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

Percentage Accurate: 91.6% → 96.7%

Time: 10.0s

Alternatives: 10

Speedup: 0.4×

• 27.9% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 1.660577077388247e+88
  2. y = 2.8426338663085804e-145
  3. z = 1.4807751446823044e-189
  4. t = 7.38863579709503e+278
  5. a = -2.209455291868154e+218

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: 91.6% 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

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+289}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \end{array} \end{array} \]

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 -2e+279)
     (- (* x (/ y a)) (* z (/ t a)))
     (if (<= t_1 5e+289) (/ t_1 a) (* x (- (/ y a) (* t (/ (/ z 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) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+279) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 5e+289) {
		tmp = t_1 / a;
	} else {
		tmp = x * ((y / a) - (t * ((z / x) / 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 <= (-2d+279)) then
        tmp = (x * (y / a)) - (z * (t / a))
    else if (t_1 <= 5d+289) then
        tmp = t_1 / a
    else
        tmp = x * ((y / a) - (t * ((z / x) / 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 <= -2e+279) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 5e+289) {
		tmp = t_1 / a;
	} else {
		tmp = x * ((y / a) - (t * ((z / x) / 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 <= -2e+279:
		tmp = (x * (y / a)) - (z * (t / a))
	elif t_1 <= 5e+289:
		tmp = t_1 / a
	else:
		tmp = x * ((y / a) - (t * ((z / x) / 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 <= -2e+279)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	elseif (t_1 <= 5e+289)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(x * Float64(Float64(y / a) - Float64(t * Float64(Float64(z / x) / 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 <= -2e+279)
		tmp = (x * (y / a)) - (z * (t / a));
	elseif (t_1 <= 5e+289)
		tmp = t_1 / a;
	else
		tmp = x * ((y / a) - (t * ((z / x) / 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[LessEqual[t$95$1, -2e+279], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+289], N[(t$95$1 / a), $MachinePrecision], N[(x * N[(N[(y / a), $MachinePrecision] - N[(t * N[(N[(z / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -2.00000000000000012e279

   1. Initial program 74.0%

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

      1. div-sub 70.5%

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

      2. associate-/l* 87.0%

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

      3. associate-/l* 89.5%

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

   4. Applied egg-rr 89.5%

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

   if -2.00000000000000012e279 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000031e289

   1. Initial program 98.3%

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

   if 5.00000000000000031e289 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 70.8%

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

   3. Taylor expanded in x around inf 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

      4. associate-/l* 86.1%

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

      5. *-commutative 86.1%

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

      6. associate-/r* 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+289}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ t_2 := z \cdot \frac{-t}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) a)) (t_2 (* z (/ (- t) a))))
   (if (<= (* x y) -1e+175)
     (* y (/ x a))
     (if (<= (* x y) -1e-24)
       t_1
       (if (<= (* x y) 1e-100)
         t_2
         (if (<= (* x y) 4e-31)
           t_1
           (if (<= (* x y) 1e+24) t_2 (/ y (/ a x)))))))))

