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

Percentage Accurate: 95.7% → 99.0%

Time: 14.8s

Alternatives: 14

Speedup: 0.9×

• 27.0% 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: 95.7% 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: 99.0% accurate, 0.1× speedup

Math

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

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 1e-71)
   (- (+ (* 27.0 (* a b)) (* x 2.0)) (* y (* (* z 9.0) t)))
   (fma a (* 27.0 b) (fma x 2.0 (* (* z y) (* t -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 <= 1e-71) {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, ((z * y) * (t * -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 <= 1e-71)
		tmp = Float64(Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)) - Float64(y * Float64(Float64(z * 9.0) * t)));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(Float64(z * y) * Float64(t * -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, 1e-71], N[(N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(N[(z * y), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.9999999999999992e-72

   1. Initial program 95.0%

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

   3. Simplified 95.9%

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

      1. fma-udef 95.9%

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

      2. associate-*l* 95.4%

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

      3. fma-udef 95.4%

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

      4. associate-*r* 95.3%

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

      5. *-commutative 95.3%

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

      6. associate-+r+ 95.3%

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

      7. *-commutative 95.3%

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

      8. associate-*r* 95.3%

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

      9. associate-*l* 95.4%

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

      10. metadata-eval 95.4%

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

      11. distribute-lft-neg-in 95.4%

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

      12. *-commutative 95.4%

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

      13. *-commutative 95.4%

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

      14. associate-+r+ 95.4%

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

      15. cancel-sign-sub-inv 95.4%

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

      16. associate-+r- 95.4%

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

   5. Applied egg-rr 95.9%

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

   if 9.9999999999999992e-72 < z

   1. Initial program 90.6%

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

   3. Simplified 91.9%

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

4. Final simplification 94.6%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -1e-10)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* t (* z -9.0)))))
   (+ (- (* x 2.0) (* 9.0 (* z (* y t)))) (* b (* 27.0 a)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -1e-10) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (t * (z * -9.0)))));
	} else {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (b * (27.0 * a));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -1e-10)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(z * -9.0)))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t)))) + Float64(b * Float64(27.0 * a)));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -1e-10], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -1.00000000000000004e-10

   1. Initial program 90.8%

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

   3. Simplified 98.5%

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

   if -1.00000000000000004e-10 < (*.f64 y 9)

   1. Initial program 94.7%

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

      1. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-*r* 97.2%

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

   6. Simplified 97.2%

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

4. Final simplification 97.5%

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

Alternative 3: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(27 \cdot a\right)\\ \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* 27.0 a))))
   (if (<= (* y 9.0) -2e+131)
     (+ t_1 (- (* x 2.0) (* (* y 9.0) (* z t))))
     (+ (- (* x 2.0) (* 9.0 (* z (* y t)))) t_1))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double tmp;
	if ((y * 9.0) <= -2e+131) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (27.0d0 * a)
    if ((y * 9.0d0) <= (-2d+131)) then
        tmp = t_1 + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (z * (y * t)))) + t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double tmp;
	if ((y * 9.0) <= -2e+131) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (27.0 * a)
	tmp = 0
	if (y * 9.0) <= -2e+131:
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(27.0 * a))
	tmp = 0.0
	if (Float64(y * 9.0) <= -2e+131)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t)))) + t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (27.0 * a);
	tmp = 0.0;
	if ((y * 9.0) <= -2e+131)
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * 9.0), $MachinePrecision], -2e+131], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -1.9999999999999998e131

   1. Initial program 86.0%

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

      1. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   if -1.9999999999999998e131 < (*.f64 y 9)

   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. Step-by-step derivation

      1. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 95.0%

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

      1. *-commutative 95.0%

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

      2. associate-*r* 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \end{array} \]

Alternative 4: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6.6 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 6.6e+121)
   (+ (* b (* 27.0 a)) (- (* x 2.0) (* (* y 9.0) (* z t))))
   (- (* 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 <= 6.6e+121) {
		tmp = (b * (27.0 * a)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} 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 <= 6.6d+121) then
        tmp = (b * (27.0d0 * a)) + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    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 <= 6.6e+121) {
		tmp = (b * (27.0 * a)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} 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 <= 6.6e+121:
		tmp = (b * (27.0 * a)) + ((x * 2.0) - ((y * 9.0) * (z * t)))
	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 <= 6.6e+121)
		tmp = Float64(Float64(b * Float64(27.0 * a)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(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 <= 6.6e+121)
		tmp = (b * (27.0 * a)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	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, 6.6e+121], N[(N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.59999999999999958e121

