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

Percentage Accurate: 95.3% → 98.5%

Time: 13.8s

Alternatives: 16

Speedup: 0.9×

• 28.1% 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: 95.3% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(\left(z \cdot y\right) \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= z 7.5e+32)
   (+ (- (* x 2.0) (* 9.0 (* y (* z t)))) (* a (* 27.0 b)))
   (fma a (* 27.0 b) (fma 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 <= 7.5e+32) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (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 <= 7.5e+32)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(Float64(z * y) * -9.0))));
	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[z, 7.5e+32], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.49999999999999959e32

   1. Initial program 95.9%

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

      1. sub-neg 95.9%

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

      2. sub-neg 95.9%

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

      3. associate-*l* 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* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-*l* 94.8%

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

      3. *-commutative 94.8%

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

   6. Simplified 94.8%

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

   if 7.49999999999999959e32 < z

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. associate-+r- 85.7%

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

      3. *-commutative 85.7%

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

      4. cancel-sign-sub-inv 85.7%

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

      5. associate-*r* 97.7%

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

      6. distribute-lft-neg-in 97.7%

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

      7. *-commutative 97.7%

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

      8. cancel-sign-sub-inv 97.7%

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

      9. associate-+r- 97.7%

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

      10. associate-*l* 97.7%

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

      11. fma-def 99.8%

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

      12. cancel-sign-sub-inv 99.8%

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

      13. fma-def 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. distribute-rgt-neg-in 99.8%

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

      16. *-commutative 99.8%

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

      17. associate-*r* 87.8%

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

      18. distribute-rgt-neg-out 87.8%

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

      19. *-commutative 87.8%

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

      20. associate-*r* 87.8%

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

   3. Simplified 87.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(\left(z \cdot y\right) \cdot -9\right)\right)\right)\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6.4 \cdot 10^{+56}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 6.4e+56)
   (+ (- (* x 2.0) (* 9.0 (* y (* z t)))) (* a (* 27.0 b)))
   (+ (* z (* -9.0 (* y t))) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6.4e+56) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 6.4d+56) then
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (z * t)))) + (a * (27.0d0 * b))
    else
        tmp = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6.4e+56) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 6.4e+56:
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b))
	else:
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 6.4e+56)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 6.4e+56)
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	else
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 6.4e+56], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.40000000000000007e56

   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* 95.4%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-*l* 94.9%

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

      3. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   if 6.40000000000000007e56 < z

   1. Initial program 85.0%

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

      1. sub-neg 85.0%

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

      2. sub-neg 85.0%

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

      3. associate-*l* 93.6%

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

      4. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around 0 69.1%

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

      1. expm1-log1p-u 43.7%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 43.7%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 43.7%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(z \cdot y\right)}\right)} - 1\right) \]

      4. associate-*r* 47.2%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot z\right) \cdot y}\right)} - 1\right) \]

   6. Applied egg-rr 47.2%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 47.3%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)\right)} \]

      2. expm1-log1p 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*l* 79.4%

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

   8. Simplified 79.4%

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

      1. sub-neg 79.4%

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

      2. +-commutative 79.4%

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

      3. distribute-lft-neg-in 79.4%

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

      4. metadata-eval 79.4%

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

      5. associate-*r* 79.4%

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

      6. *-commutative 79.4%

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

      7. associate-*l* 79.5%

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

   10. Applied egg-rr 79.5%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.4 \cdot 10^{+56}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq 6.1 \cdot 10^{+31}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(z \cdot y\right) \cdot \left(9 \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z 6.1e+31)
     (+ (- (* x 2.0) (* 9.0 (* y (* z t)))) t_1)
     (+ t_1 (- (* x 2.0) (* (* z y) (* 9.0 t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= 6.1e+31) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + t_1;
	} else {
		tmp = t_1 + ((x * 2.0) - ((z * y) * (9.0 * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= 6.1d+31) then
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (z * t)))) + t_1
    else
        tmp = t_1 + ((x * 2.0d0) - ((z * y) * (9.0d0 * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= 6.1e+31) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + t_1;
	} else {
		tmp = t_1 + ((x * 2.0) - ((z * y) * (9.0 * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= 6.1e+31:
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + t_1
	else:
		tmp = t_1 + ((x * 2.0) - ((z * y) * (9.0 * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= 6.1e+31)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(z * y) * Float64(9.0 * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= 6.1e+31)
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + t_1;
	else
		tmp = t_1 + ((x * 2.0) - ((z * y) * (9.0 * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 6.1e+31], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 6.10000000000000009e31