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) / a;
	double t_2 = z * (-t / a);
	double tmp;
	if ((x * y) <= -1e+175) {
		tmp = y * (x / a);
	} else if ((x * y) <= -1e-24) {
		tmp = t_1;
	} else if ((x * y) <= 1e-100) {
		tmp = t_2;
	} else if ((x * y) <= 4e-31) {
		tmp = t_1;
	} else if ((x * y) <= 1e+24) {
		tmp = t_2;
	} else {
		tmp = y / (a / x);
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x * y) / a
    t_2 = z * (-t / a)
    if ((x * y) <= (-1d+175)) then
        tmp = y * (x / a)
    else if ((x * y) <= (-1d-24)) then
        tmp = t_1
    else if ((x * y) <= 1d-100) then
        tmp = t_2
    else if ((x * y) <= 4d-31) then
        tmp = t_1
    else if ((x * y) <= 1d+24) then
        tmp = t_2
    else
        tmp = y / (a / x)
    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) / a;
	double t_2 = z * (-t / a);
	double tmp;
	if ((x * y) <= -1e+175) {
		tmp = y * (x / a);
	} else if ((x * y) <= -1e-24) {
		tmp = t_1;
	} else if ((x * y) <= 1e-100) {
		tmp = t_2;
	} else if ((x * y) <= 4e-31) {
		tmp = t_1;
	} else if ((x * y) <= 1e+24) {
		tmp = t_2;
	} else {
		tmp = y / (a / x);
	}
	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) / a
	t_2 = z * (-t / a)
	tmp = 0
	if (x * y) <= -1e+175:
		tmp = y * (x / a)
	elif (x * y) <= -1e-24:
		tmp = t_1
	elif (x * y) <= 1e-100:
		tmp = t_2
	elif (x * y) <= 4e-31:
		tmp = t_1
	elif (x * y) <= 1e+24:
		tmp = t_2
	else:
		tmp = y / (a / x)
	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) / a)
	t_2 = Float64(z * Float64(Float64(-t) / a))
	tmp = 0.0
	if (Float64(x * y) <= -1e+175)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= -1e-24)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-100)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e-31)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+24)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(a / x));
	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) / a;
	t_2 = z * (-t / a);
	tmp = 0.0;
	if ((x * y) <= -1e+175)
		tmp = y * (x / a);
	elseif ((x * y) <= -1e-24)
		tmp = t_1;
	elseif ((x * y) <= 1e-100)
		tmp = t_2;
	elseif ((x * y) <= 4e-31)
		tmp = t_1;
	elseif ((x * y) <= 1e+24)
		tmp = t_2;
	else
		tmp = y / (a / x);
	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] / a), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+175], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-24], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-100], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e-31], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+24], t$95$2, N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.9999999999999994e174

   1. Initial program 75.1%

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

   3. Taylor expanded in x around inf 75.1%

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

      1. associate-*r/ 90.5%

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

   5. Simplified 90.5%

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

      1. clear-num 90.4%

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

      2. un-div-inv 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/r/ 90.5%

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

   9. Applied egg-rr 90.5%

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

   if -9.9999999999999994e174 < (*.f64 x y) < -9.99999999999999924e-25 or 1e-100 < (*.f64 x y) < 4e-31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -9.99999999999999924e-25 < (*.f64 x y) < 1e-100 or 4e-31 < (*.f64 x y) < 9.9999999999999998e23

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*r/ 80.2%

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

      3. neg-mul-1 80.2%

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

      4. distribute-rgt-neg-in 80.2%

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

      5. distribute-frac-neg 80.2%

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

   5. Simplified 80.2%

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

   if 9.9999999999999998e23 < (*.f64 x y)

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf 79.8%

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

      1. associate-*r/ 84.1%

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

   5. Simplified 84.1%

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

      1. clear-num 83.5%

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

      2. un-div-inv 82.2%

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

   7. Applied egg-rr 82.2%

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

      1. associate-/r/ 79.5%

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

   9. Applied egg-rr 79.5%

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

       1. *-commutative 79.5%

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

       2. clear-num 79.3%

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

       3. un-div-inv 79.5%

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

   11. Applied egg-rr 79.5%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-100}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-100}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) a)))
   (if (<= (* x y) -1e+175)
     (* y (/ x a))
     (if (<= (* x y) -1e-24)
       t_1
       (if (<= (* x y) 1e-100)
         (/ z (/ a (- t)))
         (if (<= (* x y) 4e-31)
           t_1
           (if (<= (* x y) 1e+24) (* z (/ (- t) a)) (/ y (/ a x)))))))))