   1. Initial program 95.3%

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

      1. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   if 6.59999999999999958e121 < z

   1. Initial program 80.3%

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

      1. associate-*l* 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in a around 0 73.9%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.6 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 5: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{-102}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

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 1.6e-102)
   (- (+ (* 27.0 (* a b)) (* x 2.0)) (* y (* (* z 9.0) t)))
   (+ (- (* x 2.0) (* 9.0 (* z (* y t)))) (* b (* 27.0 a)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.6e-102) {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	} else {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (b * (27.0 * a));
	}
	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 <= 1.6d-102) then
        tmp = ((27.0d0 * (a * b)) + (x * 2.0d0)) - (y * ((z * 9.0d0) * t))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (z * (y * t)))) + (b * (27.0d0 * a))
    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 <= 1.6e-102) {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	} else {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (b * (27.0 * a));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.6e-102:
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t))
	else:
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (b * (27.0 * a))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.6e-102)
		tmp = Float64(Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)) - Float64(y * Float64(Float64(z * 9.0) * t)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t)))) + Float64(b * Float64(27.0 * a)));
	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 <= 1.6e-102)
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	else
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (b * (27.0 * a));
	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, 1.6e-102], N[(N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.59999999999999993e-102

   1. Initial program 94.8%

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

   3. Simplified 95.7%

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

      1. fma-udef 95.7%

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

      2. associate-*l* 95.2%

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

      3. fma-udef 95.2%

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

      4. associate-*r* 95.2%

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

      5. *-commutative 95.2%

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

      6. associate-+r+ 95.2%

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

      7. *-commutative 95.2%

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

      8. associate-*r* 95.2%

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

      9. associate-*l* 95.2%

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

      10. metadata-eval 95.2%

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

      11. distribute-lft-neg-in 95.2%

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

      12. *-commutative 95.2%

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

      13. *-commutative 95.2%

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

      14. associate-+r+ 95.2%

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

      15. cancel-sign-sub-inv 95.2%

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

      16. associate-+r- 95.2%

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

   5. Applied egg-rr 95.8%

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

   if 1.59999999999999993e-102 < z

   1. Initial program 91.2%

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

      1. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around 0 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*r* 94.6%

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

   6. Simplified 94.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{-102}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \end{array} \]

Alternative 6: 44.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -62000000000000 \lor \neg \left(y \leq -3.2 \cdot 10^{-53}\right) \land y \leq -2.25 \cdot 10^{-113}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))))
   (if (<= y -4.1e+138)
     t_1
     (if (<= y -1.45e+112)
       (* x 2.0)
       (if (<= y -6.2e+106)
         t_1
         (if (or (<= y -62000000000000.0)
                 (and (not (<= y -3.2e-53)) (<= y -2.25e-113)))
           (* 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 t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (y <= -4.1e+138) {
		tmp = t_1;
	} else if (y <= -1.45e+112) {
		tmp = x * 2.0;
	} else if (y <= -6.2e+106) {
		tmp = t_1;
	} else if ((y <= -62000000000000.0) || (!(y <= -3.2e-53) && (y <= -2.25e-113))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    if (y <= (-4.1d+138)) then
        tmp = t_1
    else if (y <= (-1.45d+112)) then
        tmp = x * 2.0d0
    else if (y <= (-6.2d+106)) then
        tmp = t_1
    else if ((y <= (-62000000000000.0d0)) .or. (.not. (y <= (-3.2d-53))) .and. (y <= (-2.25d-113))) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (y <= -4.1e+138) {
		tmp = t_1;
	} else if (y <= -1.45e+112) {
		tmp = x * 2.0;
	} else if (y <= -6.2e+106) {
		tmp = t_1;
	} else if ((y <= -62000000000000.0) || (!(y <= -3.2e-53) && (y <= -2.25e-113))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	tmp = 0
	if y <= -4.1e+138:
		tmp = t_1
	elif y <= -1.45e+112:
		tmp = x * 2.0
	elif y <= -6.2e+106:
		tmp = t_1
	elif (y <= -62000000000000.0) or (not (y <= -3.2e-53) and (y <= -2.25e-113)):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (y <= -4.1e+138)
		tmp = t_1;
	elseif (y <= -1.45e+112)
		tmp = Float64(x * 2.0);
	elseif (y <= -6.2e+106)
		tmp = t_1;
	elseif ((y <= -62000000000000.0) || (!(y <= -3.2e-53) && (y <= -2.25e-113)))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (y <= -4.1e+138)
		tmp = t_1;
	elseif (y <= -1.45e+112)
		tmp = x * 2.0;
	elseif (y <= -6.2e+106)
		tmp = t_1;
	elseif ((y <= -62000000000000.0) || (~((y <= -3.2e-53)) && (y <= -2.25e-113)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+138], t$95$1, If[LessEqual[y, -1.45e+112], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -6.2e+106], t$95$1, If[Or[LessEqual[y, -62000000000000.0], And[N[Not[LessEqual[y, -3.2e-53]], $MachinePrecision], LessEqual[y, -2.25e-113]]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e138 or -1.4500000000000001e112 < y < -6.1999999999999999e106

