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

Percentage Accurate: 91.4% → 95.1%

Time: 9.3s

Alternatives: 10

Speedup: 0.6×

• 27.9% 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: 91.4% 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: 95.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - z \cdot \frac{t}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= a_m 3e+15)
    (/ (fma x y (* z (- t))) a_m)
    (- (* x (/ y a_m)) (* z (/ t a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 3e+15) {
		tmp = fma(x, y, (z * -t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (a_m <= 3e+15)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(z * Float64(t / a_m)));
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[a$95$m, 3e+15], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 3e15

   1. Initial program 94.3%

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

      1. div-sub 90.2%

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

      2. *-commutative 90.2%

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

      3. div-sub 94.3%

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

      4. *-commutative 94.3%

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

      5. fma-neg 94.9%

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

      6. distribute-rgt-neg-out 94.9%

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

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}} \]
   4. Add Preprocessing

   if 3e15 < a

   1. Initial program 76.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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* 80.5%

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

      3. associate-/l* 92.9%

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

   4. Applied egg-rr 92.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := z \cdot \frac{t}{-a\_m}\\ t_2 := \frac{y}{\frac{a\_m}{x}}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 10^{-6}:\\ \;\;\;\;t \cdot \frac{z}{-a\_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* z (/ t (- a_m)))) (t_2 (/ y (/ a_m x))))
   (*
    a_s
    (if (<= (* x y) -1e+37)
      t_2
      (if (<= (* x y) 5e-135)
        t_1
        (if (<= (* x y) 5e-90)
          (* y (/ x a_m))
          (if (<= (* x y) 1e-6)
            (* t (/ z (- a_m)))
            (if (<= (* x y) 2e+26)
              (/ x (/ a_m y))
              (if (<= (* x y) 5e+112) t_1 t_2)))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = z * (t / -a_m);
	double t_2 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_2;
	} else if ((x * y) <= 5e-135) {
		tmp = t_1;
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 1e-6) {
		tmp = t * (z / -a_m);
	} else if ((x * y) <= 2e+26) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= 5e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t / -a_m)
    t_2 = y / (a_m / x)
    if ((x * y) <= (-1d+37)) then
        tmp = t_2
    else if ((x * y) <= 5d-135) then
        tmp = t_1
    else if ((x * y) <= 5d-90) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 1d-6) then
        tmp = t * (z / -a_m)
    else if ((x * y) <= 2d+26) then
        tmp = x / (a_m / y)
    else if ((x * y) <= 5d+112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = z * (t / -a_m);
	double t_2 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_2;
	} else if ((x * y) <= 5e-135) {
		tmp = t_1;
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 1e-6) {
		tmp = t * (z / -a_m);
	} else if ((x * y) <= 2e+26) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= 5e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = z * (t / -a_m)
	t_2 = y / (a_m / x)
	tmp = 0
	if (x * y) <= -1e+37:
		tmp = t_2
	elif (x * y) <= 5e-135:
		tmp = t_1
	elif (x * y) <= 5e-90:
		tmp = y * (x / a_m)
	elif (x * y) <= 1e-6:
		tmp = t * (z / -a_m)
	elif (x * y) <= 2e+26:
		tmp = x / (a_m / y)
	elif (x * y) <= 5e+112:
		tmp = t_1
	else:
		tmp = t_2
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(z * Float64(t / Float64(-a_m)))
	t_2 = Float64(y / Float64(a_m / x))
	tmp = 0.0
	if (Float64(x * y) <= -1e+37)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-135)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-90)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 1e-6)
		tmp = Float64(t * Float64(z / Float64(-a_m)));
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(x / Float64(a_m / y));
	elseif (Float64(x * y) <= 5e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = z * (t / -a_m);
	t_2 = y / (a_m / x);
	tmp = 0.0;
	if ((x * y) <= -1e+37)
		tmp = t_2;
	elseif ((x * y) <= 5e-135)
		tmp = t_1;
	elseif ((x * y) <= 5e-90)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 1e-6)
		tmp = t * (z / -a_m);
	elseif ((x * y) <= 2e+26)
		tmp = x / (a_m / y);
	elseif ((x * y) <= 5e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(z * N[(t / (-a$95$m)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+37], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-135], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-90], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-6], N[(t * N[(z / (-a$95$m)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+112], t$95$1, t$95$2]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5e112 < (*.f64 x y)

