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+77)) then
        tmp = x * 2.0d0
    else if (x <= 6.5d-243) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (x <= 1.3d-5) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+77) {
		tmp = x * 2.0;
	} else if (x <= 6.5e-243) {
		tmp = -9.0 * (t * (y * z));
	} else if (x <= 1.3e-5) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+77:
		tmp = x * 2.0
	elif x <= 6.5e-243:
		tmp = -9.0 * (t * (y * z))
	elif x <= 1.3e-5:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+77)
		tmp = Float64(x * 2.0);
	elseif (x <= 6.5e-243)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (x <= 1.3e-5)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+77)
		tmp = x * 2.0;
	elseif (x <= 6.5e-243)
		tmp = -9.0 * (t * (y * z));
	elseif (x <= 1.3e-5)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+77], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 6.5e-243], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-5], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.8000000000000002e77 or 1.29999999999999992e-5 < x

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 90.3%

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

      4. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 64.1%

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

   if -8.8000000000000002e77 < x < 6.50000000000000043e-243

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 98.6%

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

      4. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around inf 46.4%

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

   if 6.50000000000000043e-243 < x < 1.29999999999999992e-5

   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. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 94.5%

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

      4. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-+r- 94.7%

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

      3. associate-*l* 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in a around inf 55.9%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-243}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 13: 47.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 0.00023:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+78)
   (* x 2.0)
   (if (<= x 2e-242)
     (* t (* (* y z) -9.0))
     (if (<= x 0.00023) (* 27.0 (* a b)) (* x 2.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+78) {
		tmp = x * 2.0;
	} else if (x <= 2e-242) {
		tmp = t * ((y * z) * -9.0);
	} else if (x <= 0.00023) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.5d+78)) then
        tmp = x * 2.0d0
    else if (x <= 2d-242) then
        tmp = t * ((y * z) * (-9.0d0))
    else if (x <= 0.00023d0) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+78) {
		tmp = x * 2.0;
	} else if (x <= 2e-242) {
		tmp = t * ((y * z) * -9.0);
	} else if (x <= 0.00023) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+78:
		tmp = x * 2.0
	elif x <= 2e-242:
		tmp = t * ((y * z) * -9.0)
	elif x <= 0.00023:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+78)
		tmp = Float64(x * 2.0);
	elseif (x <= 2e-242)
		tmp = Float64(t * Float64(Float64(y * z) * -9.0));
	elseif (x <= 0.00023)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.5e+78)
		tmp = x * 2.0;
	elseif (x <= 2e-242)
		tmp = t * ((y * z) * -9.0);
	elseif (x <= 0.00023)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+78], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 2e-242], N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00023], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999992e78 or 2.3000000000000001e-4 < x

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 90.3%

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

      4. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 64.1%

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

   if -2.49999999999999992e78 < x < 2e-242

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 98.6%

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

      4. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-*l* 46.4%

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

      3. associate-*r* 46.3%

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

      4. *-commutative 46.3%

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

      5. associate-*l* 46.5%

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

      6. *-commutative 46.5%

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

   6. Simplified 46.5%

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

   7. Taylor expanded in z around 0 46.4%

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

   if 2e-242 < x < 2.3000000000000001e-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. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 94.5%

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

      4. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-+r- 94.7%

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

      3. associate-*l* 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in a around inf 55.9%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 0.00023:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14: 47.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+71} \lor \neg \left(x \leq 0.00017\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 (or (<= x -1.46e+71) (not (<= x 0.00017))) (* 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 ((x <= -1.46e+71) || !(x <= 0.00017)) {
		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 ((x <= (-1.46d+71)) .or. (.not. (x <= 0.00017d0))) 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 ((x <= -1.46e+71) || !(x <= 0.00017)) {
		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 (x <= -1.46e+71) or not (x <= 0.00017):
		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 ((x <= -1.46e+71) || !(x <= 0.00017))
		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 ((x <= -1.46e+71) || ~((x <= 0.00017)))
		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[Or[LessEqual[x, -1.46e+71], N[Not[LessEqual[x, 0.00017]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4600000000000001e71 or 1.7e-4 < x

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. sub-neg 94.8%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 63.0%

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

   if -1.4600000000000001e71 < x < 1.7e-4

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. sub-neg 97.0%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-+r- 97.0%

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

      3. associate-*l* 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in a around inf 48.4%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+71} \lor \neg \left(x \leq 0.00017\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 15: 30.2% 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 96.0%

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

   1. sub-neg 96.0%

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

   2. sub-neg 96.0%

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

   3. associate-*l* 94.1%

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

   4. associate-*l* 94.1%

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

3. Simplified 94.1%

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

4. Taylor expanded in x around inf 34.7%

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

5. Final simplification 34.7%

   \[\leadsto x \cdot 2 \]

Developer target: 95.2% 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 2023310 
(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)))