   1. Initial program 84.0%

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

   3. Simplified 97.1%

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

      1. fma-udef 94.3%

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

      2. associate-*l* 91.9%

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

      3. fma-udef 91.9%

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

      4. associate-*r* 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-+r+ 91.6%

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

      7. *-commutative 91.6%

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

      8. associate-*r* 91.9%

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

      9. associate-*l* 91.9%

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

      10. metadata-eval 91.9%

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

      11. distribute-lft-neg-in 91.9%

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

      12. *-commutative 91.9%

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

      13. *-commutative 91.9%

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

      14. associate-+r+ 91.9%

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

      15. cancel-sign-sub-inv 91.9%

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

      16. associate-+r- 91.9%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in y around inf 63.4%

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

   if -4.0999999999999998e138 < y < -1.4500000000000001e112 or -6.1999999999999999e106 < y < -6.2e13 or -3.2000000000000001e-53 < y < -2.2500000000000001e-113

   1. Initial program 97.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 40.7%

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

   if -6.2e13 < y < -3.2000000000000001e-53 or -2.2500000000000001e-113 < y

   1. Initial program 94.4%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in a around inf 37.0%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -62000000000000 \lor \neg \left(y \leq -3.2 \cdot 10^{-53}\right) \land y \leq -2.25 \cdot 10^{-113}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 45.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+106}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -2100000000000 \lor \neg \left(y \leq -3.1 \cdot 10^{-53}\right) \land y \leq -1.86 \cdot 10^{-115}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.1e+138)
   (* y (* -9.0 (* z t)))
   (if (<= y -1.45e+112)
     (* x 2.0)
     (if (<= y -6.8e+106)
       (* -9.0 (* t (* z y)))
       (if (or (<= y -2100000000000.0)
               (and (not (<= y -3.1e-53)) (<= y -1.86e-115)))
         (* 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 (y <= -4.1e+138) {
		tmp = y * (-9.0 * (z * t));
	} else if (y <= -1.45e+112) {
		tmp = x * 2.0;
	} else if (y <= -6.8e+106) {
		tmp = -9.0 * (t * (z * y));
	} else if ((y <= -2100000000000.0) || (!(y <= -3.1e-53) && (y <= -1.86e-115))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.1d+138)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (y <= (-1.45d+112)) then
        tmp = x * 2.0d0
    else if (y <= (-6.8d+106)) then
        tmp = (-9.0d0) * (t * (z * y))
    else if ((y <= (-2100000000000.0d0)) .or. (.not. (y <= (-3.1d-53))) .and. (y <= (-1.86d-115))) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.1e+138) {
		tmp = y * (-9.0 * (z * t));
	} else if (y <= -1.45e+112) {
		tmp = x * 2.0;
	} else if (y <= -6.8e+106) {
		tmp = -9.0 * (t * (z * y));
	} else if ((y <= -2100000000000.0) || (!(y <= -3.1e-53) && (y <= -1.86e-115))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.1e+138:
		tmp = y * (-9.0 * (z * t))
	elif y <= -1.45e+112:
		tmp = x * 2.0
	elif y <= -6.8e+106:
		tmp = -9.0 * (t * (z * y))
	elif (y <= -2100000000000.0) or (not (y <= -3.1e-53) and (y <= -1.86e-115)):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.1e+138)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (y <= -1.45e+112)
		tmp = Float64(x * 2.0);
	elseif (y <= -6.8e+106)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif ((y <= -2100000000000.0) || (!(y <= -3.1e-53) && (y <= -1.86e-115)))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.1e+138)
		tmp = y * (-9.0 * (z * t));
	elseif (y <= -1.45e+112)
		tmp = x * 2.0;
	elseif (y <= -6.8e+106)
		tmp = -9.0 * (t * (z * y));
	elseif ((y <= -2100000000000.0) || (~((y <= -3.1e-53)) && (y <= -1.86e-115)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.1e+138], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e+112], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -6.8e+106], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2100000000000.0], And[N[Not[LessEqual[y, -3.1e-53]], $MachinePrecision], LessEqual[y, -1.86e-115]]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.0999999999999998e138

