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

Percentage Accurate: 95.5% → 98.4%

Time: 11.0s

Alternatives: 16

Speedup: 1.0×

• 28.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4 \cdot 10^{+98}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= t 4e+98)
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* 9.0 (* t z))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* -9.0 (* 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 (t <= 4e+98) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (t * z)));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (-9.0 * (y * z)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 4e+98)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(y * Float64(9.0 * Float64(t * z))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(-9.0 * Float64(y * z)))));
	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[t, 4e+98], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.99999999999999999e98

   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* 96.0%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. associate-*l* 96.0%

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

   5. Applied egg-rr 96.0%

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

   if 3.99999999999999999e98 < t

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-+r- 93.4%

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

      3. *-commutative 93.4%

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

      4. cancel-sign-sub-inv 93.4%

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

      5. associate-*r* 84.3%

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

      6. distribute-lft-neg-in 84.3%

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

      7. *-commutative 84.3%

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

      8. cancel-sign-sub-inv 84.3%

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

      9. associate-+r- 84.3%

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

      10. associate-*l* 84.3%

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

      11. fma-def 87.6%

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

      12. cancel-sign-sub-inv 87.6%

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

      13. fma-def 87.6%

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

      14. distribute-lft-neg-in 87.6%

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

      15. distribute-rgt-neg-in 87.6%

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

      16. *-commutative 87.6%

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

      17. associate-*r* 96.7%

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

      18. distribute-rgt-neg-out 96.7%

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

      19. *-commutative 96.7%

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

      20. associate-*r* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4 \cdot 10^{+98}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right)\right)\\ \end{array} \]

Alternative 2: 96.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Simplified 95.0%

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

4. Final simplification 95.0%

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

Alternative 3: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+150} \lor \neg \left(t_2 \leq 4 \cdot 10^{+170}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* t (* y z)))) (t_2 (* b (* a 27.0))))
   (if (or (<= t_2 -5e+150) (not (<= t_2 4e+170)))
     (- (* 27.0 (* a b)) t_1)
     (- (* x 2.0) t_1))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (t * (y * z));
	double t_2 = b * (a * 27.0);
	double tmp;
	if ((t_2 <= -5e+150) || !(t_2 <= 4e+170)) {
		tmp = (27.0 * (a * b)) - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * (t * (y * z))
    t_2 = b * (a * 27.0d0)
    if ((t_2 <= (-5d+150)) .or. (.not. (t_2 <= 4d+170))) then
        tmp = (27.0d0 * (a * b)) - t_1
    else
        tmp = (x * 2.0d0) - t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (t * (y * z));
	double t_2 = b * (a * 27.0);
	double tmp;
	if ((t_2 <= -5e+150) || !(t_2 <= 4e+170)) {
		tmp = (27.0 * (a * b)) - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (t * (y * z))
	t_2 = b * (a * 27.0)
	tmp = 0
	if (t_2 <= -5e+150) or not (t_2 <= 4e+170):
		tmp = (27.0 * (a * b)) - t_1
	else:
		tmp = (x * 2.0) - t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if ((t_2 <= -5e+150) || !(t_2 <= 4e+170))
		tmp = Float64(Float64(27.0 * Float64(a * b)) - t_1);
	else
		tmp = Float64(Float64(x * 2.0) - t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (t * (y * z));
	t_2 = b * (a * 27.0);
	tmp = 0.0;
	if ((t_2 <= -5e+150) || ~((t_2 <= 4e+170)))
		tmp = (27.0 * (a * b)) - t_1;
	else
		tmp = (x * 2.0) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+150], N[Not[LessEqual[t$95$2, 4e+170]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a 27) b) < -5.00000000000000009e150 or 4.00000000000000014e170 < (*.f64 (*.f64 a 27) b)

   1. Initial program 91.5%

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

      1. sub-neg 91.5%

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

      2. sub-neg 91.5%

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

      3. associate-*l* 90.0%

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

      4. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 86.1%

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

   if -5.00000000000000009e150 < (*.f64 (*.f64 a 27) b) < 4.00000000000000014e170

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 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. Taylor expanded in a around 0 86.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+150} \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+170}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ t_3 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+150}:\\ \;\;\;\;t_2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot 2 - t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_3\\ \end{array} \end{array} \]

