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

Percentage Accurate: 90.9% → 97.1%

Time: 8.7s

Alternatives: 8

Speedup: 0.4×

• 28.6% 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: 90.9% 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: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{a}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+290}:\\ \;\;\;\;t\_1 - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

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 (* y (/ x a))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 -5e+290)
     (- t_1 (/ z (/ a t)))
     (if (<= t_2 2e+307) (/ t_2 a) (- t_1 (* t (/ z a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / a);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+290) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 2e+307) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (t * (z / a));
	}
	return tmp;
}

Fortran

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 = y * (x / a)
    t_2 = (x * y) - (z * t)
    if (t_2 <= (-5d+290)) then
        tmp = t_1 - (z / (a / t))
    else if (t_2 <= 2d+307) then
        tmp = t_2 / a
    else
        tmp = t_1 - (t * (z / a))
    end if
    code = tmp
end function

Java

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 = y * (x / a);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+290) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 2e+307) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (x / a)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -5e+290:
		tmp = t_1 - (z / (a / t))
	elif t_2 <= 2e+307:
		tmp = t_2 / a
	else:
		tmp = t_1 - (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / a))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+290)
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	elseif (t_2 <= 2e+307)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (x / a);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -5e+290)
		tmp = t_1 - (z / (a / t));
	elseif (t_2 <= 2e+307)
		tmp = t_2 / a;
	else
		tmp = t_1 - (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

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[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+290], N[(t$95$1 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+307], N[(t$95$2 / a), $MachinePrecision], N[(t$95$1 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.9999999999999998e290

   1. Initial program 60.4%

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

      1. div-sub 53.5%

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

      2. associate-/l* 77.4%

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

      3. associate-/l* 88.3%

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

   4. Applied egg-rr 88.3%

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

      1. associate-/r/ 90.5%

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

   6. Applied egg-rr 90.5%

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

   if -4.9999999999999998e290 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.99999999999999997e307

   1. Initial program 98.6%

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

   if 1.99999999999999997e307 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 53.4%

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

      1. div-sub 50.3%

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

      2. associate-/l* 64.7%

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

      3. associate-/l* 87.6%

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

   4. Applied egg-rr 87.6%

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

      1. associate-/r/ 84.6%

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

   6. Applied egg-rr 84.6%

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

      1. associate-/r/ 87.7%

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

   8. Applied egg-rr 87.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+290}:\\ \;\;\;\;y \cdot \frac{x}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ t_2 := \frac{x \cdot y}{a}\\ t_3 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -200000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+240}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

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 (* z (/ (- t) a))) (t_2 (/ (* x y) a)) (t_3 (* x (/ y a))))
   (if (<= (* x y) -2e+94)
     t_3
     (if (<= (* x y) -1e+57)
       t_1
       (if (<= (* x y) -200000000000.0)
         t_2
         (if (<= (* x y) 2e-124) t_1 (if (<= (* x y) 5e+240) t_2 t_3)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-t / a);
	double t_2 = (x * y) / a;
	double t_3 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+94) {
		tmp = t_3;
	} else if ((x * y) <= -1e+57) {
		tmp = t_1;
	} else if ((x * y) <= -200000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 2e-124) {
		tmp = t_1;
	} else if ((x * y) <= 5e+240) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

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) :: t_3
    real(8) :: tmp
    t_1 = z * (-t / a)
    t_2 = (x * y) / a
    t_3 = x * (y / a)
    if ((x * y) <= (-2d+94)) then
        tmp = t_3
    else if ((x * y) <= (-1d+57)) then
        tmp = t_1
    else if ((x * y) <= (-200000000000.0d0)) then
        tmp = t_2
    else if ((x * y) <= 2d-124) then
        tmp = t_1
    else if ((x * y) <= 5d+240) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

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 = z * (-t / a);
	double t_2 = (x * y) / a;
	double t_3 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+94) {
		tmp = t_3;
	} else if ((x * y) <= -1e+57) {
		tmp = t_1;
	} else if ((x * y) <= -200000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 2e-124) {
		tmp = t_1;
	} else if ((x * y) <= 5e+240) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = z * (-t / a)
	t_2 = (x * y) / a
	t_3 = x * (y / a)
	tmp = 0
	if (x * y) <= -2e+94:
		tmp = t_3
	elif (x * y) <= -1e+57:
		tmp = t_1
	elif (x * y) <= -200000000000.0:
		tmp = t_2
	elif (x * y) <= 2e-124:
		tmp = t_1
	elif (x * y) <= 5e+240:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-t) / a))
	t_2 = Float64(Float64(x * y) / a)
	t_3 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e+94)
		tmp = t_3;
	elseif (Float64(x * y) <= -1e+57)
		tmp = t_1;
	elseif (Float64(x * y) <= -200000000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e-124)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+240)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-t / a);
	t_2 = (x * y) / a;
	t_3 = x * (y / a);
	tmp = 0.0;
	if ((x * y) <= -2e+94)
		tmp = t_3;
	elseif ((x * y) <= -1e+57)
		tmp = t_1;
	elseif ((x * y) <= -200000000000.0)
		tmp = t_2;
	elseif ((x * y) <= 2e-124)
		tmp = t_1;
	elseif ((x * y) <= 5e+240)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