   1. Initial program 83.1%

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

   3. Simplified 97.0%

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

      1. fma-udef 94.0%

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

      2. associate-*l* 91.4%

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

      3. fma-udef 91.4%

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

      4. associate-*r* 91.1%

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

      5. *-commutative 91.1%

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

      6. associate-+r+ 91.1%

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

      7. *-commutative 91.1%

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

      8. associate-*r* 91.4%

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

      9. associate-*l* 91.5%

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

      10. metadata-eval 91.5%

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

      11. distribute-lft-neg-in 91.5%

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

      12. *-commutative 91.5%

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

      13. *-commutative 91.5%

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

      14. associate-+r+ 91.5%

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

      15. cancel-sign-sub-inv 91.5%

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

      16. associate-+r- 91.5%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*r* 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-*l* 66.8%

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

      5. *-commutative 66.8%

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

      6. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   if -4.0999999999999998e138 < y < -1.4500000000000001e112 or -6.79999999999999989e106 < y < -2.1e12 or -3.10000000000000015e-53 < y < -1.86e-115

   1. Initial program 97.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 40.7%

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

   if -1.4500000000000001e112 < y < -6.79999999999999989e106

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-udef 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

      7. *-commutative 100.0%

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

      8. associate-*r* 100.0%

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

      9. associate-*l* 100.0%

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

      10. metadata-eval 100.0%

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

      11. distribute-lft-neg-in 100.0%

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

      12. *-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-+r+ 100.0%

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

      15. cancel-sign-sub-inv 100.0%

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

      16. associate-+r- 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 50.2%

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

   if -2.1e12 < y < -3.10000000000000015e-53 or -1.86e-115 < y

   1. Initial program 94.4%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in a around inf 37.0%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+106}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -2100000000000 \lor \neg \left(y \leq -3.1 \cdot 10^{-53}\right) \land y \leq -1.86 \cdot 10^{-115}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-120}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.9e-7)
   (+ (* 27.0 (* a b)) (* x 2.0))
   (if (<= a 3.5e-120)
     (- (* x 2.0) (* y (* z (* 9.0 t))))
     (+ (* a (* 27.0 b)) (* -9.0 (* z (* y t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.9e-7) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if (a <= 3.5e-120) {
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	} else {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.9d-7)) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else if (a <= 3.5d-120) then
        tmp = (x * 2.0d0) - (y * (z * (9.0d0 * t)))
    else
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (z * (y * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.9e-7) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if (a <= 3.5e-120) {
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	} else {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.9e-7:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	elif a <= 3.5e-120:
		tmp = (x * 2.0) - (y * (z * (9.0 * t)))
	else:
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.9e-7)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	elseif (a <= 3.5e-120)
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(z * Float64(9.0 * t))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.9e-7)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	elseif (a <= 3.5e-120)
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	else
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.9e-7], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-120], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8999999999999998e-7

   1. Initial program 94.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 85.6%

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

   if -2.8999999999999998e-7 < a < 3.5e-120

   1. Initial program 95.2%

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

      1. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around 0 82.7%

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

      1. pow1 82.7%

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

      2. *-commutative 82.7%

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

      3. associate-*l* 78.7%

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

   6. Applied egg-rr 78.7%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-*r* 82.7%

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

      2. *-commutative 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*r* 78.7%

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

   9. Simplified 78.7%

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

   if 3.5e-120 < a

   1. Initial program 91.4%

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

      1. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 63.4%

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

      1. cancel-sign-sub-inv 63.4%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*l* 63.4%