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 (* b (* a 27.0)))
        (t_2 (* 27.0 (* a b)))
        (t_3 (* 9.0 (* t (* y z)))))
   (if (<= t_1 -5e+150)
     (- t_2 (* 9.0 (* y (* t z))))
     (if (<= t_1 4e+170) (- (* x 2.0) t_3) (- t_2 t_3)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double t_3 = 9.0 * (t * (y * z));
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = t_2 - (9.0 * (y * (t * z)));
	} else if (t_1 <= 4e+170) {
		tmp = (x * 2.0) - t_3;
	} else {
		tmp = t_2 - t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = 27.0d0 * (a * b)
    t_3 = 9.0d0 * (t * (y * z))
    if (t_1 <= (-5d+150)) then
        tmp = t_2 - (9.0d0 * (y * (t * z)))
    else if (t_1 <= 4d+170) then
        tmp = (x * 2.0d0) - t_3
    else
        tmp = t_2 - t_3
    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 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double t_3 = 9.0 * (t * (y * z));
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = t_2 - (9.0 * (y * (t * z)));
	} else if (t_1 <= 4e+170) {
		tmp = (x * 2.0) - t_3;
	} else {
		tmp = t_2 - t_3;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = 27.0 * (a * b)
	t_3 = 9.0 * (t * (y * z))
	tmp = 0
	if t_1 <= -5e+150:
		tmp = t_2 - (9.0 * (y * (t * z)))
	elif t_1 <= 4e+170:
		tmp = (x * 2.0) - t_3
	else:
		tmp = t_2 - t_3
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(27.0 * Float64(a * b))
	t_3 = Float64(9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (t_1 <= -5e+150)
		tmp = Float64(t_2 - Float64(9.0 * Float64(y * Float64(t * z))));
	elseif (t_1 <= 4e+170)
		tmp = Float64(Float64(x * 2.0) - t_3);
	else
		tmp = Float64(t_2 - t_3);
	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 = b * (a * 27.0);
	t_2 = 27.0 * (a * b);
	t_3 = 9.0 * (t * (y * z));
	tmp = 0.0;
	if (t_1 <= -5e+150)
		tmp = t_2 - (9.0 * (y * (t * z)));
	elseif (t_1 <= 4e+170)
		tmp = (x * 2.0) - t_3;
	else
		tmp = t_2 - t_3;
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+150], N[(t$95$2 - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+170], N[(N[(x * 2.0), $MachinePrecision] - t$95$3), $MachinePrecision], N[(t$95$2 - t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -5.00000000000000009e150

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around 0 89.0%

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

      1. expm1-log1p-u 18.7%

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

      2. expm1-udef 18.5%

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

      3. *-commutative 18.5%

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

      4. *-commutative 18.5%

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

      5. associate-*l* 18.5%

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

   6. Applied egg-rr 77.1%

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

      1. expm1-def 18.7%

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

      2. expm1-log1p 21.9%

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

      3. *-commutative 21.9%

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

      4. associate-*l* 19.2%

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

   8. Simplified 80.7%

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

   if -5.00000000000000009e150 < (*.f64 (*.f64 a 27) b) < 4.00000000000000014e170

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 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. Taylor expanded in a around 0 86.6%

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

   if 4.00000000000000014e170 < (*.f64 (*.f64 a 27) b)

   1. Initial program 83.0%

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

      1. sub-neg 83.0%

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

      2. sub-neg 83.0%

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

      3. associate-*l* 88.3%

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

      4. associate-*l* 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 x around 0 83.3%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+150}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 5: 79.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+150}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -5e+150)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (if (<= t_1 2e+201) (- (* x 2.0) (* 9.0 (* t (* y z)))) 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 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if (t_1 <= 2e+201) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (t_1 <= (-5d+150)) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else if (t_1 <= 2d+201) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if (t_1 <= 2e+201) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -5e+150:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	elif t_1 <= 2e+201:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -5e+150)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	elseif (t_1 <= 2e+201)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -5e+150)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	elseif (t_1 <= 2e+201)
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+150], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+201], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -5.00000000000000009e150