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[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+94], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1e+57], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -200000000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e-124], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+240], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e94 or 5.0000000000000003e240 < (*.f64 x y)

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf 72.9%

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

      1. associate-*l/ 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l/ 93.4%

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

      3. *-commutative 93.4%

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

   8. Simplified 93.4%

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

   if -2e94 < (*.f64 x y) < -1.00000000000000005e57 or -2e11 < (*.f64 x y) < 1.99999999999999987e-124

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

      1. associate-/r/ 78.4%

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

   7. Applied egg-rr 78.4%

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

   if -1.00000000000000005e57 < (*.f64 x y) < -2e11 or 1.99999999999999987e-124 < (*.f64 x y) < 5.0000000000000003e240

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 74.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq -200000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+240}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ t_2 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq -200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-124}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

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 (* x (/ y a))))
   (if (<= (* x y) -2e+94)
     t_2
     (if (<= (* x y) -1e+57)
       (* z (/ (- t) a))
       (if (<= (* x y) -200000000000.0)
         t_1
         (if (<= (* x y) 2e-124)
           (/ (- t) (/ a z))
           (if (<= (* x y) 5e+240) t_1 t_2)))))))

C

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 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+94) {
		tmp = t_2;
	} else if ((x * y) <= -1e+57) {
		tmp = z * (-t / a);
	} else if ((x * y) <= -200000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e-124) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 5e+240) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 = x * (y / a)
    if ((x * y) <= (-2d+94)) then
        tmp = t_2
    else if ((x * y) <= (-1d+57)) then
        tmp = z * (-t / a)
    else if ((x * y) <= (-200000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 2d-124) then
        tmp = -t / (a / z)
    else if ((x * y) <= 5d+240) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+94) {
		tmp = t_2;
	} else if ((x * y) <= -1e+57) {
		tmp = z * (-t / a);
	} else if ((x * y) <= -200000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e-124) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 5e+240) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 = x * (y / a)
	tmp = 0
	if (x * y) <= -2e+94:
		tmp = t_2
	elif (x * y) <= -1e+57:
		tmp = z * (-t / a)
	elif (x * y) <= -200000000000.0:
		tmp = t_1
	elif (x * y) <= 2e-124:
		tmp = -t / (a / z)
	elif (x * y) <= 5e+240:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

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(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e+94)
		tmp = t_2;
	elseif (Float64(x * y) <= -1e+57)
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (Float64(x * y) <= -200000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-124)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (Float64(x * y) <= 5e+240)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

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 = x * (y / a);
	tmp = 0.0;
	if ((x * y) <= -2e+94)
		tmp = t_2;
	elseif ((x * y) <= -1e+57)
		tmp = z * (-t / a);
	elseif ((x * y) <= -200000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 2e-124)
		tmp = -t / (a / z);
	elseif ((x * y) <= 5e+240)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+94], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1e+57], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -200000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-124], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+240], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e94 or 5.0000000000000003e240 < (*.f64 x y)

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf 72.9%

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

      1. associate-*l/ 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l/ 93.4%

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

      3. *-commutative 93.4%

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

   8. Simplified 93.4%

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

   if -2e94 < (*.f64 x y) < -1.00000000000000005e57

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

      1. associate-/r/ 73.6%

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

   7. Applied egg-rr 73.6%

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

   if -1.00000000000000005e57 < (*.f64 x y) < -2e11 or 1.99999999999999987e-124 < (*.f64 x y) < 5.0000000000000003e240

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 74.4%

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

   if -2e11 < (*.f64 x y) < 1.99999999999999987e-124

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq -200000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-124}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+240}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+290} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -5e+290) (not (<= t_1 2e+307)))
     (- (* y (/ x a)) (* t (/ z a)))
     (/ t_1 a))))

C

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 <= -5e+290) || !(t_1 <= 2e+307)) {
		tmp = (y * (x / a)) - (t * (z / 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.
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 <= (-5d+290)) .or. (.not. (t_1 <= 2d+307))) then
        tmp = (y * (x / a)) - (t * (z / a))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