   1. Initial program 82.1%

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

      1. div-sub 74.9%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in x around 0 74.9%

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

   6. Taylor expanded in x around inf 74.1%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-/r/ 81.3%

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

   8. Simplified 81.3%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135 or 2.0000000000000001e26 < (*.f64 x y) < 5e112

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*r/ 75.7%

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

      3. neg-mul-1 75.7%

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

      4. distribute-rgt-neg-in 75.7%

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

      5. distribute-frac-neg 75.7%

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

   5. Simplified 75.7%

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

   if 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. associate-*r/ 79.5%

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

   5. Simplified 79.5%

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

      1. clear-num 79.5%

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

      2. un-div-inv 69.2%

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

   7. Applied egg-rr 69.2%

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

      1. associate-/r/ 79.4%

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

   9. Applied egg-rr 79.4%

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

   if 5.00000000000000019e-90 < (*.f64 x y) < 9.99999999999999955e-7

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/l* 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-neg-frac2 73.7%

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

   5. Simplified 73.7%

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

   if 9.99999999999999955e-7 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 84.0%

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

      1. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-6}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{z}{-a\_m}\\ t_2 := \frac{y}{\frac{a\_m}{x}}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* t (/ z (- a_m)))) (t_2 (/ y (/ a_m x))))
   (*
    a_s
    (if (<= (* x y) -1e+37)
      t_2
      (if (<= (* x y) 5e-135)
        t_1
        (if (<= (* x y) 5e-90)
          (* y (/ x a_m))
          (if (<= (* x y) 5e+112) t_1 t_2)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (z / -a_m);
	double t_2 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_2;
	} else if ((x * y) <= 5e-135) {
		tmp = t_1;
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (z / -a_m)
    t_2 = y / (a_m / x)
    if ((x * y) <= (-1d+37)) then
        tmp = t_2
    else if ((x * y) <= 5d-135) then
        tmp = t_1
    else if ((x * y) <= 5d-90) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d+112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (z / -a_m);
	double t_2 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_2;
	} else if ((x * y) <= 5e-135) {
		tmp = t_1;
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = t * (z / -a_m)
	t_2 = y / (a_m / x)
	tmp = 0
	if (x * y) <= -1e+37:
		tmp = t_2
	elif (x * y) <= 5e-135:
		tmp = t_1
	elif (x * y) <= 5e-90:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e+112:
		tmp = t_1
	else:
		tmp = t_2
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(t * Float64(z / Float64(-a_m)))
	t_2 = Float64(y / Float64(a_m / x))
	tmp = 0.0
	if (Float64(x * y) <= -1e+37)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-135)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-90)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = t * (z / -a_m);
	t_2 = y / (a_m / x);
	tmp = 0.0;
	if ((x * y) <= -1e+37)
		tmp = t_2;
	elseif ((x * y) <= 5e-135)
		tmp = t_1;
	elseif ((x * y) <= 5e-90)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(t * N[(z / (-a$95$m)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+37], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-135], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-90], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+112], t$95$1, t$95$2]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5e112 < (*.f64 x y)

   1. Initial program 82.1%

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

      1. div-sub 74.9%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in x around 0 74.9%

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

   6. Taylor expanded in x around inf 74.1%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-/r/ 81.3%

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

   8. Simplified 81.3%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135 or 5.00000000000000019e-90 < (*.f64 x y) < 5e112