   1. Initial program 95.9%

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

      1. sub-neg 95.9%

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

      2. sub-neg 95.9%

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

      3. associate-*l* 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* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-*l* 94.8%

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

      3. *-commutative 94.8%

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

   6. Simplified 94.8%

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

   if 6.10000000000000009e31 < z

   1. Initial program 85.7%

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

      1. sub-neg 85.7%

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

      2. sub-neg 85.7%

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

      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 y around 0 85.7%

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

      1. associate-*r* 85.6%

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

   6. Simplified 85.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.1 \cdot 10^{+31}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(z \cdot y\right) \cdot \left(9 \cdot t\right)\right)\\ \end{array} \]

Alternative 4: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-123}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3e-123)
   (+ (- (* x 2.0) (* 9.0 (* y (* z t)))) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* t (* 9.0 (* z y)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-123) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3d-123)) then
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (z * t)))) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (t * (9.0d0 * (z * y)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-123) {
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3e-123:
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3e-123)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(z * y)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3e-123)
		tmp = ((x * 2.0) - (9.0 * (y * (z * t)))) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3e-123], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999984e-123

   1. Initial program 92.5%

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

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 90.4%

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

      4. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in y around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 90.3%

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

      3. *-commutative 90.3%

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

   6. Simplified 90.3%

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

   if -2.99999999999999984e-123 < z

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 94.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-123}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 5: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1000.0)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* 9.0 y) (* z t))))
   (+ (- (* x 2.0) (* t (* z (* 9.0 y)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1000.0) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((9.0 * y) * (z * t)));
	} else {
		tmp = ((x * 2.0) - (t * (z * (9.0 * y)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1000.0d0)) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((9.0d0 * y) * (z * t)))
    else
        tmp = ((x * 2.0d0) - (t * (z * (9.0d0 * y)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1000.0) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((9.0 * y) * (z * t)));
	} else {
		tmp = ((x * 2.0) - (t * (z * (9.0 * y)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1000.0:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((9.0 * y) * (z * t)))
	else:
		tmp = ((x * 2.0) - (t * (z * (9.0 * y)))) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(9.0 * y) * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(9.0 * y)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((9.0 * y) * (z * t)));
	else
		tmp = ((x * 2.0) - (t * (z * (9.0 * y)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1000.0], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   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* 86.5%

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

      4. associate-*l* 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%

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

   if -1e3 < z

   1. Initial program 95.6%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 6: 49.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-179}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-191}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (* -9.0 (* t (* z y)))))
   (if (<= z -1.45e-62)
     t_2
     (if (<= z -2.75e-179)
       (* x 2.0)
       (if (<= z -1.5e-259)
         t_1
         (if (<= z 2.25e-191) (* x 2.0) (if (<= z 3.3e-25) t_1 t_2)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = -9.0 * (t * (z * y));
	double tmp;
	if (z <= -1.45e-62) {
		tmp = t_2;
	} else if (z <= -2.75e-179) {
		tmp = x * 2.0;
	} else if (z <= -1.5e-259) {
		tmp = t_1;
	} else if (z <= 2.25e-191) {
		tmp = x * 2.0;
	} else if (z <= 3.3e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (-9.0d0) * (t * (z * y))
    if (z <= (-1.45d-62)) then
        tmp = t_2
    else if (z <= (-2.75d-179)) then
        tmp = x * 2.0d0
    else if (z <= (-1.5d-259)) then
        tmp = t_1
    else if (z <= 2.25d-191) then
        tmp = x * 2.0d0
    else if (z <= 3.3d-25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = -9.0 * (t * (z * y));
	double tmp;
	if (z <= -1.45e-62) {
		tmp = t_2;
	} else if (z <= -2.75e-179) {
		tmp = x * 2.0;
	} else if (z <= -1.5e-259) {
		tmp = t_1;
	} else if (z <= 2.25e-191) {
		tmp = x * 2.0;
	} else if (z <= 3.3e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = -9.0 * (t * (z * y))
	tmp = 0
	if z <= -1.45e-62:
		tmp = t_2
	elif z <= -2.75e-179:
		tmp = x * 2.0
	elif z <= -1.5e-259:
		tmp = t_1
	elif z <= 2.25e-191:
		tmp = x * 2.0
	elif z <= 3.3e-25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (z <= -1.45e-62)
		tmp = t_2;
	elseif (z <= -2.75e-179)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.5e-259)
		tmp = t_1;
	elseif (z <= 2.25e-191)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.3e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (z <= -1.45e-62)
		tmp = t_2;
	elseif (z <= -2.75e-179)
		tmp = x * 2.0;
	elseif (z <= -1.5e-259)
		tmp = t_1;
	elseif (z <= 2.25e-191)
		tmp = x * 2.0;
	elseif (z <= 3.3e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-62], t$95$2, If[LessEqual[z, -2.75e-179], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.5e-259], t$95$1, If[LessEqual[z, 2.25e-191], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.3e-25], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999993e-62 or 3.2999999999999998e-25 < z

