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

Percentage Accurate: 91.8% → 95.9%

Time: 11.7s

Alternatives: 6

Speedup: 0.7×

• 28.8% 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: 91.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x - \frac{t}{\frac{y}{z}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z t)) a)))
   (if (<= t_1 (- INFINITY))
     (- (* x (/ y a)) (* t (/ z a)))
     (if (<= t_1 2e+287) t_1 (/ y (/ a (- x (/ t (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (y / a)) - (t * (z / a));
	} else if (t_1 <= 2e+287) {
		tmp = t_1;
	} else {
		tmp = y / (a / (x - (t / (y / z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / a)) - (t * (z / a));
	} else if (t_1 <= 2e+287) {
		tmp = t_1;
	} else {
		tmp = y / (a / (x - (t / (y / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x * y) - (z * t)) / a
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y / a)) - (t * (z / a))
	elif t_1 <= 2e+287:
		tmp = t_1
	else:
		tmp = y / (a / (x - (t / (y / z))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t * Float64(z / a)));
	elseif (t_1 <= 2e+287)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / Float64(x - Float64(t / Float64(y / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y / a)) - (t * (z / a));
	elseif (t_1 <= 2e+287)
		tmp = t_1;
	else
		tmp = y / (a / (x - (t / (y / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], t$95$1, N[(y / N[(a / N[(x - N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -inf.0

   1. Initial program 79.7%

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

      1. div-sub 75.8%

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

      2. associate-/l* 86.9%

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

      3. *-commutative 86.9%

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

      4. *-un-lft-identity 86.9%

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

      5. times-frac 96.0%

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

   3. Applied egg-rr 96.0%

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

      1. div-inv 96.0%

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

      2. *-commutative 96.0%

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

      3. clear-num 96.1%

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

   5. Applied egg-rr 96.1%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 2.0000000000000002e287

   1. Initial program 98.1%

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

   if 2.0000000000000002e287 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 82.1%

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

      1. div-sub 77.9%

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

      2. associate-/l* 79.4%

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

      3. *-commutative 79.4%

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

      4. *-un-lft-identity 79.4%

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

      5. times-frac 81.2%

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

   3. Applied egg-rr 81.2%

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

      1. associate-*r/ 79.4%

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

      2. *-commutative 79.4%

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

      3. frac-sub 71.3%

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

      4. *-commutative 71.3%

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

   5. Applied egg-rr 71.3%

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

   6. Taylor expanded in a around 0 86.3%

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

      1. associate-/l* 94.1%

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

      2. associate-/l* 96.2%

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

   8. Simplified 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot t}{a} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x - \frac{t}{\frac{y}{z}}}}\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+221} \lor \neg \left(t_1 \leq 5 \cdot 10^{+259}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -5e+221) (not (<= t_1 5e+259)))
     (- (* x (/ y a)) (* t (/ z a)))
     (/ t_1 a))))

C

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+221) || !(t_1 <= 5e+259)) {
		tmp = (x * (y / a)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	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 = (x * y) - (z * t)
    if ((t_1 <= (-5d+221)) .or. (.not. (t_1 <= 5d+259))) then
        tmp = (x * (y / a)) - (t * (z / a))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

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+221) || !(t_1 <= 5e+259)) {
		tmp = (x * (y / a)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -5e+221) or not (t_1 <= 5e+259):
		tmp = (x * (y / a)) - (t * (z / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -5e+221) || !(t_1 <= 5e+259))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -5e+221) || ~((t_1 <= 5e+259)))
		tmp = (x * (y / a)) - (t * (z / a));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

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+221], N[Not[LessEqual[t$95$1, 5e+259]], $MachinePrecision]], N[(N[(x * N[(y / 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)) < -5.0000000000000002e221 or 5.00000000000000033e259 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 78.4%

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

      1. div-sub 77.3%

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

      2. associate-/l* 86.8%

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

      3. *-commutative 86.8%

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

      4. *-un-lft-identity 86.8%

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

      5. times-frac 94.2%

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

   3. Applied egg-rr 94.2%

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

      1. div-inv 94.2%

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

      2. *-commutative 94.2%

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

      3. clear-num 94.3%

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

   5. Applied egg-rr 94.3%

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

   if -5.0000000000000002e221 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000033e259

   1. Initial program 98.3%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+221} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+259}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 3: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+250}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -5e+250)
     (- (/ x (/ a y)) (/ z (/ a t)))
     (if (<= t_1 5e+259) (/ t_1 a) (- (* x (/ y a)) (* t (/ z a)))))))

