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

Percentage Accurate: 91.2% → 97.0%

Time: 7.8s

Alternatives: 8

Speedup: 0.4×

• 28.7% 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: 91.2% 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: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+277}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

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 (- INFINITY)) (not (<= t_1 2e+277)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ 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 <= -((double) INFINITY)) || !(t_1 <= 2e+277)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+277)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} 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 <= -math.inf) or not (t_1 <= 2e+277):
		tmp = (x / (a / y)) - (z / (a / t))
	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 <= Float64(-Inf)) || !(t_1 <= 2e+277))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	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 <= -Inf) || ~((t_1 <= 2e+277)))
		tmp = (x / (a / y)) - (z / (a / t));
	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, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+277]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $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)) < -inf.0 or 2.00000000000000001e277 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 63.1%

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

      1. div-sub 59.7%

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

      2. associate-/l* 74.1%

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

      3. associate-/l* 93.1%

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

   4. Applied egg-rr 93.1%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000001e277

   1. Initial program 99.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+277}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+32} \lor \neg \left(z \leq 1.25 \cdot 10^{-148}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ a z))))
   (if (<= z -1.25e+92)
     t_1
     (if (<= z -2.3e+59)
       (/ x (/ a y))
       (if (or (<= z -1.05e+32) (not (<= z 1.25e-148))) t_1 (/ y (/ a x)))))))

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 = -t / (a / z);
	double tmp;
	if (z <= -1.25e+92) {
		tmp = t_1;
	} else if (z <= -2.3e+59) {
		tmp = x / (a / y);
	} else if ((z <= -1.05e+32) || !(z <= 1.25e-148)) {
		tmp = t_1;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = -t / (a / z)
    if (z <= (-1.25d+92)) then
        tmp = t_1
    else if (z <= (-2.3d+59)) then
        tmp = x / (a / y)
    else if ((z <= (-1.05d+32)) .or. (.not. (z <= 1.25d-148))) then
        tmp = t_1
    else
        tmp = y / (a / x)
    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 = -t / (a / z);
	double tmp;
	if (z <= -1.25e+92) {
		tmp = t_1;
	} else if (z <= -2.3e+59) {
		tmp = x / (a / y);
	} else if ((z <= -1.05e+32) || !(z <= 1.25e-148)) {
		tmp = t_1;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -t / (a / z)
	tmp = 0
	if z <= -1.25e+92:
		tmp = t_1
	elif z <= -2.3e+59:
		tmp = x / (a / y)
	elif (z <= -1.05e+32) or not (z <= 1.25e-148):
		tmp = t_1
	else:
		tmp = y / (a / x)
	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(-t) / Float64(a / z))
	tmp = 0.0
	if (z <= -1.25e+92)
		tmp = t_1;
	elseif (z <= -2.3e+59)
		tmp = Float64(x / Float64(a / y));
	elseif ((z <= -1.05e+32) || !(z <= 1.25e-148))
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / x));
	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 = -t / (a / z);
	tmp = 0.0;
	if (z <= -1.25e+92)
		tmp = t_1;
	elseif (z <= -2.3e+59)
		tmp = x / (a / y);
	elseif ((z <= -1.05e+32) || ~((z <= 1.25e-148)))
		tmp = t_1;
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+92], t$95$1, If[LessEqual[z, -2.3e+59], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.05e+32], N[Not[LessEqual[z, 1.25e-148]], $MachinePrecision]], t$95$1, N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25000000000000005e92 or -2.30000000000000008e59 < z < -1.05e32 or 1.25e-148 < z

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   if -1.25000000000000005e92 < z < -2.30000000000000008e59