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. sub-neg 89.8%

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

      3. associate-*l* 91.2%

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

      4. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 50.7%

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

   if -1.44999999999999993e-62 < z < -2.7500000000000001e-179 or -1.5000000000000001e-259 < z < 2.25000000000000004e-191

   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* 99.8%

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

      4. associate-*l* 99.7%

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

   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 x around inf 44.7%

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

   if -2.7500000000000001e-179 < z < -1.5000000000000001e-259 or 2.25000000000000004e-191 < z < 3.2999999999999998e-25

   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* 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* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 74.4%

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

   5. Taylor expanded in x around 0 49.9%

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

      1. associate-*r* 49.9%

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

      2. *-commutative 49.9%

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

   7. Simplified 49.9%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-62}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-179}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-259}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-191}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 7: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-180}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-192}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= z -3.7e-62)
     (* -9.0 (* z (* y t)))
     (if (<= z -8.5e-180)
       (* x 2.0)
       (if (<= z -1.02e-253)
         t_1
         (if (<= z 9.5e-192)
           (* x 2.0)
           (if (<= z 7.5e-23) t_1 (* -9.0 (* t (* z y))))))))))

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 (z <= -3.7e-62) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -8.5e-180) {
		tmp = x * 2.0;
	} else if (z <= -1.02e-253) {
		tmp = t_1;
	} else if (z <= 9.5e-192) {
		tmp = x * 2.0;
	} else if (z <= 7.5e-23) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 (z <= (-3.7d-62)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= (-8.5d-180)) then
        tmp = x * 2.0d0
    else if (z <= (-1.02d-253)) then
        tmp = t_1
    else if (z <= 9.5d-192) then
        tmp = x * 2.0d0
    else if (z <= 7.5d-23) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (t * (z * y))
    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 (z <= -3.7e-62) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -8.5e-180) {
		tmp = x * 2.0;
	} else if (z <= -1.02e-253) {
		tmp = t_1;
	} else if (z <= 9.5e-192) {
		tmp = x * 2.0;
	} else if (z <= 7.5e-23) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 z <= -3.7e-62:
		tmp = -9.0 * (z * (y * t))
	elif z <= -8.5e-180:
		tmp = x * 2.0
	elif z <= -1.02e-253:
		tmp = t_1
	elif z <= 9.5e-192:
		tmp = x * 2.0
	elif z <= 7.5e-23:
		tmp = t_1
	else:
		tmp = -9.0 * (t * (z * y))
	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 (z <= -3.7e-62)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= -8.5e-180)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.02e-253)
		tmp = t_1;
	elseif (z <= 9.5e-192)
		tmp = Float64(x * 2.0);
	elseif (z <= 7.5e-23)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	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 (z <= -3.7e-62)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= -8.5e-180)
		tmp = x * 2.0;
	elseif (z <= -1.02e-253)
		tmp = t_1;
	elseif (z <= 9.5e-192)
		tmp = x * 2.0;
	elseif (z <= 7.5e-23)
		tmp = t_1;
	else
		tmp = -9.0 * (t * (z * y));
	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[z, -3.7e-62], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e-180], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.02e-253], t$95$1, If[LessEqual[z, 9.5e-192], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 7.5e-23], t$95$1, N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6999999999999998e-62

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 90.9%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. *-commutative 51.3%

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

      3. associate-*l* 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   if -3.6999999999999998e-62 < z < -8.4999999999999993e-180 or -1.02e-253 < z < 9.4999999999999996e-192