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around 0 83.8%

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

   if -5.00000000000000009e150 < (*.f64 (*.f64 a 27) b) < 2.00000000000000008e201

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. sub-neg 96.3%

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

      3. associate-*l* 95.5%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 85.1%

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

   if 2.00000000000000008e201 < (*.f64 (*.f64 a 27) b)

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. sub-neg 86.5%

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

      3. associate-*l* 86.4%

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

      4. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in a around inf 83.1%

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

      1. associate-*r* 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-*r* 83.3%

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

   6. Simplified 83.3%

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

      1. add-sqr-sqrt 83.2%

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

      2. pow2 83.2%

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

   8. Applied egg-rr 83.2%

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

      1. unpow2 83.2%

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

      2. add-sqr-sqrt 83.3%

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

      3. associate-*r* 83.1%

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

   10. Applied egg-rr 83.1%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+150}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 6: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+150}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -5e+150) (* 27.0 (* a b)) (if (<= t_1 4e+170) (* 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 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 4e+170) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (t_1 <= (-5d+150)) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 4d+170) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 4e+170) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -5e+150:
		tmp = 27.0 * (a * b)
	elif t_1 <= 4e+170:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -5e+150)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 4e+170)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -5e+150)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 4e+170)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+150], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+170], N[(x * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -5.00000000000000009e150

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 72.9%

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

   if -5.00000000000000009e150 < (*.f64 (*.f64 a 27) b) < 4.00000000000000014e170

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 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. Taylor expanded in x around inf 47.1%

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

   if 4.00000000000000014e170 < (*.f64 (*.f64 a 27) b)

   1. Initial program 83.0%

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

      1. sub-neg 83.0%

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

      2. sub-neg 83.0%

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

      3. associate-*l* 88.3%

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

      4. associate-*l* 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 inf 77.5%

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

      1. associate-*r* 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*r* 77.7%

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

   6. Simplified 77.7%

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

      1. add-sqr-sqrt 77.6%

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

      2. pow2 77.6%

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

   8. Applied egg-rr 77.6%

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

      1. unpow2 77.6%

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

      2. add-sqr-sqrt 77.7%

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

      3. associate-*r* 77.6%

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

   10. Applied egg-rr 77.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+150}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 7: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((t * z) * (y * 9.0d0)))
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 (a * (27.0 * b)) + ((x * 2.0) - ((t * z) * (y * 9.0)));
}

Python

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

Julia

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

MATLAB

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

Derivation

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* 93.9%

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

   4. associate-*l* 93.9%

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

3. Simplified 93.9%

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

4. Final simplification 93.9%

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

Alternative 8: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = ((a * (27.0d0 * b)) + (x * 2.0d0)) - (y * (9.0d0 * (t * z)))
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 ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (t * z)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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* 93.9%

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

   4. associate-*l* 93.9%

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

3. Simplified 93.9%

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

   1. +-commutative 93.9%

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

   2. associate-+r- 93.9%

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

   3. associate-*l* 94.3%

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

5. Applied egg-rr 94.3%

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

6. Final simplification 94.3%

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

Alternative 9: 48.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -4800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))))
   (if (<= z -4800000000000.0)
     t_1
     (if (<= z 2.1e-236) (* x 2.0) (if (<= z 4e-68) (* b (* a 27.0)) t_1)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -4800000000000.0) {
		tmp = t_1;
	} else if (z <= 2.1e-236) {
		tmp = x * 2.0;
	} else if (z <= 4e-68) {
		tmp = b * (a * 27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    if (z <= (-4800000000000.0d0)) then
        tmp = t_1
    else if (z <= 2.1d-236) then
        tmp = x * 2.0d0
    else if (z <= 4d-68) then
        tmp = b * (a * 27.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -4800000000000.0) {
		tmp = t_1;
	} else if (z <= 2.1e-236) {
		tmp = x * 2.0;
	} else if (z <= 4e-68) {
		tmp = b * (a * 27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -4800000000000.0:
		tmp = t_1
	elif z <= 2.1e-236:
		tmp = x * 2.0
	elif z <= 4e-68:
		tmp = b * (a * 27.0)
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -4800000000000.0)
		tmp = t_1;
	elseif (z <= 2.1e-236)
		tmp = Float64(x * 2.0);
	elseif (z <= 4e-68)
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -4800000000000.0)
		tmp = t_1;
	elseif (z <= 2.1e-236)
		tmp = x * 2.0;
	elseif (z <= 4e-68)
		tmp = b * (a * 27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4800000000000.0], t$95$1, If[LessEqual[z, 2.1e-236], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4e-68], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e12 or 4.00000000000000027e-68 < z