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. associate-/l* 76.0%

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

      3. distribute-rgt-neg-in 76.0%

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

      4. distribute-neg-frac2 76.0%

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

   5. Simplified 76.0%

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

   if 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. associate-*r/ 79.5%

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

   5. Simplified 79.5%

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

      1. clear-num 79.5%

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

      2. un-div-inv 69.2%

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

   7. Applied egg-rr 69.2%

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

      1. associate-/r/ 79.4%

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

   9. Applied egg-rr 79.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{y}{\frac{a\_m}{x}}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \frac{t}{-a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{\frac{a\_m}{-t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ y (/ a_m x))))
   (*
    a_s
    (if (<= (* x y) -1e+37)
      t_1
      (if (<= (* x y) 5e-135)
        (* z (/ t (- a_m)))
        (if (<= (* x y) 5e-90)
          (* y (/ x a_m))
          (if (<= (* x y) 5e+112) (/ z (/ a_m (- t))) t_1)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = z * (t / -a_m);
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+112) {
		tmp = z / (a_m / -t);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a_m / x)
    if ((x * y) <= (-1d+37)) then
        tmp = t_1
    else if ((x * y) <= 5d-135) then
        tmp = z * (t / -a_m)
    else if ((x * y) <= 5d-90) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d+112) then
        tmp = z / (a_m / -t)
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = z * (t / -a_m);
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+112) {
		tmp = z / (a_m / -t);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = y / (a_m / x)
	tmp = 0
	if (x * y) <= -1e+37:
		tmp = t_1
	elif (x * y) <= 5e-135:
		tmp = z * (t / -a_m)
	elif (x * y) <= 5e-90:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e+112:
		tmp = z / (a_m / -t)
	else:
		tmp = t_1
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(y / Float64(a_m / x))
	tmp = 0.0
	if (Float64(x * y) <= -1e+37)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-135)
		tmp = Float64(z * Float64(t / Float64(-a_m)));
	elseif (Float64(x * y) <= 5e-90)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e+112)
		tmp = Float64(z / Float64(a_m / Float64(-t)));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = y / (a_m / x);
	tmp = 0.0;
	if ((x * y) <= -1e+37)
		tmp = t_1;
	elseif ((x * y) <= 5e-135)
		tmp = z * (t / -a_m);
	elseif ((x * y) <= 5e-90)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e+112)
		tmp = z / (a_m / -t);
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+37], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-135], N[(z * N[(t / (-a$95$m)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-90], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+112], N[(z / N[(a$95$m / (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5e112 < (*.f64 x y)

   1. Initial program 82.1%

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

      1. div-sub 74.9%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in x around 0 74.9%