   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* 99.8%

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

      4. associate-*l* 99.7%

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

   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 x around inf 45.5%

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

   if -8.4999999999999993e-180 < z < -1.02e-253 or 9.4999999999999996e-192 < z < 7.4999999999999998e-23

   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* 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* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 73.9%

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

   5. Taylor expanded in x around 0 50.8%

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

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if 7.4999999999999998e-23 < z

   1. Initial program 88.4%

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

      1. sub-neg 88.4%

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

      2. sub-neg 88.4%

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

      3. associate-*l* 95.1%

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

      4. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 50.0%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-180}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-253}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-192}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-23}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 8: 80.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-62} \lor \neg \left(z \leq 1.5 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.56e-62) (not (<= z 1.5e-28)))
   (+ (* z (* -9.0 (* y t))) (* x 2.0))
   (+ (* x 2.0) (* 27.0 (* a b)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.56e-62) || !(z <= 1.5e-28)) {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.56d-62)) .or. (.not. (z <= 1.5d-28))) then
        tmp = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.56e-62) || !(z <= 1.5e-28)) {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.56e-62) or not (z <= 1.5e-28):
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0)
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.56e-62) || !(z <= 1.5e-28))
		tmp = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.56e-62) || ~((z <= 1.5e-28)))
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.56e-62], N[Not[LessEqual[z, 1.5e-28]], $MachinePrecision]], N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.56000000000000009e-62 or 1.50000000000000001e-28 < z

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. sub-neg 89.8%

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

      3. associate-*l* 91.2%

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

      4. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around 0 74.5%

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

      1. expm1-log1p-u 50.9%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 47.2%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 47.2%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(z \cdot y\right)}\right)} - 1\right) \]

      4. associate-*r* 49.1%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot z\right) \cdot y}\right)} - 1\right) \]

   6. Applied egg-rr 49.1%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 52.7%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)\right)} \]

      2. expm1-log1p 75.9%

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

      3. *-commutative 75.9%

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

      4. associate-*l* 79.5%

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

   8. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. +-commutative 79.5%

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

      3. distribute-lft-neg-in 79.5%

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

      4. metadata-eval 79.5%

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

      5. associate-*r* 79.5%

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

      6. *-commutative 79.5%

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

      7. associate-*l* 79.6%

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

   10. Applied egg-rr 79.6%

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

   if -1.56000000000000009e-62 < z < 1.50000000000000001e-28

   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* 99.3%

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

      4. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 76.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-62} \lor \neg \left(z \leq 1.5 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 9: 80.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3e-62)
   (+ (* x 2.0) (* z (* t (* y -9.0))))
   (if (<= z 1.1e-22)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (+ (* z (* -9.0 (* y t))) (* x 2.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-62) {
		tmp = (x * 2.0) + (z * (t * (y * -9.0)));
	} else if (z <= 1.1e-22) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3d-62)) then
        tmp = (x * 2.0d0) + (z * (t * (y * (-9.0d0))))
    else if (z <= 1.1d-22) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-62) {
		tmp = (x * 2.0) + (z * (t * (y * -9.0)));
	} else if (z <= 1.1e-22) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3e-62:
		tmp = (x * 2.0) + (z * (t * (y * -9.0)))
	elif z <= 1.1e-22:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3e-62)
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(t * Float64(y * -9.0))));
	elseif (z <= 1.1e-22)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3e-62)
		tmp = (x * 2.0) + (z * (t * (y * -9.0)));
	elseif (z <= 1.1e-22)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3e-62], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-22], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e-62

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 88.4%

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

      4. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in a around 0 74.6%

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

      1. expm1-log1p-u 53.3%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 46.9%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 46.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(z \cdot y\right)}\right)} - 1\right) \]

      4. associate-*r* 48.1%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot z\right) \cdot y}\right)} - 1\right) \]

   6. Applied egg-rr 48.1%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 54.5%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)\right)} \]

      2. expm1-log1p 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*l* 78.5%

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

   8. Simplified 78.5%

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

      1. sub-neg 78.5%

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

      2. +-commutative 78.5%

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

      3. distribute-lft-neg-in 78.5%

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

      4. metadata-eval 78.5%

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

      5. associate-*r* 78.4%

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

      6. *-commutative 78.4%

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

      7. associate-*l* 78.5%

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

   10. Applied egg-rr 78.5%

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

       1. expm1-log1p-u 64.9%

          \[\leadsto z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(t \cdot y\right)\right)\right)} + 2 \cdot x \]

