Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.7% → 96.7%

Time: 7.4s

Alternatives: 9

Speedup: 0.4×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+194}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -4e+306)
     (- (* x (/ y a)) (* z (/ t a)))
     (if (<= t_1 1e+194) (/ t_1 a) (- (/ x (/ a y)) (/ z (/ a t)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -4e+306) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 1e+194) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-4d+306)) then
        tmp = (x * (y / a)) - (z * (t / a))
    else if (t_1 <= 1d+194) then
        tmp = t_1 / a
    else
        tmp = (x / (a / y)) - (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -4e+306) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 1e+194) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -4e+306:
		tmp = (x * (y / a)) - (z * (t / a))
	elif t_1 <= 1e+194:
		tmp = t_1 / a
	else:
		tmp = (x / (a / y)) - (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -4e+306)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	elseif (t_1 <= 1e+194)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -4e+306)
		tmp = (x * (y / a)) - (z * (t / a));
	elseif (t_1 <= 1e+194)
		tmp = t_1 / a;
	else
		tmp = (x / (a / y)) - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+306], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+194], N[(t$95$1 / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.00000000000000007e306

   1. Initial program 56.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 56.9%

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

      2. *-commutative 56.9%

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

      3. cancel-sign-sub-inv 56.9%

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

      4. *-commutative 56.9%

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

      5. add-sqr-sqrt 13.7%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}\right) \cdot \frac{1}{a} \]

      6. sqrt-unprod 40.5%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}\right) \cdot \frac{1}{a} \]

      7. sqr-neg 40.5%

         \[\leadsto \left(x \cdot y + z \cdot \sqrt{\color{blue}{t \cdot t}}\right) \cdot \frac{1}{a} \]

      8. sqrt-unprod 27.0%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right) \cdot \frac{1}{a} \]

      9. add-sqr-sqrt 35.0%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{t}\right) \cdot \frac{1}{a} \]

      10. fma-def 35.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \frac{1}{a} \]

   4. Applied egg-rr 35.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \frac{1}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 35.0%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \mathsf{fma}\left(x, y, z \cdot t\right)} \]

      2. fma-udef 35.0%

         \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(x \cdot y + z \cdot t\right)} \]

      3. distribute-rgt-in 35.0%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{a} + \left(z \cdot t\right) \cdot \frac{1}{a}} \]

      4. div-inv 35.0%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a}} + \left(z \cdot t\right) \cdot \frac{1}{a} \]

      5. associate-/l* 53.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} + \left(z \cdot t\right) \cdot \frac{1}{a} \]

      6. *-commutative 53.8%

         \[\leadsto \frac{x}{\frac{a}{y}} + \color{blue}{\left(t \cdot z\right)} \cdot \frac{1}{a} \]

      7. add-sqr-sqrt 33.3%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right) \cdot \frac{1}{a} \]

      8. sqrt-unprod 46.7%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\sqrt{z \cdot z}}\right) \cdot \frac{1}{a} \]

      9. sqr-neg 46.7%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}\right) \cdot \frac{1}{a} \]

      10. sqrt-unprod 23.7%

          \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right) \cdot \frac{1}{a} \]

      11. add-sqr-sqrt 68.0%

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

      12. *-commutative 68.0%

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

      13. associate-*l* 91.9%

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

      14. div-inv 92.0%

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

      15. cancel-sign-sub-inv 92.0%

          \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}} \]

      16. div-inv 92.0%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} - z \cdot \frac{t}{a} \]

      17. clear-num 92.1%

          \[\leadsto x \cdot \color{blue}{\frac{y}{a}} - z \cdot \frac{t}{a} \]

   6. Applied egg-rr 92.1%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}} \]

   if -4.00000000000000007e306 < (-.f64 (*.f64 x y) (*.f64 z t)) < 9.99999999999999945e193

   1. Initial program 99.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 9.99999999999999945e193 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 81.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 76.8%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} - \frac{z \cdot t}{a}} \]

      2. associate-/l* 89.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} - \frac{z \cdot t}{a} \]

      3. associate-/l* 95.4%

         \[\leadsto \frac{x}{\frac{a}{y}} - \color{blue}{\frac{z}{\frac{a}{t}}} \]