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) / a;
	double tmp;
	if ((x * y) <= -1e+175) {
		tmp = y * (x / a);
	} else if ((x * y) <= -1e-24) {
		tmp = t_1;
	} else if ((x * y) <= 1e-100) {
		tmp = z / (a / -t);
	} else if ((x * y) <= 4e-31) {
		tmp = t_1;
	} else if ((x * y) <= 1e+24) {
		tmp = z * (-t / a);
	} else {
		tmp = y / (a / x);
	}
	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) / a
    if ((x * y) <= (-1d+175)) then
        tmp = y * (x / a)
    else if ((x * y) <= (-1d-24)) then
        tmp = t_1
    else if ((x * y) <= 1d-100) then
        tmp = z / (a / -t)
    else if ((x * y) <= 4d-31) then
        tmp = t_1
    else if ((x * y) <= 1d+24) then
        tmp = z * (-t / a)
    else
        tmp = y / (a / x)
    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) / a;
	double tmp;
	if ((x * y) <= -1e+175) {
		tmp = y * (x / a);
	} else if ((x * y) <= -1e-24) {
		tmp = t_1;
	} else if ((x * y) <= 1e-100) {
		tmp = z / (a / -t);
	} else if ((x * y) <= 4e-31) {
		tmp = t_1;
	} else if ((x * y) <= 1e+24) {
		tmp = z * (-t / a);
	} else {
		tmp = y / (a / x);
	}
	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) / a
	tmp = 0
	if (x * y) <= -1e+175:
		tmp = y * (x / a)
	elif (x * y) <= -1e-24:
		tmp = t_1
	elif (x * y) <= 1e-100:
		tmp = z / (a / -t)
	elif (x * y) <= 4e-31:
		tmp = t_1
	elif (x * y) <= 1e+24:
		tmp = z * (-t / a)
	else:
		tmp = y / (a / x)
	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) / a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+175)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= -1e-24)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-100)
		tmp = Float64(z / Float64(a / Float64(-t)));
	elseif (Float64(x * y) <= 4e-31)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+24)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(y / Float64(a / x));
	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) / a;
	tmp = 0.0;
	if ((x * y) <= -1e+175)
		tmp = y * (x / a);
	elseif ((x * y) <= -1e-24)
		tmp = t_1;
	elseif ((x * y) <= 1e-100)
		tmp = z / (a / -t);
	elseif ((x * y) <= 4e-31)
		tmp = t_1;
	elseif ((x * y) <= 1e+24)
		tmp = z * (-t / a);
	else
		tmp = y / (a / x);
	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] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+175], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-24], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-100], N[(z / N[(a / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-31], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+24], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.9999999999999994e174

   1. Initial program 75.1%

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

   3. Taylor expanded in x around inf 75.1%

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

      1. associate-*r/ 90.5%

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

   5. Simplified 90.5%

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

      1. clear-num 90.4%

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

      2. un-div-inv 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/r/ 90.5%

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

   9. Applied egg-rr 90.5%

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

   if -9.9999999999999994e174 < (*.f64 x y) < -9.99999999999999924e-25 or 1e-100 < (*.f64 x y) < 4e-31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -9.99999999999999924e-25 < (*.f64 x y) < 1e-100

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 79.4%

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

      1. mul-1-neg 79.4%

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

      2. associate-/l* 79.2%

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

      3. distribute-rgt-neg-in 79.2%

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

      4. distribute-neg-frac2 79.2%

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

   5. Simplified 79.2%

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

      1. *-commutative 79.2%

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

      2. distribute-frac-neg2 79.2%

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

      3. distribute-lft-neg-in 79.2%

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

      4. associate-/r/ 80.9%

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

      5. distribute-neg-frac 80.9%

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

   7. Applied egg-rr 80.9%

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

   if 4e-31 < (*.f64 x y) < 9.9999999999999998e23

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r/ 67.3%

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

      3. neg-mul-1 67.3%

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

      4. distribute-rgt-neg-in 67.3%

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

      5. distribute-frac-neg 67.3%

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

   5. Simplified 67.3%

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

   if 9.9999999999999998e23 < (*.f64 x y)

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf 79.8%

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

      1. associate-*r/ 84.1%

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

   5. Simplified 84.1%

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

      1. clear-num 83.5%

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

      2. un-div-inv 82.2%

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

   7. Applied egg-rr 82.2%

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

      1. associate-/r/ 79.5%

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

   9. Applied egg-rr 79.5%

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

       1. *-commutative 79.5%

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

       2. clear-num 79.3%

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

       3. un-div-inv 79.5%

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

   11. Applied egg-rr 79.5%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-100}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+284}\right):\\ \;\;\;\;\left(y - t \cdot \frac{z}{x}\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