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

   6. Taylor expanded in x around inf 74.1%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-/r/ 81.3%

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

   8. Simplified 81.3%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 79.3%

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

      1. *-commutative 79.3%

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

      2. associate-*r/ 77.5%

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

      3. neg-mul-1 77.5%

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

      4. distribute-rgt-neg-in 77.5%

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

      5. distribute-frac-neg 77.5%

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

   5. Simplified 77.5%

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

   if 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. associate-*r/ 79.5%

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

   5. Simplified 79.5%

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

      1. clear-num 79.5%

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

      2. un-div-inv 69.2%

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

   7. Applied egg-rr 69.2%

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

      1. associate-/r/ 79.4%

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

   9. Applied egg-rr 79.4%

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

   if 5.00000000000000019e-90 < (*.f64 x y) < 5e112

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 64.9%

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

      1. mul-1-neg 64.9%

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

      2. associate-/l* 64.5%

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

      3. distribute-rgt-neg-in 64.5%

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

      4. distribute-neg-frac2 64.5%

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

   5. Simplified 64.5%

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

      1. *-commutative 64.5%

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

      2. distribute-frac-neg2 64.5%

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

      3. distribute-lft-neg-in 64.5%

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

      4. associate-/r/ 62.2%

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

      5. distribute-neg-frac 62.2%

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

   7. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{y}{\frac{a\_m}{x}}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{\frac{a\_m}{-t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ y (/ a_m x))))
   (*
    a_s
    (if (<= (* x y) -1e+37)
      t_1
      (if (<= (* x y) 5e-135)
        (/ (* z (- t)) a_m)
        (if (<= (* x y) 5e-90)
          (* y (/ x a_m))
          (if (<= (* x y) 5e+112) (/ z (/ a_m (- t))) t_1)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = (z * -t) / a_m;
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+112) {
		tmp = z / (a_m / -t);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a_m / x)
    if ((x * y) <= (-1d+37)) then
        tmp = t_1
    else if ((x * y) <= 5d-135) then
        tmp = (z * -t) / a_m
    else if ((x * y) <= 5d-90) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d+112) then
        tmp = z / (a_m / -t)
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y / (a_m / x);
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = (z * -t) / a_m;
	} else if ((x * y) <= 5e-90) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+112) {
		tmp = z / (a_m / -t);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = y / (a_m / x)
	tmp = 0
	if (x * y) <= -1e+37:
		tmp = t_1
	elif (x * y) <= 5e-135:
		tmp = (z * -t) / a_m
	elif (x * y) <= 5e-90:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e+112:
		tmp = z / (a_m / -t)
	else:
		tmp = t_1
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(y / Float64(a_m / x))
	tmp = 0.0
	if (Float64(x * y) <= -1e+37)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-135)
		tmp = Float64(Float64(z * Float64(-t)) / a_m);
	elseif (Float64(x * y) <= 5e-90)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e+112)
		tmp = Float64(z / Float64(a_m / Float64(-t)));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = y / (a_m / x);
	tmp = 0.0;
	if ((x * y) <= -1e+37)
		tmp = t_1;
	elseif ((x * y) <= 5e-135)
		tmp = (z * -t) / a_m;
	elseif ((x * y) <= 5e-90)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e+112)
		tmp = z / (a_m / -t);
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+37], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-135], N[(N[(z * (-t)), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-90], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+112], N[(z / N[(a$95$m / (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5e112 < (*.f64 x y)

   1. Initial program 82.1%

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

      1. div-sub 74.9%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in x around 0 74.9%

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

   6. Taylor expanded in x around inf 74.1%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-/r/ 81.3%

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

   8. Simplified 81.3%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 79.3%

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

      1. associate-*r* 79.3%

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

      2. mul-1-neg 79.3%

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

   5. Simplified 79.3%

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

   if 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. associate-*r/ 79.5%

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

   5. Simplified 79.5%

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

      1. clear-num 79.5%

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

      2. un-div-inv 69.2%

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

   7. Applied egg-rr 69.2%

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

      1. associate-/r/ 79.4%

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

   9. Applied egg-rr 79.4%

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

   if 5.00000000000000019e-90 < (*.f64 x y) < 5e112

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 64.9%

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

      1. mul-1-neg 64.9%

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

      2. associate-/l* 64.5%

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

      3. distribute-rgt-neg-in 64.5%

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

      4. distribute-neg-frac2 64.5%

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

   5. Simplified 64.5%

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

      1. *-commutative 64.5%

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

      2. distribute-frac-neg2 64.5%

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

      3. distribute-lft-neg-in 64.5%

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

      4. associate-/r/ 62.2%

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

      5. distribute-neg-frac 62.2%

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

   7. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+303}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -5e+303)
    (* y (/ x a_m))
    (if (<= (* x y) 5e+258) (/ (- (* x y) (* z t)) a_m) (* x (/ y a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -5e+303) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+258) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-5d+303)) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d+258) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = x * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -5e+303) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e+258) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -5e+303:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e+258:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = x * (y / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -5e+303)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e+258)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(x * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -5e+303)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e+258)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = x * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+303], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+258], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999997e303

   1. Initial program 62.4%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. associate-*r/ 96.0%

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

   5. Simplified 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 95.9%

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

   7. Applied egg-rr 95.9%

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

      1. associate-/r/ 96.1%

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

   9. Applied egg-rr 96.1%

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

   if -4.9999999999999997e303 < (*.f64 x y) < 5e258

   1. Initial program 95.0%

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

   if 5e258 < (*.f64 x y)