   4. Applied egg-rr 95.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -4 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+306} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+202}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -4e+306) (not (<= t_1 5e+202)))
     (- (* x (/ y a)) (* z (/ t a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -4e+306) || !(t_1 <= 5e+202)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if ((t_1 <= (-4d+306)) .or. (.not. (t_1 <= 5d+202))) then
        tmp = (x * (y / a)) - (z * (t / a))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -4e+306) || !(t_1 <= 5e+202)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -4e+306) or not (t_1 <= 5e+202):
		tmp = (x * (y / a)) - (z * (t / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -4e+306) || !(t_1 <= 5e+202))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -4e+306) || ~((t_1 <= 5e+202)))
		tmp = (x * (y / a)) - (z * (t / a));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+306], N[Not[LessEqual[t$95$1, 5e+202]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.00000000000000007e306 or 4.9999999999999999e202 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 69.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 69.3%

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

      2. *-commutative 69.3%

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

      3. cancel-sign-sub-inv 69.3%

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

      4. *-commutative 69.3%

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

      5. add-sqr-sqrt 23.6%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}\right) \cdot \frac{1}{a} \]

      6. sqrt-unprod 50.8%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}\right) \cdot \frac{1}{a} \]

      7. sqr-neg 50.8%

         \[\leadsto \left(x \cdot y + z \cdot \sqrt{\color{blue}{t \cdot t}}\right) \cdot \frac{1}{a} \]

      8. sqrt-unprod 29.8%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right) \cdot \frac{1}{a} \]

      9. add-sqr-sqrt 43.4%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{t}\right) \cdot \frac{1}{a} \]

      10. fma-def 43.4%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \frac{1}{a} \]

   4. Applied egg-rr 43.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \frac{1}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \mathsf{fma}\left(x, y, z \cdot t\right)} \]

      2. fma-udef 43.4%

         \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(x \cdot y + z \cdot t\right)} \]

      3. distribute-rgt-in 42.2%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{a} + \left(z \cdot t\right) \cdot \frac{1}{a}} \]

      4. div-inv 42.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a}} + \left(z \cdot t\right) \cdot \frac{1}{a} \]

      5. associate-/l* 57.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} + \left(z \cdot t\right) \cdot \frac{1}{a} \]

      6. *-commutative 57.8%

         \[\leadsto \frac{x}{\frac{a}{y}} + \color{blue}{\left(t \cdot z\right)} \cdot \frac{1}{a} \]

      7. add-sqr-sqrt 30.1%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right) \cdot \frac{1}{a} \]

      8. sqrt-unprod 59.5%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\sqrt{z \cdot z}}\right) \cdot \frac{1}{a} \]

      9. sqr-neg 59.5%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}\right) \cdot \frac{1}{a} \]

      10. sqrt-unprod 37.6%

          \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right) \cdot \frac{1}{a} \]

      11. add-sqr-sqrt 78.9%

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

      12. *-commutative 78.9%

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

      13. associate-*l* 93.7%

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

      14. div-inv 93.7%

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

      15. cancel-sign-sub-inv 93.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}} \]

      16. div-inv 93.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} - z \cdot \frac{t}{a} \]

      17. clear-num 93.8%

          \[\leadsto x \cdot \color{blue}{\frac{y}{a}} - z \cdot \frac{t}{a} \]

   6. Applied egg-rr 93.8%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}} \]

   if -4.00000000000000007e306 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e202

   1. Initial program 99.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -4 \cdot 10^{+306} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+202}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-51}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ a y))))
   (if (<= (* x y) -0.1)
     t_1
     (if (<= (* x y) 1e-51)
       (/ (- t) (/ a z))
       (if (<= (* x y) 1e+194) (/ (* x y) a) t_1)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = t_1;
	} else if ((x * y) <= 1e-51) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 1e+194) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = x / (a / y)
    if ((x * y) <= (-0.1d0)) then
        tmp = t_1
    else if ((x * y) <= 1d-51) then
        tmp = -t / (a / z)
    else if ((x * y) <= 1d+194) then
        tmp = (x * y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = t_1;
	} else if ((x * y) <= 1e-51) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 1e+194) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	tmp = 0
	if (x * y) <= -0.1:
		tmp = t_1
	elif (x * y) <= 1e-51:
		tmp = -t / (a / z)
	elif (x * y) <= 1e+194:
		tmp = (x * y) / a
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -0.1)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-51)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (Float64(x * y) <= 1e+194)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -0.1)
		tmp = t_1;
	elseif ((x * y) <= 1e-51)
		tmp = -t / (a / z);
	elseif ((x * y) <= 1e+194)
		tmp = (x * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.1], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-51], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+194], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.10000000000000001 or 9.99999999999999945e193 < (*.f64 x y)

   1. Initial program 81.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 79.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   6. Step-by-step derivation

      1. associate-/r/ 80.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -0.10000000000000001 < (*.f64 x y) < 1e-51

   1. Initial program 94.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 80.5%

         \[\leadsto \color{blue}{-\frac{t \cdot z}{a}} \]