       2. expm1-udef 50.6%

          \[\leadsto z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(t \cdot y\right)\right)} - 1\right)} + 2 \cdot x \]

       3. *-commutative 50.6%

          \[\leadsto z \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot y\right) \cdot -9}\right)} - 1\right) + 2 \cdot x \]

       4. associate-*l* 50.6%

          \[\leadsto z \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{t \cdot \left(y \cdot -9\right)}\right)} - 1\right) + 2 \cdot x \]

   12. Applied egg-rr 50.6%

       \[\leadsto z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot -9\right)\right)} - 1\right)} + 2 \cdot x \]
   13. Step-by-step derivation

       1. expm1-def 64.9%

          \[\leadsto z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot -9\right)\right)\right)} + 2 \cdot x \]

       2. expm1-log1p 78.4%

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

       3. *-commutative 78.4%

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

   14. Simplified 78.4%

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

   if -3.0000000000000001e-62 < z < 1.1e-22

   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* 99.3%

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

      4. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 76.4%

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

   if 1.1e-22 < z

   1. Initial program 88.4%

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

      1. sub-neg 88.4%

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

      2. sub-neg 88.4%

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

      3. associate-*l* 95.1%

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

      4. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around 0 74.3%

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

      1. expm1-log1p-u 47.7%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 47.7%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 47.7%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(z \cdot y\right)}\right)} - 1\right) \]

      4. associate-*r* 50.4%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot z\right) \cdot y}\right)} - 1\right) \]

   6. Applied egg-rr 50.4%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 50.4%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)\right)} \]

      2. expm1-log1p 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-*l* 80.9%

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

   8. Simplified 80.9%

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

      1. sub-neg 80.9%

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

      2. +-commutative 80.9%

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

      3. distribute-lft-neg-in 80.9%

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

      4. metadata-eval 80.9%

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

      5. associate-*r* 80.9%

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

      6. *-commutative 80.9%

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

      7. associate-*l* 81.0%

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

   10. Applied egg-rr 81.0%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \]

Alternative 10: 81.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -1.9e-62)
   (+ (* x 2.0) (* z (* t (* y -9.0))))
   (if (<= z 3.8e-28)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e-62) {
		tmp = (x * 2.0) + (z * (t * (y * -9.0)));
	} else if (z <= 3.8e-28) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 <= (-1.9d-62)) then
        tmp = (x * 2.0d0) + (z * (t * (y * (-9.0d0))))
    else if (z <= 3.8d-28) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    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 <= -1.9e-62) {
		tmp = (x * 2.0) + (z * (t * (y * -9.0)));
	} else if (z <= 3.8e-28) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9e-62:
		tmp = (x * 2.0) + (z * (t * (y * -9.0)))
	elif z <= 3.8e-28:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e-62)
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(t * Float64(y * -9.0))));
	elseif (z <= 3.8e-28)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	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 <= -1.9e-62)
		tmp = (x * 2.0) + (z * (t * (y * -9.0)));
	elseif (z <= 3.8e-28)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	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, -1.9e-62], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-28], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000003e-62

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 88.4%

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

      4. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in a around 0 74.6%

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

      1. expm1-log1p-u 53.3%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 46.9%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 46.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(z \cdot y\right)}\right)} - 1\right) \]

      4. associate-*r* 48.1%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot z\right) \cdot y}\right)} - 1\right) \]

   6. Applied egg-rr 48.1%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 54.5%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot z\right) \cdot y\right)\right)} \]

      2. expm1-log1p 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*l* 78.5%

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

   8. Simplified 78.5%

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

      1. sub-neg 78.5%

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

      2. +-commutative 78.5%

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

      3. distribute-lft-neg-in 78.5%

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

      4. metadata-eval 78.5%

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

      5. associate-*r* 78.4%

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

      6. *-commutative 78.4%

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

      7. associate-*l* 78.5%

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

   10. Applied egg-rr 78.5%

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

       1. expm1-log1p-u 64.9%

          \[\leadsto z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(t \cdot y\right)\right)\right)} + 2 \cdot x \]

       2. expm1-udef 50.6%

          \[\leadsto z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(t \cdot y\right)\right)} - 1\right)} + 2 \cdot x \]