   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* 89.8%

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

      4. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in y around inf 48.2%

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

   if -4.8e12 < z < 2.09999999999999979e-236

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 98.8%

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

      4. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 44.7%

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

   if 2.09999999999999979e-236 < z < 4.00000000000000027e-68

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   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 inf 43.5%

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

      1. associate-*r* 43.5%

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

      2. *-commutative 43.5%

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

      3. associate-*r* 43.5%

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

   6. Simplified 43.5%

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

      1. add-sqr-sqrt 31.1%

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

      2. pow2 31.1%

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

   8. Applied egg-rr 31.1%

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

      1. unpow2 31.1%

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

      2. add-sqr-sqrt 43.5%

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

      3. associate-*r* 43.5%

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

   10. Applied egg-rr 43.5%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4800000000000:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 10: 49.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8200000:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-237}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 -8200000.0)
   (* -9.0 (* y (* t z)))
   (if (<= z 5.8e-237)
     (* x 2.0)
     (if (<= z 6.5e-63) (* b (* a 27.0)) (* -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 <= -8200000.0) {
		tmp = -9.0 * (y * (t * z));
	} else if (z <= 5.8e-237) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-63) {
		tmp = b * (a * 27.0);
	} else {
		tmp = -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 <= (-8200000.0d0)) then
        tmp = (-9.0d0) * (y * (t * z))
    else if (z <= 5.8d-237) then
        tmp = x * 2.0d0
    else if (z <= 6.5d-63) then
        tmp = b * (a * 27.0d0)
    else
        tmp = (-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 <= -8200000.0) {
		tmp = -9.0 * (y * (t * z));
	} else if (z <= 5.8e-237) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-63) {
		tmp = b * (a * 27.0);
	} else {
		tmp = -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 <= -8200000.0:
		tmp = -9.0 * (y * (t * z))
	elif z <= 5.8e-237:
		tmp = x * 2.0
	elif z <= 6.5e-63:
		tmp = b * (a * 27.0)
	else:
		tmp = -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 <= -8200000.0)
		tmp = Float64(-9.0 * Float64(y * Float64(t * z)));
	elseif (z <= 5.8e-237)
		tmp = Float64(x * 2.0);
	elseif (z <= 6.5e-63)
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = 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 <= -8200000.0)
		tmp = -9.0 * (y * (t * z));
	elseif (z <= 5.8e-237)
		tmp = x * 2.0;
	elseif (z <= 6.5e-63)
		tmp = b * (a * 27.0);
	else
		tmp = -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, -8200000.0], N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-237], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6.5e-63], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2e6

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. associate-*l* 84.9%

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

      4. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in y around inf 55.5%

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

      1. expm1-log1p-u 26.4%

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

      2. expm1-udef 26.3%

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

      3. *-commutative 26.3%

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

      4. *-commutative 26.3%

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

      5. associate-*l* 26.3%

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

   6. Applied egg-rr 26.3%

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

      1. expm1-def 26.4%

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

      2. expm1-log1p 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-*l* 45.9%

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

   8. Simplified 45.9%

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

   if -8.2e6 < z < 5.80000000000000022e-237

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 98.8%

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

      4. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 45.2%

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

   if 5.80000000000000022e-237 < z < 6.4999999999999998e-63

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   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 inf 43.5%