      2. associate-/l* 80.4%

         \[\leadsto -\color{blue}{\frac{t}{\frac{a}{z}}} \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{-\frac{t}{\frac{a}{z}}} \]

   if 1e-51 < (*.f64 x y) < 9.99999999999999945e193

   1. Initial program 99.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-51}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-51}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ a y))))
   (if (<= (* x y) -0.1)
     t_1
     (if (<= (* x y) 1e-51)
       (* (/ t a) (- z))
       (if (<= (* x y) 1e+194) (/ (* x y) a) t_1)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = t_1;
	} else if ((x * y) <= 1e-51) {
		tmp = (t / a) * -z;
	} else if ((x * y) <= 1e+194) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = x / (a / y)
    if ((x * y) <= (-0.1d0)) then
        tmp = t_1
    else if ((x * y) <= 1d-51) then
        tmp = (t / a) * -z
    else if ((x * y) <= 1d+194) then
        tmp = (x * y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = t_1;
	} else if ((x * y) <= 1e-51) {
		tmp = (t / a) * -z;
	} else if ((x * y) <= 1e+194) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	tmp = 0
	if (x * y) <= -0.1:
		tmp = t_1
	elif (x * y) <= 1e-51:
		tmp = (t / a) * -z
	elif (x * y) <= 1e+194:
		tmp = (x * y) / a
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -0.1)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-51)
		tmp = Float64(Float64(t / a) * Float64(-z));
	elseif (Float64(x * y) <= 1e+194)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -0.1)
		tmp = t_1;
	elseif ((x * y) <= 1e-51)
		tmp = (t / a) * -z;
	elseif ((x * y) <= 1e+194)
		tmp = (x * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.1], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-51], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+194], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.10000000000000001 or 9.99999999999999945e193 < (*.f64 x y)

   1. Initial program 81.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 79.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   6. Step-by-step derivation

      1. associate-/r/ 80.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -0.10000000000000001 < (*.f64 x y) < 1e-51

   1. Initial program 94.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 94.6%

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

      2. *-commutative 94.6%

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

      3. cancel-sign-sub-inv 94.6%

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

      4. *-commutative 94.6%

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

      5. add-sqr-sqrt 52.0%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}\right) \cdot \frac{1}{a} \]

      6. sqrt-unprod 50.1%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}\right) \cdot \frac{1}{a} \]

      7. sqr-neg 50.1%

         \[\leadsto \left(x \cdot y + z \cdot \sqrt{\color{blue}{t \cdot t}}\right) \cdot \frac{1}{a} \]

      8. sqrt-unprod 13.4%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right) \cdot \frac{1}{a} \]

      9. add-sqr-sqrt 27.1%

         \[\leadsto \left(x \cdot y + z \cdot \color{blue}{t}\right) \cdot \frac{1}{a} \]

      10. fma-def 27.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \frac{1}{a} \]

   4. Applied egg-rr 27.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \frac{1}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \mathsf{fma}\left(x, y, z \cdot t\right)} \]

      2. fma-udef 27.1%

         \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(x \cdot y + z \cdot t\right)} \]

      3. distribute-rgt-in 27.1%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{a} + \left(z \cdot t\right) \cdot \frac{1}{a}} \]

      4. div-inv 27.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a}} + \left(z \cdot t\right) \cdot \frac{1}{a} \]

      5. associate-/l* 26.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} + \left(z \cdot t\right) \cdot \frac{1}{a} \]

      6. *-commutative 26.0%

         \[\leadsto \frac{x}{\frac{a}{y}} + \color{blue}{\left(t \cdot z\right)} \cdot \frac{1}{a} \]

      7. add-sqr-sqrt 13.6%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right) \cdot \frac{1}{a} \]

      8. sqrt-unprod 45.7%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\sqrt{z \cdot z}}\right) \cdot \frac{1}{a} \]

      9. sqr-neg 45.7%

         \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}\right) \cdot \frac{1}{a} \]

      10. sqrt-unprod 44.5%

          \[\leadsto \frac{x}{\frac{a}{y}} + \left(t \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right) \cdot \frac{1}{a} \]

      11. add-sqr-sqrt 93.5%

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

      12. *-commutative 93.5%

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

      13. associate-*l* 87.3%

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

      14. div-inv 87.3%

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

      15. cancel-sign-sub-inv 87.3%

          \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}} \]

      16. div-inv 87.3%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} - z \cdot \frac{t}{a} \]

      17. clear-num 87.3%

          \[\leadsto x \cdot \color{blue}{\frac{y}{a}} - z \cdot \frac{t}{a} \]

   6. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}} \]