       3. *-commutative 50.6%

          \[\leadsto z \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot y\right) \cdot -9}\right)} - 1\right) + 2 \cdot x \]

       4. associate-*l* 50.6%

          \[\leadsto z \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{t \cdot \left(y \cdot -9\right)}\right)} - 1\right) + 2 \cdot x \]

   12. Applied egg-rr 50.6%

       \[\leadsto z \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot -9\right)\right)} - 1\right)} + 2 \cdot x \]
   13. Step-by-step derivation

       1. expm1-def 64.9%

          \[\leadsto z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot -9\right)\right)\right)} + 2 \cdot x \]

       2. expm1-log1p 78.4%

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

       3. *-commutative 78.4%

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

   14. Simplified 78.4%

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

   if -1.90000000000000003e-62 < z < 3.80000000000000009e-28

   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* 99.3%

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

      4. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 76.4%

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

   if 3.80000000000000009e-28 < z

   1. Initial program 88.4%

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

      1. sub-neg 88.4%

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

      2. sub-neg 88.4%

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

      3. associate-*l* 95.1%

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

      4. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around 0 74.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 11: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -1.55e-62)
   (+ (* z (* -9.0 (* y t))) (* b (* a 27.0)))
   (if (<= z 1.45e-28)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.55e-62) {
		tmp = (z * (-9.0 * (y * t))) + (b * (a * 27.0));
	} else if (z <= 1.45e-28) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 <= (-1.55d-62)) then
        tmp = (z * ((-9.0d0) * (y * t))) + (b * (a * 27.0d0))
    else if (z <= 1.45d-28) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    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 <= -1.55e-62) {
		tmp = (z * (-9.0 * (y * t))) + (b * (a * 27.0));
	} else if (z <= 1.45e-28) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.55e-62:
		tmp = (z * (-9.0 * (y * t))) + (b * (a * 27.0))
	elif z <= 1.45e-28:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.55e-62)
		tmp = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(b * Float64(a * 27.0)));
	elseif (z <= 1.45e-28)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	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 <= -1.55e-62)
		tmp = (z * (-9.0 * (y * t))) + (b * (a * 27.0));
	elseif (z <= 1.45e-28)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	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, -1.55e-62], N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-28], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e-62

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 88.4%

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

      4. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around 0 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 69.2%

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

      3. *-commutative 69.2%

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

      4. *-commutative 69.2%

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

      5. sub-neg 69.2%

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

      6. +-commutative 69.2%

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

      7. distribute-lft-neg-in 69.2%

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

      8. metadata-eval 69.2%

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

      9. associate-*r* 69.2%

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

      10. *-commutative 69.2%

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

      11. associate-*l* 69.3%

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

      12. associate-*r* 69.3%

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

      13. *-commutative 69.3%

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

   6. Applied egg-rr 69.3%

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

   if -1.55e-62 < z < 1.45000000000000006e-28

   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* 99.3%

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

      4. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 76.4%

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

   if 1.45000000000000006e-28 < z

   1. Initial program 88.4%

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

      1. sub-neg 88.4%

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

      2. sub-neg 88.4%

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

      3. associate-*l* 95.1%

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

      4. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around 0 74.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 12: 76.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -4.5e-6)
   (* y (* t (* z -9.0)))
   (if (<= z 1.95e-22) (+ (* x 2.0) (* 27.0 (* a b))) (* -9.0 (* t (* z y))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e-6) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 1.95e-22) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 <= (-4.5d-6)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 1.95d-22) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (-9.0d0) * (t * (z * y))
    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 <= -4.5e-6) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 1.95e-22) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.5e-6:
		tmp = y * (t * (z * -9.0))
	elif z <= 1.95e-22:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.5e-6)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 1.95e-22)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	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 <= -4.5e-6)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 1.95e-22)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = -9.0 * (t * (z * y));
	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, -4.5e-6], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-22], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000011e-6

   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. Taylor expanded in y around 0 89.4%

