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

Percentage Accurate: 91.2% → 96.8%

Time: 8.4s

Alternatives: 10

Speedup: 0.5×

• 29.0% 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: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+260}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (- INFINITY))
     (fma -1.0 (/ t (/ a z)) (* y (/ x a)))
     (if (<= t_1 1e+260)
       (/ (fma x y (* t (- z))) a)
       (- (/ x (/ a y)) (/ z (/ a t)))))))

C

assert(x < y);
assert(z < t);
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)) {
		tmp = fma(-1.0, (t / (a / z)), (y * (x / a)));
	} else if (t_1 <= 1e+260) {
		tmp = fma(x, y, (t * -z)) / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(-1.0, Float64(t / Float64(a / z)), Float64(y * Float64(x / a)));
	elseif (t_1 <= 1e+260)
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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, (-Infinity)], N[(-1.0 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+260], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.6%

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

   2. Taylor expanded in x around 0 63.2%

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

      1. fma-def 63.2%

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

      2. associate-/l* 78.2%

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

      3. associate-*l/ 90.1%

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

   4. Simplified 90.1%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000007e260

   1. Initial program 97.8%

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

      1. fma-neg 97.8%

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

      2. distribute-lft-neg-out 97.8%

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

      3. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   if 1.00000000000000007e260 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 65.7%

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

      1. div-sub 65.7%

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

      2. associate-/l* 80.5%

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

      3. associate-/l* 93.1%

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

   3. Applied egg-rr 93.1%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+260}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 2: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+260}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 1e+260)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ (fma x y (* t (- z))) a))))

C

assert(x < y);
assert(z < t);
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 <= 1e+260)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = fma(x, y, (t * -z)) / a;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
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 <= 1e+260))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) / a);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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, 1e+260]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 1.00000000000000007e260 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.3%

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

      1. div-sub 64.7%

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

      2. associate-/l* 79.6%

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

      3. associate-/l* 91.9%

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

   3. Applied egg-rr 91.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000007e260

   1. Initial program 97.8%

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

      1. fma-neg 97.8%

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

      2. distribute-lft-neg-out 97.8%

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

      3. *-commutative 97.8%

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

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+260}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \end{array} \]

Alternative 3: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+260}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 1e+260)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ t_1 a))))

C

assert(x < y);
assert(z < t);
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 <= 1e+260)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
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 <= 1e+260)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+260):
		tmp = (x / (a / y)) - (z / (a / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
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 <= 1e+260))
		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 = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+260)))
		tmp = (x / (a / y)) - (z / (a / t));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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, 1e+260]], $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 1.00000000000000007e260 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.3%

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

      1. div-sub 64.7%

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

      2. associate-/l* 79.6%

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

      3. associate-/l* 91.9%

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

   3. Applied egg-rr 91.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000007e260

   1. Initial program 97.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+260}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ t_2 := \left(-z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)) (t_2 (* (- z) (/ t a))))
   (if (<= (* x y) (- INFINITY))
     (/ y (/ a x))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         t_2
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74) t_2 (/ x (/ a y)))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double t_2 = -z * (t / a);
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y / (a / x);
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = t_2;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = t_2;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double t_2 = -z * (t / a);
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y / (a / x);
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = t_2;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = t_2;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / a
	t_2 = -z * (t / a)
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y / (a / x)
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = t_2
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = t_2
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	t_2 = Float64(Float64(-z) * Float64(t / a))
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	t_2 = -z * (t / a);
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y / (a / x);
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = t_2;
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = t_2;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], t$95$2, N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 64.1%

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

   2. Taylor expanded in x around inf 64.1%

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

      1. associate-*l/ 93.6%

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

   4. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. clear-num 93.6%

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

      3. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 73.3%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61 or 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 92.0%

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

   2. Taylor expanded in x around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. associate-/l* 79.2%

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

      3. associate-/r/ 85.0%

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

      4. distribute-rgt-neg-in 85.0%

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

   4. Simplified 85.0%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 81.2%

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

   2. Taylor expanded in x around inf 75.7%

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

      1. associate-*r/ 89.1%

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

   4. Simplified 89.1%

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

      1. associate-*r/ 75.7%

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

      2. associate-/l* 89.2%

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

   6. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) (- INFINITY))
     (/ y (/ a x))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         (* t (/ (- z) a))
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74) (* (- z) (/ t a)) (/ x (/ a y)))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y / (a / x);
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -z * (t / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y / (a / x);
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -z * (t / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y / (a / x)
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = t * (-z / a)
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = -z * (t / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y / (a / x);
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = t * (-z / a);
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = -z * (t / a);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.1%