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

      1. associate-*r* 43.5%

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

      2. *-commutative 43.5%

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

      3. associate-*r* 43.5%

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

   6. Simplified 43.5%

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

      1. add-sqr-sqrt 31.1%

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

      2. pow2 31.1%

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

   8. Applied egg-rr 31.1%

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

      1. unpow2 31.1%

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

      2. add-sqr-sqrt 43.5%

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

      3. associate-*r* 43.5%

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

   10. Applied egg-rr 43.5%

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

   if 6.4999999999999998e-63 < z

   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* 93.2%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 43.9%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8200000:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-237}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 11: 49.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -450000000:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-248}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -450000000.0)
   (* -9.0 (* y (* t z)))
   (if (<= z 1.75e-248)
     (* x 2.0)
     (if (<= z 3.5e-65) (* b (* a 27.0)) (* t (* z (* y -9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -450000000.0) {
		tmp = -9.0 * (y * (t * z));
	} else if (z <= 1.75e-248) {
		tmp = x * 2.0;
	} else if (z <= 3.5e-65) {
		tmp = b * (a * 27.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-450000000.0d0)) then
        tmp = (-9.0d0) * (y * (t * z))
    else if (z <= 1.75d-248) then
        tmp = x * 2.0d0
    else if (z <= 3.5d-65) then
        tmp = b * (a * 27.0d0)
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -450000000.0) {
		tmp = -9.0 * (y * (t * z));
	} else if (z <= 1.75e-248) {
		tmp = x * 2.0;
	} else if (z <= 3.5e-65) {
		tmp = b * (a * 27.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -450000000.0:
		tmp = -9.0 * (y * (t * z))
	elif z <= 1.75e-248:
		tmp = x * 2.0
	elif z <= 3.5e-65:
		tmp = b * (a * 27.0)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -450000000.0)
		tmp = Float64(-9.0 * Float64(y * Float64(t * z)));
	elseif (z <= 1.75e-248)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.5e-65)
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -450000000.0)
		tmp = -9.0 * (y * (t * z));
	elseif (z <= 1.75e-248)
		tmp = x * 2.0;
	elseif (z <= 3.5e-65)
		tmp = b * (a * 27.0);
	else
		tmp = t * (z * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -450000000.0], N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-248], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.5e-65], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5e8

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. associate-*l* 84.9%

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

      4. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in y around inf 55.5%

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

      1. expm1-log1p-u 26.4%

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

      2. expm1-udef 26.3%

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

      3. *-commutative 26.3%

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

      4. *-commutative 26.3%

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

      5. associate-*l* 26.3%

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

   6. Applied egg-rr 26.3%

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

      1. expm1-def 26.4%

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

      2. expm1-log1p 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-*l* 45.9%

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

   8. Simplified 45.9%

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

   if -4.5e8 < z < 1.74999999999999991e-248

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 98.8%

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

      4. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 45.7%

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

   if 1.74999999999999991e-248 < z < 3.50000000000000005e-65

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 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 inf 45.6%

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

      1. associate-*r* 45.6%

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

      2. *-commutative 45.6%

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

      3. associate-*r* 45.6%

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

   6. Simplified 45.6%

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

      1. add-sqr-sqrt 33.6%

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

      2. pow2 33.6%

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

   8. Applied egg-rr 33.6%

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

      1. unpow2 33.6%

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

      2. add-sqr-sqrt 45.6%

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

      3. associate-*r* 45.6%

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

   10. Applied egg-rr 45.6%

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

   if 3.50000000000000005e-65 < z

   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* 93.2%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+r- 93.3%

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

      3. associate-*l* 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. associate-*r* 43.8%

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

      2. associate-*r* 46.0%

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

      3. *-commutative 46.0%

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

   8. Simplified 46.0%

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

   9. Taylor expanded in t around 0 43.9%

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

       1. associate-*r* 46.1%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 46.1%