   1. Initial program 61.7%

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

   3. Taylor expanded in x around inf 62.0%

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

      1. associate-*r/ 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+303}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;\frac{t\_1}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\frac{x \cdot y}{z} - t}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (* a_s (if (<= t_1 5e+269) (/ t_1 a_m) (* z (/ (- (/ (* x y) z) t) a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 5e+269) {
		tmp = t_1 / a_m;
	} else {
		tmp = z * ((((x * y) / z) - t) / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= 5d+269) then
        tmp = t_1 / a_m
    else
        tmp = z * ((((x * y) / z) - t) / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 5e+269) {
		tmp = t_1 / a_m;
	} else {
		tmp = z * ((((x * y) / z) - t) / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= 5e+269:
		tmp = t_1 / a_m
	else:
		tmp = z * ((((x * y) / z) - t) / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= 5e+269)
		tmp = Float64(t_1 / a_m);
	else
		tmp = Float64(z * Float64(Float64(Float64(Float64(x * y) / z) - t) / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 5e+269)
		tmp = t_1 / a_m;
	else
		tmp = z * ((((x * y) / z) - t) / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, 5e+269], N[(t$95$1 / a$95$m), $MachinePrecision], N[(z * N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] - t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000002e269

   1. Initial program 95.8%

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

   if 5.0000000000000002e269 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.3%

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

      1. div-sub 50.7%

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

      2. associate-/l* 60.3%

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

      3. associate-/l* 87.1%

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

   4. Applied egg-rr 87.1%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.1%

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

   6. Applied egg-rr 87.1%

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

   7. Taylor expanded in z around inf 72.6%

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

      1. times-frac 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in a around 0 80.6%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+269}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\frac{x \cdot y}{z} - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 9 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - z \cdot \frac{t}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= a_m 9e+14)
    (/ (- (* x y) (* z t)) a_m)
    (- (* x (/ y a_m)) (* z (/ t a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 9e+14) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (a_m <= 9d+14) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = (x * (y / a_m)) - (z * (t / a_m))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (a_m <= 9e+14) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if a_m <= 9e+14:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = (x * (y / a_m)) - (z * (t / a_m))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (a_m <= 9e+14)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(z * Float64(t / a_m)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (a_m <= 9e+14)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = (x * (y / a_m)) - (z * (t / a_m));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[a$95$m, 9e+14], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 9e14

   1. Initial program 94.3%

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

   if 9e14 < a

   1. Initial program 76.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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* 80.5%

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

      3. associate-/l* 92.9%

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

   4. Applied egg-rr 92.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= z -4.6e-122) (* x (/ y a_m)) (* y (/ x a_m)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -4.6e-122) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (z <= (-4.6d-122)) then
        tmp = x * (y / a_m)
    else
        tmp = y * (x / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -4.6e-122) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if z <= -4.6e-122:
		tmp = x * (y / a_m)
	else:
		tmp = y * (x / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (z <= -4.6e-122)
		tmp = Float64(x * Float64(y / a_m));
	else
		tmp = Float64(y * Float64(x / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (z <= -4.6e-122)
		tmp = x * (y / a_m);
	else
		tmp = y * (x / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[z, -4.6e-122], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000014e-122

   1. Initial program 88.9%

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

   3. Taylor expanded in x around inf 41.4%

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

      1. associate-*r/ 45.3%

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

   5. Simplified 45.3%

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

   if -4.60000000000000014e-122 < z

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 53.1%

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

      1. associate-*r/ 56.6%

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

   5. Simplified 56.6%

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

      1. clear-num 56.6%

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

      2. un-div-inv 55.3%

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

   7. Applied egg-rr 55.3%

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

      1. associate-/r/ 56.2%

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

   9. Applied egg-rr 56.2%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(x \cdot \frac{y}{a\_m}\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* x (/ y a_m))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * (x * (y / a_m))
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (x * (y / a_m))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(x * Float64(y / a_m)))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (x * (y / a_m));
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.1%

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

3. Taylor expanded in x around inf 48.7%

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

   1. associate-*r/ 52.3%

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

5. Simplified 52.3%

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

6. Final simplification 52.3%

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