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 60.5%

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

      1. associate-*l/ 60.5%

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

   5. Simplified 60.5%

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

      1. associate-/r/ 60.9%

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

   7. Applied egg-rr 60.9%

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

   if -1.05e32 < z < 1.25e-148

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. associate-*l/ 76.3%

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

   5. Simplified 76.3%

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

      1. *-commutative 76.3%

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

      2. clear-num 76.3%

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

      3. un-div-inv 77.0%

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

   7. Applied egg-rr 77.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+92}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+32} \lor \neg \left(z \leq 1.25 \cdot 10^{-148}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (- t) (/ a z))))
   (if (<= z -2.2e+90)
     t_1
     (if (<= z -4.6e+54)
       (/ x (/ a y))
       (if (<= z -2.3e+31)
         t_1
         (if (<= z 1.25e-148) (/ y (/ a x)) (* 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 t_1 = -t / (a / z);
	double tmp;
	if (z <= -2.2e+90) {
		tmp = t_1;
	} else if (z <= -4.6e+54) {
		tmp = x / (a / y);
	} else if (z <= -2.3e+31) {
		tmp = t_1;
	} else if (z <= 1.25e-148) {
		tmp = y / (a / x);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = -t / (a / z)
    if (z <= (-2.2d+90)) then
        tmp = t_1
    else if (z <= (-4.6d+54)) then
        tmp = x / (a / y)
    else if (z <= (-2.3d+31)) then
        tmp = t_1
    else if (z <= 1.25d-148) then
        tmp = y / (a / x)
    else
        tmp = 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 t_1 = -t / (a / z);
	double tmp;
	if (z <= -2.2e+90) {
		tmp = t_1;
	} else if (z <= -4.6e+54) {
		tmp = x / (a / y);
	} else if (z <= -2.3e+31) {
		tmp = t_1;
	} else if (z <= 1.25e-148) {
		tmp = y / (a / x);
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -t / (a / z)
	tmp = 0
	if z <= -2.2e+90:
		tmp = t_1
	elif z <= -4.6e+54:
		tmp = x / (a / y)
	elif z <= -2.3e+31:
		tmp = t_1
	elif z <= 1.25e-148:
		tmp = y / (a / x)
	else:
		tmp = z * (-t / 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(-t) / Float64(a / z))
	tmp = 0.0
	if (z <= -2.2e+90)
		tmp = t_1;
	elseif (z <= -4.6e+54)
		tmp = Float64(x / Float64(a / y));
	elseif (z <= -2.3e+31)
		tmp = t_1;
	elseif (z <= 1.25e-148)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(z * Float64(Float64(-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)
	t_1 = -t / (a / z);
	tmp = 0.0;
	if (z <= -2.2e+90)
		tmp = t_1;
	elseif (z <= -4.6e+54)
		tmp = x / (a / y);
	elseif (z <= -2.3e+31)
		tmp = t_1;
	elseif (z <= 1.25e-148)
		tmp = y / (a / x);
	else
		tmp = 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_] := Block[{t$95$1 = N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+90], t$95$1, If[LessEqual[z, -4.6e+54], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e+31], t$95$1, If[LessEqual[z, 1.25e-148], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999999e90 or -4.59999999999999988e54 < z < -2.3e31

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -2.1999999999999999e90 < z < -4.59999999999999988e54

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 60.5%

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

      1. associate-*l/ 60.5%

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

   5. Simplified 60.5%

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

      1. associate-/r/ 60.9%

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

   7. Applied egg-rr 60.9%

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

   if -2.3e31 < z < 1.25e-148

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. associate-*l/ 76.3%

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

   5. Simplified 76.3%

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

      1. *-commutative 76.3%

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

      2. clear-num 76.3%

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

      3. un-div-inv 77.0%

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

   7. Applied egg-rr 77.0%

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

   if 1.25e-148 < z

   1. Initial program 90.8%

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

      1. div-sub 90.8%

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

      2. associate-/l* 90.8%

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

      3. associate-/l* 93.0%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in x around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. associate-*l/ 59.3%

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

      3. *-commutative 59.3%

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

      4. distribute-lft-neg-in 59.3%

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

   7. Simplified 59.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \end{array} \end{array} \]

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 (/ (- t) (/ a z))))
   (if (<= z -2.1e+90)
     t_1
     (if (<= z -4.4e+57)
       (/ x (/ a y))
       (if (<= z -7.5e+32)
         t_1
         (if (<= z 1.25e-148) (/ y (/ a x)) (* (/ z a) (- t))))))))