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

       5. associate-*l* 43.9%

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

       6. *-commutative 43.9%

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

   11. Simplified 43.9%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -450000000:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-248}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 12: 49.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-241}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -48000000.0)
   (* z (* -9.0 (* y t)))
   (if (<= z 3.4e-241)
     (* x 2.0)
     (if (<= z 1.7e-68) (* b (* a 27.0)) (* t (* z (* y -9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -48000000.0) {
		tmp = z * (-9.0 * (y * t));
	} else if (z <= 3.4e-241) {
		tmp = x * 2.0;
	} else if (z <= 1.7e-68) {
		tmp = b * (a * 27.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-48000000.0d0)) then
        tmp = z * ((-9.0d0) * (y * t))
    else if (z <= 3.4d-241) then
        tmp = x * 2.0d0
    else if (z <= 1.7d-68) then
        tmp = b * (a * 27.0d0)
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -48000000.0) {
		tmp = z * (-9.0 * (y * t));
	} else if (z <= 3.4e-241) {
		tmp = x * 2.0;
	} else if (z <= 1.7e-68) {
		tmp = b * (a * 27.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -48000000.0:
		tmp = z * (-9.0 * (y * t))
	elif z <= 3.4e-241:
		tmp = x * 2.0
	elif z <= 1.7e-68:
		tmp = b * (a * 27.0)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -48000000.0)
		tmp = Float64(z * Float64(-9.0 * Float64(y * t)));
	elseif (z <= 3.4e-241)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.7e-68)
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -48000000.0)
		tmp = z * (-9.0 * (y * t));
	elseif (z <= 3.4e-241)
		tmp = x * 2.0;
	elseif (z <= 1.7e-68)
		tmp = b * (a * 27.0);
	else
		tmp = t * (z * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -48000000.0], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-241], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.7e-68], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e7

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. associate-*l* 84.9%

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

      4. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

      1. +-commutative 84.9%

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

      2. associate-+r- 84.9%

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

      3. associate-*l* 85.0%

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

   5. Applied egg-rr 85.0%

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

   6. Taylor expanded in y around inf 55.5%

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

      1. associate-*r* 55.5%

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

      2. associate-*r* 55.6%

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

      3. *-commutative 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in t around 0 55.6%

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

   if -4.8e7 < z < 3.3999999999999999e-241

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 98.8%

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

      4. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 45.7%

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

   if 3.3999999999999999e-241 < z < 1.70000000000000009e-68

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 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 inf 45.6%

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

      1. associate-*r* 45.6%

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

      2. *-commutative 45.6%

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

      3. associate-*r* 45.6%

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

   6. Simplified 45.6%

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

      1. add-sqr-sqrt 33.6%

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

      2. pow2 33.6%

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

   8. Applied egg-rr 33.6%

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

      1. unpow2 33.6%

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

      2. add-sqr-sqrt 45.6%

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

      3. associate-*r* 45.6%

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

   10. Applied egg-rr 45.6%

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

   if 1.70000000000000009e-68 < z

   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* 93.2%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+r- 93.3%

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

      3. associate-*l* 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. associate-*r* 43.8%

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

      2. associate-*r* 46.0%

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

      3. *-commutative 46.0%

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

   8. Simplified 46.0%

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

   9. Taylor expanded in t around 0 43.9%

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

       1. associate-*r* 46.1%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 46.1%

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

       5. associate-*l* 43.9%

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

       6. *-commutative 43.9%

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

   11. Simplified 43.9%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-241}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 13: 75.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+104}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.75e+60)
   (* z (* -9.0 (* y t)))
   (if (<= z 2.75e+104)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (* t (* z (* y -9.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+60) {
		tmp = z * (-9.0 * (y * t));
	} else if (z <= 2.75e+104) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.75d+60)) then
        tmp = z * ((-9.0d0) * (y * t))
    else if (z <= 2.75d+104) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+60) {
		tmp = z * (-9.0 * (y * t));
	} else if (z <= 2.75e+104) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.75e+60:
		tmp = z * (-9.0 * (y * t))
	elif z <= 2.75e+104:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.75e+60)
		tmp = Float64(z * Float64(-9.0 * Float64(y * t)));
	elseif (z <= 2.75e+104)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.75e+60)
		tmp = z * (-9.0 * (y * t));
	elseif (z <= 2.75e+104)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = t * (z * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.75e+60], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e+104], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7500000000000001e60