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

   3. Taylor expanded in y around inf 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-*r* 57.9%

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

      3. *-commutative 57.9%

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

      4. associate-*l* 57.9%

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

      5. associate-*l* 56.6%

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

   5. Simplified 56.6%

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

   if -4.50000000000000011e-6 < z < 1.94999999999999999e-22

   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* 99.4%

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

      4. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 78.3%

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

   if 1.94999999999999999e-22 < z

   1. Initial program 88.4%

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

      1. sub-neg 88.4%

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

      2. sub-neg 88.4%

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

      3. associate-*l* 95.1%

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

      4. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 50.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 13: 48.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-93} \lor \neg \left(b \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.2e-93) (not (<= b 3.7e-9))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.2e-93) || !(b <= 3.7e-9)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.2d-93)) .or. (.not. (b <= 3.7d-9))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.2e-93) || !(b <= 3.7e-9)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.2e-93) or not (b <= 3.7e-9):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.2e-93) || !(b <= 3.7e-9))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.2e-93) || ~((b <= 3.7e-9)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.2e-93], N[Not[LessEqual[b, 3.7e-9]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999996e-93 or 3.7e-9 < b

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. sub-neg 92.9%

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

      3. associate-*l* 94.0%

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

      4. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 48.4%

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

   if -2.19999999999999996e-93 < b < 3.7e-9

   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* 96.6%

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

      4. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 43.8%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-93} \lor \neg \left(b \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14: 48.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-92}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

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 (<= b -1.35e-92)
   (* 27.0 (* a b))
   (if (<= b 3.8e-9) (* 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 (b <= -1.35e-92) {
		tmp = 27.0 * (a * b);
	} else if (b <= 3.8e-9) {
		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 (b <= (-1.35d-92)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 3.8d-9) 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 (b <= -1.35e-92) {
		tmp = 27.0 * (a * b);
	} else if (b <= 3.8e-9) {
		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 b <= -1.35e-92:
		tmp = 27.0 * (a * b)
	elif b <= 3.8e-9:
		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 (b <= -1.35e-92)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 3.8e-9)
		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 (b <= -1.35e-92)
		tmp = 27.0 * (a * b);
	elseif (b <= 3.8e-9)
		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[LessEqual[b, -1.35e-92], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-9], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.34999999999999998e-92

   1. Initial program 92.5%

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

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 94.9%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 41.0%

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

   if -1.34999999999999998e-92 < b < 3.80000000000000011e-9

   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* 96.6%

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

      4. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 43.8%

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

   if 3.80000000000000011e-9 < b

   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. sub-neg 93.4%

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

      2. sub-neg 93.4%

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

      3. associate-*l* 93.1%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 56.2%

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

      1. associate-*r* 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*r* 56.2%

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

   6. Simplified 56.2%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-92}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 15: 48.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

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 (<= b -1.25e-92)
   (* b (* a 27.0))
   (if (<= b 2e-8) (* 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 (b <= -1.25e-92) {
		tmp = b * (a * 27.0);
	} else if (b <= 2e-8) {
		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 (b <= (-1.25d-92)) then
        tmp = b * (a * 27.0d0)
    else if (b <= 2d-8) 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 (b <= -1.25e-92) {
		tmp = b * (a * 27.0);
	} else if (b <= 2e-8) {
		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 b <= -1.25e-92:
		tmp = b * (a * 27.0)
	elif b <= 2e-8:
		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 (b <= -1.25e-92)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (b <= 2e-8)
		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 (b <= -1.25e-92)
		tmp = b * (a * 27.0);
	elseif (b <= 2e-8)
		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[LessEqual[b, -1.25e-92], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-8], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000003e-92

   1. Initial program 92.5%

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

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 94.9%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 68.3%

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

   5. Taylor expanded in x around 0 41.0%

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

      1. associate-*r* 41.0%

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

      2. *-commutative 41.0%

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

   7. Simplified 41.0%

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

   if -1.25000000000000003e-92 < b < 2e-8

   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* 96.6%

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

      4. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 43.8%

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

   if 2e-8 < b

   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. sub-neg 93.4%

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

      2. sub-neg 93.4%

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

      3. associate-*l* 93.1%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 56.2%

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

      1. associate-*r* 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*r* 56.2%

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

   6. Simplified 56.2%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 16: 31.8% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.0%

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

   1. sub-neg 94.0%

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

   2. sub-neg 94.0%

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

   3. associate-*l* 95.1%

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

   4. associate-*l* 94.7%

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

3. Simplified 94.7%

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

4. Taylor expanded in x around inf 31.6%

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

5. Final simplification 31.6%

   \[\leadsto x \cdot 2 \]

Developer target: 94.8% 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 2023305 
(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)))