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 <= -5e+290) || !(t_1 <= 2e+307)) {
		tmp = (y * (x / a)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[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 <= -5e+290) or not (t_1 <= 2e+307):
		tmp = (y * (x / a)) - (t * (z / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

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 <= -5e+290) || !(t_1 <= 2e+307))
		tmp = Float64(Float64(y * Float64(x / a)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

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 <= -5e+290) || ~((t_1 <= 2e+307)))
		tmp = (y * (x / a)) - (t * (z / 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.
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, -5e+290], N[Not[LessEqual[t$95$1, 2e+307]], $MachinePrecision]], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.9999999999999998e290 or 1.99999999999999997e307 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 57.4%

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

      1. div-sub 52.1%

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

      2. associate-/l* 71.9%

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

      3. associate-/l* 88.0%

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

   4. Applied egg-rr 88.0%

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

      1. associate-/r/ 88.0%

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

   6. Applied egg-rr 88.0%

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

      1. associate-/r/ 90.6%

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

   8. Applied egg-rr 90.6%

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

   if -4.9999999999999998e290 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.99999999999999997e307

   1. Initial program 98.6%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+290} \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+265} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+248}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+265) (not (<= (* x y) 5e+248)))
   (* x (/ y a))
   (/ (- (* x y) (* z t)) a)))

C

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+265) || !((x * y) <= 5e+248)) {
		tmp = x * (y / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Fortran

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+265)) .or. (.not. ((x * y) <= 5d+248))) then
        tmp = x * (y / a)
    else
        tmp = ((x * y) - (z * t)) / a
    end if
    code = tmp
end function

Java

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+265) || !((x * y) <= 5e+248)) {
		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])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+265) or not ((x * y) <= 5e+248):
		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])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+265) || !(Float64(x * y) <= 5e+248))
		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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+265) || ~(((x * y) <= 5e+248)))
		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.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+265], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+248]], $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) < -5.0000000000000002e265 or 4.9999999999999996e248 < (*.f64 x y)

   1. Initial program 62.9%

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

   3. Taylor expanded in x around inf 66.6%

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

      1. associate-*l/ 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in x around 0 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*l/ 98.1%

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

      3. *-commutative 98.1%

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

   8. Simplified 98.1%

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

   if -5.0000000000000002e265 < (*.f64 x y) < 4.9999999999999996e248

   1. Initial program 92.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+265} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+248}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

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 -5e-102) (* y (/ x a)) (* x (/ y a))))

C

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 <= -5e-102) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

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 <= (-5d-102)) then
        tmp = y * (x / a)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

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 <= -5e-102) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -5e-102:
		tmp = y * (x / a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5e-102)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

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 <= -5e-102)
		tmp = y * (x / a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

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[x, -5e-102], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000026e-102

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. associate-*l/ 71.0%

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

   5. Simplified 71.0%

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

   if -5.00000000000000026e-102 < x

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf 46.7%

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

      1. associate-*l/ 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in x around 0 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-*l/ 49.9%

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

      3. *-commutative 49.9%

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

   8. Simplified 49.9%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

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 -6.2e-102) (/ y (/ a x)) (* x (/ y a))))

C

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 <= -6.2e-102) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

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 <= (-6.2d-102)) then
        tmp = y / (a / x)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

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 <= -6.2e-102) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.2e-102:
		tmp = y / (a / x)
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.2e-102)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

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 <= -6.2e-102)
		tmp = y / (a / x);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

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[x, -6.2e-102], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.20000000000000026e-102

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. associate-*l/ 71.0%

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

   5. Simplified 71.0%

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

      1. *-commutative 71.0%

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

      2. clear-num 71.0%

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

      3. un-div-inv 71.1%

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

   7. Applied egg-rr 71.1%

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

   if -6.20000000000000026e-102 < x

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf 46.7%

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

      1. associate-*l/ 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in x around 0 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-*l/ 49.9%

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

      3. *-commutative 49.9%

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

   8. Simplified 49.9%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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.
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;
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])
def code(x, y, z, t, a):
	return x * (y / a)

Julia

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])){:}
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.
code[x_, y_, z_, t_, a_] := N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.4%

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

3. Taylor expanded in x around inf 51.7%

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

   1. associate-*l/ 54.8%

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

5. Simplified 54.8%

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

6. Taylor expanded in x around 0 51.7%

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

   1. *-commutative 51.7%

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

   2. associate-*l/ 55.2%

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

   3. *-commutative 55.2%

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

8. Simplified 55.2%

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

9. Final simplification 55.2%

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

Developer target: 91.6% 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 2024041 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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