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 = -t / (a / z);
	double tmp;
	if (z <= -2.1e+90) {
		tmp = t_1;
	} else if (z <= -4.4e+57) {
		tmp = x / (a / y);
	} else if (z <= -7.5e+32) {
		tmp = t_1;
	} else if (z <= 1.25e-148) {
		tmp = y / (a / x);
	} else {
		tmp = (z / a) * -t;
	}
	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 = -t / (a / z)
    if (z <= (-2.1d+90)) then
        tmp = t_1
    else if (z <= (-4.4d+57)) then
        tmp = x / (a / y)
    else if (z <= (-7.5d+32)) then
        tmp = t_1
    else if (z <= 1.25d-148) then
        tmp = y / (a / x)
    else
        tmp = (z / a) * -t
    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 = -t / (a / z);
	double tmp;
	if (z <= -2.1e+90) {
		tmp = t_1;
	} else if (z <= -4.4e+57) {
		tmp = x / (a / y);
	} else if (z <= -7.5e+32) {
		tmp = t_1;
	} else if (z <= 1.25e-148) {
		tmp = y / (a / x);
	} else {
		tmp = (z / a) * -t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -t / (a / z)
	tmp = 0
	if z <= -2.1e+90:
		tmp = t_1
	elif z <= -4.4e+57:
		tmp = x / (a / y)
	elif z <= -7.5e+32:
		tmp = t_1
	elif z <= 1.25e-148:
		tmp = y / (a / x)
	else:
		tmp = (z / a) * -t
	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(-t) / Float64(a / z))
	tmp = 0.0
	if (z <= -2.1e+90)
		tmp = t_1;
	elseif (z <= -4.4e+57)
		tmp = Float64(x / Float64(a / y));
	elseif (z <= -7.5e+32)
		tmp = t_1;
	elseif (z <= 1.25e-148)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(Float64(z / a) * Float64(-t));
	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 = -t / (a / z);
	tmp = 0.0;
	if (z <= -2.1e+90)
		tmp = t_1;
	elseif (z <= -4.4e+57)
		tmp = x / (a / y);
	elseif (z <= -7.5e+32)
		tmp = t_1;
	elseif (z <= 1.25e-148)
		tmp = y / (a / x);
	else
		tmp = (z / a) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+90], t$95$1, If[LessEqual[z, -4.4e+57], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e+32], t$95$1, If[LessEqual[z, 1.25e-148], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.09999999999999981e90 or -4.4000000000000001e57 < z < -7.49999999999999959e32

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -2.09999999999999981e90 < z < -4.4000000000000001e57

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 60.5%

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

      1. associate-*l/ 60.5%

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

   5. Simplified 60.5%

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

      1. associate-/r/ 60.9%

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

   7. Applied egg-rr 60.9%

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

   if -7.49999999999999959e32 < z < 1.25e-148

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. associate-*l/ 76.3%

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

   5. Simplified 76.3%

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

      1. *-commutative 76.3%

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

      2. clear-num 76.3%

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

      3. un-div-inv 77.0%

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

   7. Applied egg-rr 77.0%

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

   if 1.25e-148 < z

   1. Initial program 90.8%

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

   3. Taylor expanded in x around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*l/ 57.7%

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

      4. distribute-rgt-neg-in 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+193}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+260}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

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 (<= (* z t) -2e+193)
   (/ z (/ (- a) t))
   (if (<= (* z t) 5e+260) (/ (- (* x y) (* z t)) a) (* 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 ((z * t) <= -2e+193) {
		tmp = z / (-a / t);
	} else if ((z * t) <= 5e+260) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = 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 ((z * t) <= (-2d+193)) then
        tmp = z / (-a / t)
    else if ((z * t) <= 5d+260) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = 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 ((z * t) <= -2e+193) {
		tmp = z / (-a / t);
	} else if ((z * t) <= 5e+260) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = 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 (z * t) <= -2e+193:
		tmp = z / (-a / t)
	elif (z * t) <= 5e+260:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = 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(z * t) <= -2e+193)
		tmp = Float64(z / Float64(Float64(-a) / t));
	elseif (Float64(z * t) <= 5e+260)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(z * Float64(Float64(-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 ((z * t) <= -2e+193)
		tmp = z / (-a / t);
	elseif ((z * t) <= 5e+260)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = 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[LessEqual[N[(z * t), $MachinePrecision], -2e+193], N[(z / N[((-a) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+260], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.00000000000000013e193