   7. Taylor expanded in x around 0 80.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-*r/ 80.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. mul-1-neg 80.5%

         \[\leadsto \frac{\color{blue}{-t \cdot z}}{a} \]

      3. distribute-lft-neg-out 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-*r/ 74.3%

         \[\leadsto \color{blue}{z \cdot \frac{-t}{a}} \]

   9. Simplified 74.3%

      \[\leadsto \color{blue}{z \cdot \frac{-t}{a}} \]

   if 1e-51 < (*.f64 x y) < 9.99999999999999945e193

   1. Initial program 99.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-51}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-51}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ a y))))
   (if (<= (* x y) -0.1)
     t_1
     (if (<= (* x y) 1e-51)
       (/ (* t (- z)) a)
       (if (<= (* x y) 1e+194) (/ (* x y) a) t_1)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = t_1;
	} else if ((x * y) <= 1e-51) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 1e+194) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = x / (a / y)
    if ((x * y) <= (-0.1d0)) then
        tmp = t_1
    else if ((x * y) <= 1d-51) then
        tmp = (t * -z) / a
    else if ((x * y) <= 1d+194) then
        tmp = (x * y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = t_1;
	} else if ((x * y) <= 1e-51) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 1e+194) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	tmp = 0
	if (x * y) <= -0.1:
		tmp = t_1
	elif (x * y) <= 1e-51:
		tmp = (t * -z) / a
	elif (x * y) <= 1e+194:
		tmp = (x * y) / a
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -0.1)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-51)
		tmp = Float64(Float64(t * Float64(-z)) / a);
	elseif (Float64(x * y) <= 1e+194)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	tmp = 0.0;
	if ((x * y) <= -0.1)
		tmp = t_1;
	elseif ((x * y) <= 1e-51)
		tmp = (t * -z) / a;
	elseif ((x * y) <= 1e+194)
		tmp = (x * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.1], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-51], N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+194], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.10000000000000001 or 9.99999999999999945e193 < (*.f64 x y)

   1. Initial program 81.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 79.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   6. Step-by-step derivation

      1. associate-/r/ 80.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -0.10000000000000001 < (*.f64 x y) < 1e-51

   1. Initial program 94.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(t \cdot z\right)}}{a} \]
   4. Step-by-step derivation

      1. mul-1-neg 80.5%

         \[\leadsto \frac{\color{blue}{-t \cdot z}}{a} \]

      2. distribute-rgt-neg-in 80.5%

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

   5. Simplified 80.5%

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

   if 1e-51 < (*.f64 x y) < 9.99999999999999945e193

   1. Initial program 99.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-51}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+194}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+205}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+243)
   (* x (/ y a))
   (if (<= (* x y) 5e+205) (/ (- (* x y) (* z t)) a) (/ x (/ a y)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+243) {
		tmp = x * (y / a);
	} else if ((x * y) <= 5e+205) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-5d+243)) then
        tmp = x * (y / a)
    else if ((x * y) <= 5d+205) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+243) {
		tmp = x * (y / a);
	} else if ((x * y) <= 5e+205) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+243:
		tmp = x * (y / a)
	elif (x * y) <= 5e+205:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+243)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 5e+205)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+243)
		tmp = x * (y / a);
	elseif ((x * y) <= 5e+205)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+243], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+205], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000037e243

   1. Initial program 71.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 71.8%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \]

      2. associate-*l/ 97.0%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   5. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   if -5.00000000000000037e243 < (*.f64 x y) < 5.0000000000000002e205

   1. Initial program 94.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.0000000000000002e205 < (*.f64 x y)

   1. Initial program 75.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ 90.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

   5. Simplified 90.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   6. Step-by-step derivation

      1. associate-/r/ 93.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Applied egg-rr 93.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+205}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 55.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. associate-*l/ 57.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

5. Simplified 57.8%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

6. Final simplification 57.8%

   \[\leadsto y \cdot \frac{x}{a} \]
7. Add Preprocessing

Alternative 8: 50.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 55.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. *-commutative 55.9%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \]

   2. associate-*l/ 57.7%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

5. Applied egg-rr 57.7%

   \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

6. Final simplification 57.7%

   \[\leadsto x \cdot \frac{y}{a} \]
7. Add Preprocessing

Alternative 9: 50.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 55.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. associate-*l/ 57.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

5. Simplified 57.8%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
6. Step-by-step derivation

   1. associate-/r/ 58.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

7. Applied egg-rr 58.2%

   \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

8. Final simplification 58.2%

   \[\leadsto \frac{x}{\frac{a}{y}} \]
9. Add Preprocessing

Developer target: 91.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))