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

Percentage Accurate: 91.2% → 94.1%

Time: 8.5s

Alternatives: 8

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% 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: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \end{array} \end{array} \]

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 (<= (- (* x y) (* z t)) 5e+297)
   (/ (fma x y (* z (- t))) a)
   (* x (/ (- y (* t (/ z 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 (((x * y) - (z * t)) <= 5e+297) {
		tmp = fma(x, y, (z * -t)) / a;
	} else {
		tmp = x * ((y - (t * (z / 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 (Float64(Float64(x * y) - Float64(z * t)) <= 5e+297)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a);
	else
		tmp = Float64(x * Float64(Float64(y - Float64(t * Float64(z / x))) / a));
	end
	return 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[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision], 5e+297], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(N[(y - N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e297

   1. Initial program 97.5%

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

      1. div-sub 97.5%

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

      2. *-commutative 97.5%

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

      3. div-sub 97.5%

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

      4. *-commutative 97.5%

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

      5. fma-neg 97.5%

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

      6. distribute-rgt-neg-out 97.5%

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

   3. Simplified 97.5%

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

   if 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.6%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in x around inf 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. times-frac 83.7%

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

      5. associate-*l/ 79.5%

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

      6. associate-/l* 75.0%

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

      7. div-sub 86.7%

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

      8. associate-/l* 91.1%

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

   8. Simplified 91.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 5e+297) (/ t_1 a) (* x (/ (- y (* t (/ z 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = x * ((y - (t * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= 5d+297) then
        tmp = t_1 / a
    else
        tmp = x * ((y - (t * (z / 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = x * ((y - (t * (z / x))) / 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+297:
		tmp = t_1 / a
	else:
		tmp = x * ((y - (t * (z / x))) / 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+297)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(x * Float64(Float64(y - Float64(t * Float64(z / 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 5e+297)
		tmp = t_1 / a;
	else
		tmp = x * ((y - (t * (z / x))) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+297], N[(t$95$1 / a), $MachinePrecision], N[(x * N[(N[(y - N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e297

   1. Initial program 97.5%

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

   if 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.6%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in x around inf 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. times-frac 83.7%

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

      5. associate-*l/ 79.5%

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

      6. associate-/l* 75.0%

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

      7. div-sub 86.7%

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

      8. associate-/l* 91.1%

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

   8. Simplified 91.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - t \cdot \frac{z}{x}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-84} \lor \neg \left(z \cdot t \leq 10^{-36}\right):\\ \;\;\;\;-\frac{z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 (or (<= (* z t) -1e-84) (not (<= (* z t) 1e-36)))
   (- (* (/ z a) t))
   (/ (* 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 (((z * t) <= -1e-84) || !((z * t) <= 1e-36)) {
		tmp = -((z / a) * t);
	} 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 (((z * t) <= (-1d-84)) .or. (.not. ((z * t) <= 1d-36))) then
        tmp = -((z / a) * t)
    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 (((z * t) <= -1e-84) || !((z * t) <= 1e-36)) {
		tmp = -((z / a) * t);
	} 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 ((z * t) <= -1e-84) or not ((z * t) <= 1e-36):
		tmp = -((z / a) * t)
	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 ((Float64(z * t) <= -1e-84) || !(Float64(z * t) <= 1e-36))
		tmp = Float64(-Float64(Float64(z / a) * t));
	else
		tmp = Float64(Float64(x * 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 (((z * t) <= -1e-84) || ~(((z * t) <= 1e-36)))
		tmp = -((z / a) * t);
	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[Or[LessEqual[N[(z * t), $MachinePrecision], -1e-84], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e-36]], $MachinePrecision]], (-N[(N[(z / a), $MachinePrecision] * t), $MachinePrecision]), N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1e-84 or 9.9999999999999994e-37 < (*.f64 z t)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-/l* 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. distribute-neg-frac2 70.3%

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

   5. Simplified 70.3%

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

   if -1e-84 < (*.f64 z t) < 9.9999999999999994e-37

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 83.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-84} \lor \neg \left(z \cdot t \leq 10^{-36}\right):\\ \;\;\;\;-\frac{z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+297}:\\ \;\;\;\;-\frac{z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= (* z t) -2e+297) (- (* (/ z a) t)) (/ (- (* 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 ((z * t) <= -2e+297) {
		tmp = -((z / a) * t);
	} 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 ((z * t) <= (-2d+297)) then
        tmp = -((z / a) * t)
    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 ((z * t) <= -2e+297) {
		tmp = -((z / a) * t);
	} 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 (z * t) <= -2e+297:
		tmp = -((z / a) * t)
	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(z * t) <= -2e+297)
		tmp = Float64(-Float64(Float64(z / a) * t));
	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 ((z * t) <= -2e+297)
		tmp = -((z / a) * t);
	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[LessEqual[N[(z * t), $MachinePrecision], -2e+297], (-N[(N[(z / a), $MachinePrecision] * t), $MachinePrecision]), N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2e297

   1. Initial program 79.6%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

   5. Simplified 99.9%

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

   if -2e297 < (*.f64 z t)

   1. Initial program 95.2%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+297}:\\ \;\;\;\;-\frac{z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+192}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 5e+192) (/ (* x y) a) (* 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 ((x * y) <= 5e+192) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+192) then
        tmp = (x * y) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 5e+192) {
		tmp = (x * y) / a;
	} 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 (x * y) <= 5e+192:
		tmp = (x * y) / a
	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 (Float64(x * y) <= 5e+192)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 5e+192)
		tmp = (x * y) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 5e+192], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.00000000000000033e192

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 46.6%

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

   if 5.00000000000000033e192 < (*.f64 x y)

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 93.3%

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

      1. +-commutative 93.3%

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

      2. mul-1-neg 93.3%

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

      3. unsub-neg 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in x around inf 90.1%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+192}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 5.5e-133) (* x (/ y a)) (* 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 (a <= 5.5e-133) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 5.5d-133) then
        tmp = x * (y / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 5.5e-133) {
		tmp = x * (y / a);
	} 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 a <= 5.5e-133:
		tmp = x * (y / a)
	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 (a <= 5.5e-133)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 5.5e-133)
		tmp = x * (y / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 5.5e-133], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.49999999999999977e-133

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 51.5%

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

      1. associate-*r/ 49.4%

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

   5. Simplified 49.4%

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

   if 5.49999999999999977e-133 < a

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. mul-1-neg 81.4%

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

      3. unsub-neg 81.4%

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

      4. *-commutative 81.4%

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

      5. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in x around inf 48.1%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% 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 93.5%

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

3. Taylor expanded in x around inf 50.1%

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

   1. associate-*r/ 49.0%

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

5. Simplified 49.0%

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

6. Final simplification 49.0%

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

Alternative 8: 51.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

3. Taylor expanded in x around inf 50.1%

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

   1. associate-*r/ 49.0%

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

5. Simplified 49.0%

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

   1. clear-num 49.0%

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

   2. un-div-inv 49.2%

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

7. Applied egg-rr 49.2%

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

8. Final simplification 49.2%

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

Developer target: 91.3% 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 2024077 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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