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. sub-neg 89.5%

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

      3. associate-*l* 81.8%

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

      4. associate-*l* 81.8%

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

   3. Simplified 81.8%

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

      1. +-commutative 81.8%

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

      2. associate-+r- 81.8%

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

      3. associate-*l* 81.9%

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

   5. Applied egg-rr 81.9%

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

   6. Taylor expanded in y around inf 59.7%

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

      1. associate-*r* 59.7%

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

      2. associate-*r* 59.7%

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

      3. *-commutative 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in t around 0 59.8%

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

   if -1.7500000000000001e60 < z < 2.75000000000000008e104

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. sub-neg 99.3%

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

      3. associate-*l* 98.7%

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

      4. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around 0 76.4%

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

   if 2.75000000000000008e104 < z

   1. Initial program 88.6%

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

      1. sub-neg 88.6%

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

      2. sub-neg 88.6%

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

      3. associate-*l* 88.8%

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

      4. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

      1. +-commutative 88.9%

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

      2. associate-+r- 88.9%

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

      3. associate-*l* 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in y around inf 57.3%

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

      1. associate-*r* 57.2%

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

      2. associate-*r* 61.7%

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

      3. *-commutative 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in t around 0 57.3%

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

       1. associate-*r* 61.7%

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

       2. associate-*r* 61.7%

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

       3. *-commutative 61.7%

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

       4. associate-*r* 61.7%

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

       5. associate-*l* 57.3%

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

       6. *-commutative 57.3%

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

   11. Simplified 57.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+104}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 14: 47.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-23} \lor \neg \left(x \leq 2.1 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 -4.8e-23) (not (<= x 2.1e+43))) (* 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 <= -4.8e-23) || !(x <= 2.1e+43)) {
		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 <= (-4.8d-23)) .or. (.not. (x <= 2.1d+43))) 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 <= -4.8e-23) || !(x <= 2.1e+43)) {
		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 <= -4.8e-23) or not (x <= 2.1e+43):
		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 <= -4.8e-23) || !(x <= 2.1e+43))
		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 <= -4.8e-23) || ~((x <= 2.1e+43)))
		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, -4.8e-23], N[Not[LessEqual[x, 2.1e+43]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999993e-23 or 2.10000000000000002e43 < x

   1. Initial program 93.8%

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

      1. sub-neg 93.8%

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

      2. sub-neg 93.8%

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

      3. associate-*l* 96.8%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 55.9%

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

   if -4.79999999999999993e-23 < x < 2.10000000000000002e43

   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* 90.8%

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

      4. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around inf 44.0%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-23} \lor \neg \left(x \leq 2.1 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 15: 47.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-29} \lor \neg \left(x \leq 1.08 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

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 -3e-29) (not (<= x 1.08e+42))) (* x 2.0) (* a (* 27.0 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 <= -3e-29) || !(x <= 1.08e+42)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * 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 <= (-3d-29)) .or. (.not. (x <= 1.08d+42))) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * 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 <= -3e-29) || !(x <= 1.08e+42)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -3e-29) or not (x <= 1.08e+42):
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -3e-29) || !(x <= 1.08e+42))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * 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 <= -3e-29) || ~((x <= 1.08e+42)))
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * 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, -3e-29], N[Not[LessEqual[x, 1.08e+42]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000003e-29 or 1.08e42 < x

   1. Initial program 93.8%

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

      1. sub-neg 93.8%

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

      2. sub-neg 93.8%

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

      3. associate-*l* 96.8%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 55.9%

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

   if -3.0000000000000003e-29 < x < 1.08e42

   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* 90.8%

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

      4. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around inf 44.0%

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

      1. associate-*r* 44.0%

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

      2. *-commutative 44.0%

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

      3. associate-*r* 44.0%

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

   6. Simplified 44.0%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-29} \lor \neg \left(x \leq 1.08 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 16: 31.1% 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 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* 93.9%

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

   4. associate-*l* 93.9%

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

3. Simplified 93.9%

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

4. Taylor expanded in x around inf 36.6%

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

5. Final simplification 36.6%

   \[\leadsto x \cdot 2 \]

Developer target: 95.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(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)))