   1. Initial program 61.1%

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

      1. div-sub 55.2%

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

      2. associate-/l* 55.2%

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

      3. associate-/l* 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in x around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. distribute-lft-neg-in 99.6%

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

   7. Simplified 99.6%

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

      1. add-sqr-sqrt 70.1%

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

      2. sqrt-unprod 26.5%

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

      3. sqr-neg 26.5%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 0.4%

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

      6. clear-num 0.4%

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

      7. div-inv 0.4%

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

      8. frac-2neg 0.4%

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

      9. add-sqr-sqrt 0.3%

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

      10. sqrt-unprod 18.6%

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

      11. sqr-neg 18.6%

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

      12. sqrt-unprod 29.4%

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

      13. add-sqr-sqrt 100.0%

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

      14. distribute-neg-frac 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -2.00000000000000013e193 < (*.f64 z t) < 4.9999999999999996e260

   1. Initial program 95.9%

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

   if 4.9999999999999996e260 < (*.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 45.8%

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

      2. associate-/l* 46.0%

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

      3. associate-/l* 87.1%

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

   4. Applied egg-rr 87.1%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. associate-*l/ 98.9%

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

      3. *-commutative 98.9%

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

      4. distribute-lft-neg-in 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+193}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+260}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+76) (/ x (/ a y)) (* y (/ x 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 (z <= -1.25e+76) {
		tmp = x / (a / y);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (z <= (-1.25d+76)) then
        tmp = x / (a / y)
    else
        tmp = y * (x / 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 (z <= -1.25e+76) {
		tmp = x / (a / y);
	} else {
		tmp = y * (x / 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 z <= -1.25e+76:
		tmp = x / (a / y)
	else:
		tmp = y * (x / 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 (z <= -1.25e+76)
		tmp = Float64(x / Float64(a / y));
	else
		tmp = Float64(y * Float64(x / 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 (z <= -1.25e+76)
		tmp = x / (a / y);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+76], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999998e76

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 25.6%

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

      1. associate-*l/ 22.1%

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

   5. Simplified 22.1%

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

      1. associate-/r/ 27.6%

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

   7. Applied egg-rr 27.6%

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

   if -1.24999999999999998e76 < z

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf 58.3%

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

      1. associate-*l/ 59.5%

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

   5. Simplified 59.5%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+90) (/ x (/ a y)) (/ y (/ a x))))

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 (z <= -1.15e+90) {
		tmp = x / (a / y);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (z <= (-1.15d+90)) then
        tmp = x / (a / y)
    else
        tmp = y / (a / x)
    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 (z <= -1.15e+90) {
		tmp = x / (a / y);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+90:
		tmp = x / (a / y)
	else:
		tmp = y / (a / x)
	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 (z <= -1.15e+90)
		tmp = Float64(x / Float64(a / y));
	else
		tmp = Float64(y / Float64(a / x));
	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 (z <= -1.15e+90)
		tmp = x / (a / y);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+90], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e90

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf 26.1%

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

      1. associate-*l/ 22.5%

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

   5. Simplified 22.5%

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

      1. associate-/r/ 28.1%

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

   7. Applied egg-rr 28.1%

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

   if -1.15e90 < z

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf 58.1%

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

      1. associate-*l/ 59.2%

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

   5. Simplified 59.2%

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

      1. *-commutative 59.2%

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

      2. clear-num 59.0%

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

      3. un-div-inv 59.3%

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

   7. Applied egg-rr 59.3%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

3. Taylor expanded in x around inf 51.8%

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

   1. associate-*l/ 52.1%

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

5. Simplified 52.1%

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

6. Final simplification 52.1%

   \[\leadsto y \cdot \frac{x}{a} \]
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 2024019 
(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))