C

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+250) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else if (t_1 <= 5e+259) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (t * (z / a));
	}
	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 = (x * y) - (z * t)
    if (t_1 <= (-5d+250)) then
        tmp = (x / (a / y)) - (z / (a / t))
    else if (t_1 <= 5d+259) then
        tmp = t_1 / a
    else
        tmp = (x * (y / a)) - (t * (z / a))
    end if
    code = tmp
end function

Java

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+250) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else if (t_1 <= 5e+259) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (t * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -5e+250:
		tmp = (x / (a / y)) - (z / (a / t))
	elif t_1 <= 5e+259:
		tmp = t_1 / a
	else:
		tmp = (x * (y / a)) - (t * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -5e+250)
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	elseif (t_1 <= 5e+259)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -5e+250)
		tmp = (x / (a / y)) - (z / (a / t));
	elseif (t_1 <= 5e+259)
		tmp = t_1 / a;
	else
		tmp = (x * (y / a)) - (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

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+250], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], N[(t$95$1 / a), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000002e250

   1. Initial program 76.5%

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

      1. div-sub 76.5%

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

      2. associate-/l* 92.1%

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

      3. *-commutative 92.1%

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

      4. *-un-lft-identity 92.1%

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

      5. times-frac 97.1%

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

   3. Applied egg-rr 97.1%

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

      1. associate-*r/ 92.1%

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

      2. *-commutative 92.1%

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

      3. associate-/l* 97.2%

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

   5. Applied egg-rr 97.2%

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

   if -5.0000000000000002e250 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000033e259

   1. Initial program 98.4%

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

   if 5.00000000000000033e259 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 74.9%

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

      1. div-sub 72.5%

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

      2. associate-/l* 79.1%

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

      3. *-commutative 79.1%

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

      4. *-un-lft-identity 79.1%

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

      5. times-frac 90.3%

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

   3. Applied egg-rr 90.3%

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

      1. div-inv 90.4%

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

      2. *-commutative 90.4%

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

      3. clear-num 90.4%

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

   5. Applied egg-rr 90.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+250}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - t \cdot \frac{z}{a}\\ \end{array} \]

Alternative 4: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+49)
   (/ x (/ a y))
   (if (<= (* x y) 1e+35) (* t (/ (- z) a)) (* y (/ x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+35) {
		tmp = t * (-z / a);
	} else {
		tmp = y * (x / a);
	}
	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) :: tmp
    if ((x * y) <= (-1d+49)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d+35) then
        tmp = t * (-z / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+35) {
		tmp = t * (-z / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+49:
		tmp = x / (a / y)
	elif (x * y) <= 1e+35:
		tmp = t * (-z / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+49)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e+35)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+49)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e+35)
		tmp = t * (-z / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+49], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+35], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999946e48

   1. Initial program 80.7%

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

   2. Taylor expanded in x around inf 69.2%

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

      1. associate-*l/ 79.6%

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

   4. Simplified 79.6%

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

      1. clear-num 79.5%

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

      2. associate-*l/ 79.6%

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

      3. *-un-lft-identity 79.6%

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

   6. Applied egg-rr 79.6%

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

      1. div-inv 79.5%

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

      2. add-sqr-sqrt 35.6%

         \[\leadsto \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot \frac{1}{\frac{a}{x}} \]

      3. associate-*l* 35.7%

         \[\leadsto \color{blue}{\sqrt{y} \cdot \left(\sqrt{y} \cdot \frac{1}{\frac{a}{x}}\right)} \]

      4. clear-num 35.7%

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

   8. Applied egg-rr 35.7%

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

      1. associate-*r* 35.6%

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

      2. *-commutative 35.6%

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

   10. Simplified 35.6%

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

       1. rem-square-sqrt 79.6%

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

       2. associate-/r/ 80.9%

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

   12. Applied egg-rr 80.9%

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

   if -9.99999999999999946e48 < (*.f64 x y) < 9.9999999999999997e34

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-*r/ 79.2%

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

      3. distribute-rgt-neg-in 79.2%

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

      4. distribute-neg-frac 79.2%

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

   4. Simplified 79.2%

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

   if 9.9999999999999997e34 < (*.f64 x y)

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf 85.7%

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

      1. associate-*l/ 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY)) (* y (/ x a)) (/ (- (* x y) (* z t)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y * (x / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y * (x / a)
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y * (x / a);
	else
		tmp = ((x * y) - (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 52.2%

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

   2. Taylor expanded in x around inf 57.7%

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

      1. associate-*l/ 94.4%

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

   4. Simplified 94.4%

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

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

   1. Initial program 94.4%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 6: 50.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return y * (x / 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 = y * (x / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.4%

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

2. Taylor expanded in x around inf 50.2%

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

   1. associate-*l/ 52.3%

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

4. Simplified 52.3%

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

5. Final simplification 52.3%

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

Developer target: 91.2% accurate, 0.6× 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 2023301 
(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))