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

      5. metadata-eval 63.4%

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

      6. associate-*r* 66.2%

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

      7. *-commutative 66.2%

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

      8. *-commutative 66.2%

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

   6. Applied egg-rr 66.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-120}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 77.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-7} \lor \neg \left(a \leq 4.9 \cdot 10^{-30}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (or (<= a -4.6e-7) (not (<= a 4.9e-30)))
   (+ (* 27.0 (* a b)) (* x 2.0))
   (- (* 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 ((a <= -4.6e-7) || !(a <= 4.9e-30)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} 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 ((a <= (-4.6d-7)) .or. (.not. (a <= 4.9d-30))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    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 ((a <= -4.6e-7) || !(a <= 4.9e-30)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} 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 (a <= -4.6e-7) or not (a <= 4.9e-30):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	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 ((a <= -4.6e-7) || !(a <= 4.9e-30))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	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 ((a <= -4.6e-7) || ~((a <= 4.9e-30)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	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[Or[LessEqual[a, -4.6e-7], N[Not[LessEqual[a, 4.9e-30]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $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 2 regimes

2. if a < -4.5999999999999999e-7 or 4.89999999999999971e-30 < a

   1. Initial program 92.9%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 74.6%

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

   if -4.5999999999999999e-7 < a < 4.89999999999999971e-30

   1. Initial program 94.3%

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

      1. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around 0 81.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-7} \lor \neg \left(a \leq 4.9 \cdot 10^{-30}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 10: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-7} \lor \neg \left(a \leq 1.08 \cdot 10^{-38}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\\ \end{array} \end{array} \]

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
 (if (or (<= a -1.55e-7) (not (<= a 1.08e-38)))
   (+ (* 27.0 (* a b)) (* x 2.0))
   (- (* x 2.0) (* y (* z (* 9.0 t))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.55e-7) || !(a <= 1.08e-38)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (y * (z * (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) :: tmp
    if ((a <= (-1.55d-7)) .or. (.not. (a <= 1.08d-38))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (y * (z * (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 tmp;
	if ((a <= -1.55e-7) || !(a <= 1.08e-38)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.55e-7) or not (a <= 1.08e-38):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (y * (z * (9.0 * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.55e-7) || !(a <= 1.08e-38))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(z * 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)
	tmp = 0.0;
	if ((a <= -1.55e-7) || ~((a <= 1.08e-38)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (y * (z * (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_] := If[Or[LessEqual[a, -1.55e-7], N[Not[LessEqual[a, 1.08e-38]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e-7 or 1.08e-38 < a

   1. Initial program 92.9%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 74.6%

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

   if -1.55e-7 < a < 1.08e-38

   1. Initial program 94.3%

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

      1. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around 0 81.6%

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

      1. pow1 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*l* 79.9%

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

   6. Applied egg-rr 79.9%

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

   7. Taylor expanded in y around 0 81.6%

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

      1. associate-*r* 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*r* 79.8%

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

   9. Simplified 79.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-7} \lor \neg \left(a \leq 1.08 \cdot 10^{-38}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 76.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

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 -1.1e-16)
   (* y (* t (* z -9.0)))
   (if (<= z 2.5e+38) (+ (* 27.0 (* a b)) (* x 2.0)) (* (* z y) (* t -9.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e-16) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 2.5e+38) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (z * y) * (t * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.1d-16)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 2.5d+38) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (z * y) * (t * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e-16) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 2.5e+38) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (z * y) * (t * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.1e-16:
		tmp = y * (t * (z * -9.0))
	elif z <= 2.5e+38:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (z * y) * (t * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.1e-16)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 2.5e+38)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(z * y) * Float64(t * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.1e-16)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 2.5e+38)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (z * y) * (t * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.1e-16], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+38], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-16

   1. Initial program 88.8%

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

   3. Simplified 91.4%

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

      1. fma-udef 91.4%

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

      2. associate-*l* 90.1%

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

      3. fma-udef 90.1%

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

      4. associate-*r* 90.1%

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

      5. *-commutative 90.1%

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

      6. associate-+r+ 90.1%

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

      7. *-commutative 90.1%

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

      8. associate-*r* 90.1%

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

      9. associate-*l* 90.1%

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

      10. metadata-eval 90.1%

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

      11. distribute-lft-neg-in 90.1%

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

      12. *-commutative 90.1%

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

      13. *-commutative 90.1%

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

      14. associate-+r+ 90.1%

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

      15. cancel-sign-sub-inv 90.1%

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

      16. associate-+r- 90.1%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in y around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. associate-*r* 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-*l* 44.4%