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 (- INFINITY)) (not (<= t_1 1e+284)))
     (* (- y (* t (/ z x))) (/ x 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 <= -((double) INFINITY)) || !(t_1 <= 1e+284)) {
		tmp = (y - (t * (z / x))) * (x / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+284)) {
		tmp = (y - (t * (z / x))) * (x / 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 <= -math.inf) or not (t_1 <= 1e+284):
		tmp = (y - (t * (z / x))) * (x / 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 <= Float64(-Inf)) || !(t_1 <= 1e+284))
		tmp = Float64(Float64(y - Float64(t * Float64(z / x))) * Float64(x / 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 <= -Inf) || ~((t_1 <= 1e+284)))
		tmp = (y - (t * (z / x))) * (x / 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, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+284]], $MachinePrecision]], N[(N[(y - N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 1.00000000000000008e284 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 69.1%

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

      1. div-sub 64.4%

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

      2. associate-/l* 77.4%

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

      3. associate-/l* 87.4%

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

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in x around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. +-commutative 78.9%

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

      3. mul-1-neg 78.9%

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

      4. sub-neg 78.9%

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

      5. times-frac 81.6%

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

      6. associate-*l/ 80.4%

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

      7. div-sub 86.6%

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

      8. associate-*l/ 69.2%

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

      9. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000008e284

   1. Initial program 98.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+284}\right):\\ \;\;\;\;\left(y - t \cdot \frac{z}{x}\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+279} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+279}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

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 -2e+279) (not (<= t_1 5e+279)))
     (- (* 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 <= -2e+279) || !(t_1 <= 5e+279)) {
		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 <= (-2d+279)) .or. (.not. (t_1 <= 5d+279))) 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 <= -2e+279) || !(t_1 <= 5e+279)) {
		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 <= -2e+279) or not (t_1 <= 5e+279):
		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 <= -2e+279) || !(t_1 <= 5e+279))
		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 <= -2e+279) || ~((t_1 <= 5e+279)))
		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, -2e+279], N[Not[LessEqual[t$95$1, 5e+279]], $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)) < -2.00000000000000012e279 or 5.0000000000000002e279 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.2%

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

      1. div-sub 69.2%

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

      2. associate-/l* 80.4%

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

      3. associate-/l* 89.1%

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

   4. Applied egg-rr 89.1%

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

   if -2.00000000000000012e279 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000002e279

   1. Initial program 98.3%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+279} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+279}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+271}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

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
 (if (or (<= (* x y) (- INFINITY)) (not (<= (* x y) 2e+271)))
   (* x (/ y a))
   (/ (- (* x y) (* z t)) 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 tmp;
	if (((x * y) <= -((double) INFINITY)) || !((x * y) <= 2e+271)) {
		tmp = x * (y / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

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) <= -Double.POSITIVE_INFINITY) || !((x * y) <= 2e+271)) {
		tmp = x * (y / a);
	} else {
		tmp = ((x * y) - (z * t)) / 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):
	tmp = 0
	if ((x * y) <= -math.inf) or not ((x * y) <= 2e+271):
		tmp = x * (y / a)
	else:
		tmp = ((x * y) - (z * t)) / 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)
	tmp = 0.0
	if ((Float64(x * y) <= Float64(-Inf)) || !(Float64(x * y) <= 2e+271))
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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)
	tmp = 0.0;
	if (((x * y) <= -Inf) || ~(((x * y) <= 2e+271)))
		tmp = x * (y / a);
	else
		tmp = ((x * y) - (z * t)) / 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_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+271]], $MachinePrecision]], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 1.99999999999999991e271 < (*.f64 x y)

   1. Initial program 65.7%

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

   3. Taylor expanded in x around inf 68.7%

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

      1. associate-*r/ 96.9%

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

   5. Simplified 96.9%

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

   if -inf.0 < (*.f64 x y) < 1.99999999999999991e271

   1. Initial program 94.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+271}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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+86)
   (/ x (/ a y))
   (if (<= (* x y) 1e+24) (* t (/ (- z) a)) (/ y (/ a x)))))

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+86) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+24) {
		tmp = t * (-z / a);
	} else {
		tmp = y / (a / x);
	}
	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+86)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d+24) then
        tmp = t * (-z / a)
    else
        tmp = y / (a / x)
    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+86) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+24) {
		tmp = t * (-z / a);
	} else {
		tmp = y / (a / x);
	}
	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+86:
		tmp = x / (a / y)
	elif (x * y) <= 1e+24:
		tmp = t * (-z / a)
	else:
		tmp = y / (a / x)
	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+86)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e+24)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(y / Float64(a / x));
	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+86)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e+24)
		tmp = t * (-z / a);
	else
		tmp = y / (a / x);
	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+86], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+24], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999998e86

   1. Initial program 83.1%

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

   3. Taylor expanded in x around inf 76.7%

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

      1. associate-*r/ 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 83.0%

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

      2. un-div-inv 83.2%

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

   7. Applied egg-rr 83.2%

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

   if -4.9999999999999998e86 < (*.f64 x y) < 9.9999999999999998e23

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-/l* 71.6%

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

      3. distribute-rgt-neg-in 71.6%

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

      4. distribute-neg-frac2 71.6%

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

   5. Simplified 71.6%

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

   if 9.9999999999999998e23 < (*.f64 x y)

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf 79.8%

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

      1. associate-*r/ 84.1%

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

   5. Simplified 84.1%

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

      1. clear-num 83.5%

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

      2. un-div-inv 82.2%

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

   7. Applied egg-rr 82.2%

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

      1. associate-/r/ 79.5%

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

   9. Applied egg-rr 79.5%

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

       1. *-commutative 79.5%

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

       2. clear-num 79.3%

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

       3. un-div-inv 79.5%

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

   11. Applied egg-rr 79.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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
 (if (<= a 3.6e-60) (* x (/ y a)) (* 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) {
	double tmp;
	if (a <= 3.6e-60) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / 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) :: tmp
    if (a <= 3.6d-60) then
        tmp = x * (y / a)
    else
        tmp = y * (x / 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 tmp;
	if (a <= 3.6e-60) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / 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):
	tmp = 0
	if a <= 3.6e-60:
		tmp = x * (y / a)
	else:
		tmp = y * (x / 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)
	tmp = 0.0
	if (a <= 3.6e-60)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / 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)
	tmp = 0.0;
	if (a <= 3.6e-60)
		tmp = x * (y / a);
	else
		tmp = y * (x / 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_] := If[LessEqual[a, 3.6e-60], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.6e-60

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 53.7%

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

      1. associate-*r/ 54.6%

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

   5. Simplified 54.6%

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

   if 3.6e-60 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in x around inf 52.7%

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

      1. associate-*r/ 54.3%

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

   5. Simplified 54.3%

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

      1. clear-num 53.8%

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

      2. un-div-inv 53.9%

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

   7. Applied egg-rr 53.9%

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

      1. associate-/r/ 56.4%

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

   9. Applied egg-rr 56.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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
 (if (<= a 5.5e-63) (/ (* x y) a) (* 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) {
	double tmp;
	if (a <= 5.5e-63) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / 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) :: tmp
    if (a <= 5.5d-63) then
        tmp = (x * y) / a
    else
        tmp = y * (x / 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 tmp;
	if (a <= 5.5e-63) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / 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):
	tmp = 0
	if a <= 5.5e-63:
		tmp = (x * y) / a
	else:
		tmp = y * (x / 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)
	tmp = 0.0
	if (a <= 5.5e-63)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / 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)
	tmp = 0.0;
	if (a <= 5.5e-63)
		tmp = (x * y) / a;
	else
		tmp = y * (x / 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_] := If[LessEqual[a, 5.5e-63], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.50000000000000043e-63

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 54.0%

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

   if 5.50000000000000043e-63 < a

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 52.1%

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

      1. associate-*r/ 54.8%

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

   5. Simplified 54.8%

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

      1. clear-num 54.4%

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

      2. un-div-inv 53.3%

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

   7. Applied egg-rr 53.3%

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

      1. associate-/r/ 55.7%

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

   9. Applied egg-rr 55.7%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 91.0%

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

3. Taylor expanded in x around inf 53.4%

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

   1. associate-*r/ 54.5%

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

5. Simplified 54.5%

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

6. Final simplification 54.5%

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

Developer target: 92.0% 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 2024073 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (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))