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

      5. *-commutative 44.4%

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

      6. *-commutative 44.4%

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

   8. Simplified 44.4%

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

      1. expm1-log1p-u 21.8%

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

      2. expm1-udef 17.1%

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

      3. associate-*r* 17.1%

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

      4. *-commutative 17.1%

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

      5. *-commutative 17.1%

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

   10. Applied egg-rr 17.1%

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

       1. expm1-def 21.8%

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

       2. expm1-log1p 44.4%

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

       3. associate-*r* 44.4%

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

       4. *-commutative 44.4%

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

       5. associate-*l* 44.4%

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

   12. Simplified 44.4%

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

   if -1.1e-16 < z < 2.49999999999999985e38

   1. Initial program 99.4%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 81.1%

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

   if 2.49999999999999985e38 < z

   1. Initial program 86.3%

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

   3. Simplified 91.6%

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

      1. fma-udef 89.9%

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

      2. associate-*l* 89.8%

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

      3. fma-udef 89.8%

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

      4. associate-*r* 89.8%

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

      5. *-commutative 89.8%

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

      6. associate-+r+ 89.8%

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

      7. *-commutative 89.8%

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

      8. associate-*r* 89.8%

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

      9. associate-*l* 89.9%

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

      10. metadata-eval 89.9%

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

      11. distribute-lft-neg-in 89.9%

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

      12. *-commutative 89.9%

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

      13. *-commutative 89.9%

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

      14. associate-+r+ 89.9%

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

      15. cancel-sign-sub-inv 89.9%

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

      16. associate-+r- 89.9%

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

   5. Applied egg-rr 89.9%

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

   6. Taylor expanded in y around inf 52.2%

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

      1. associate-*r* 52.2%

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

   8. Simplified 52.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 12: 47.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-41} \lor \neg \left(b \leq 5.1 \cdot 10^{+91}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 -4e-41) (not (<= b 5.1e+91))) (* 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 <= -4e-41) || !(b <= 5.1e+91)) {
		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 <= (-4d-41)) .or. (.not. (b <= 5.1d+91))) 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 <= -4e-41) || !(b <= 5.1e+91)) {
		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 <= -4e-41) or not (b <= 5.1e+91):
		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 <= -4e-41) || !(b <= 5.1e+91))
		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 <= -4e-41) || ~((b <= 5.1e+91)))
		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, -4e-41], N[Not[LessEqual[b, 5.1e+91]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.00000000000000002e-41 or 5.10000000000000013e91 < b

   1. Initial program 94.4%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around inf 60.2%

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

   if -4.00000000000000002e-41 < b < 5.10000000000000013e91

   1. Initial program 93.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 41.2%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-41} \lor \neg \left(b \leq 5.1 \cdot 10^{+91}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 13: 48.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-32}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

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 -3.5e-32)
   (* 27.0 (* a b))
   (if (<= b 9.5e+92) (* 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 <= -3.5e-32) {
		tmp = 27.0 * (a * b);
	} else if (b <= 9.5e+92) {
		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 <= (-3.5d-32)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 9.5d+92) 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 <= -3.5e-32) {
		tmp = 27.0 * (a * b);
	} else if (b <= 9.5e+92) {
		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 <= -3.5e-32:
		tmp = 27.0 * (a * b)
	elif b <= 9.5e+92:
		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 <= -3.5e-32)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 9.5e+92)
		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 <= -3.5e-32)
		tmp = 27.0 * (a * b);
	elseif (b <= 9.5e+92)
		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, -3.5e-32], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+92], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4999999999999999e-32

   1. Initial program 94.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around inf 58.0%

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

   if -3.4999999999999999e-32 < b < 9.4999999999999995e92

   1. Initial program 93.0%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 42.0%

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

   if 9.4999999999999995e92 < b

   1. Initial program 94.4%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 67.7%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r* 67.6%

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

   6. Simplified 67.6%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-32}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 14: 31.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

3. Simplified 95.3%

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

4. Taylor expanded in x around inf 32.6%

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

5. Final simplification 32.6%

   \[\leadsto x \cdot 2 \]

Developer target: 95.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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)))