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

   2. Taylor expanded in x around inf 64.1%

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

      1. associate-*l/ 93.6%

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

   4. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. clear-num 93.6%

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

      3. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 73.3%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61

   1. Initial program 92.4%

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

   2. Taylor expanded in x around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-*l/ 80.0%

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

      3. associate-*r* 80.0%

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

      4. neg-mul-1 80.0%

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

      5. distribute-frac-neg 80.0%

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

   4. Simplified 80.0%

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

   if 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-/l* 75.5%

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

      3. associate-/r/ 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

   4. Simplified 75.6%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 81.2%

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

   2. Taylor expanded in x around inf 75.7%

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

      1. associate-*r/ 89.1%

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

   4. Simplified 89.1%

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

      1. associate-*r/ 75.7%

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

      2. associate-/l* 89.2%

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

   6. Applied egg-rr 89.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) (- INFINITY))
     (/ y (/ a x))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         (/ (* t (- z)) a)
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74) (* (- z) (/ t a)) (/ x (/ a y)))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y / (a / x);
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -z * (t / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y / (a / x);
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -z * (t / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y / (a / x)
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = (t * -z) / a
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = -z * (t / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = Float64(Float64(t * Float64(-z)) / a);
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y / (a / x);
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = (t * -z) / a;
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = -z * (t / a);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.1%

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

   2. Taylor expanded in x around inf 64.1%

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

      1. associate-*l/ 93.6%

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

   4. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. clear-num 93.6%

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

      3. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 73.3%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61

   1. Initial program 92.4%

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

   2. Taylor expanded in x around 0 86.6%

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

      1. associate-*r/ 86.6%

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

      2. associate-*r* 86.6%

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

      3. neg-mul-1 86.6%

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

   4. Simplified 86.6%

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

   if 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-/l* 75.5%

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

      3. associate-/r/ 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

   4. Simplified 75.6%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 81.2%

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

   2. Taylor expanded in x around inf 75.7%

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

      1. associate-*r/ 89.1%

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

   4. Simplified 89.1%

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

      1. associate-*r/ 75.7%

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

      2. associate-/l* 89.2%

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

   6. Applied egg-rr 89.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+199}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ (- t) (/ a z))
   (if (<= (* z t) 5e+199) (/ (- (* x y) (* z t)) a) (* t (/ (- z) a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = -t / (a / z);
	} else if ((z * t) <= 5e+199) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = -t / (a / z);
	} else if ((z * t) <= 5e+199) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = -t / (a / z)
	elif (z * t) <= 5e+199:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t * (-z / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (Float64(z * t) <= 5e+199)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(t * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = -t / (a / z);
	elseif ((z * t) <= 5e+199)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t * (-z / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+199], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 60.2%

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

   2. Taylor expanded in x around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*l/ 94.9%

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

      3. associate-*r* 94.9%

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

      4. neg-mul-1 94.9%

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

      5. distribute-frac-neg 94.9%

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

   4. Simplified 94.9%

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

      1. distribute-frac-neg 94.9%

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

      2. distribute-lft-neg-out 94.9%

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

      3. clear-num 94.9%

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

      4. associate-/r/ 94.8%

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

      5. clear-num 94.9%

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

      6. distribute-neg-frac 94.9%

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

   6. Applied egg-rr 94.9%

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

   if -inf.0 < (*.f64 z t) < 4.9999999999999998e199

   1. Initial program 92.7%

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

   if 4.9999999999999998e199 < (*.f64 z t)

   1. Initial program 80.3%

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

   2. Taylor expanded in x around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-*l/ 99.8%

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

      3. associate-*r* 99.8%

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

      4. neg-mul-1 99.8%

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

      5. distribute-frac-neg 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+199}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \]

Alternative 8: 51.2% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 88.9%

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

2. Taylor expanded in x around inf 51.0%

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

   1. associate-*r/ 53.5%

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

4. Simplified 53.5%

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

5. Final simplification 53.5%

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

Alternative 9: 51.0% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 88.9%

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

2. Taylor expanded in x around inf 51.0%

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

   1. associate-*l/ 52.2%

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

4. Simplified 52.2%

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

5. Final simplification 52.2%

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

Alternative 10: 50.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

2. Taylor expanded in x around inf 51.0%

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

   1. associate-*l/ 52.2%

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

4. Simplified 52.2%

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

   1. *-commutative 52.2%

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

   2. clear-num 51.9%

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

   3. un-div-inv 52.2%

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

6. Applied egg-rr 52.2%

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

7. Final simplification 52.2%

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

Developer target: 91.6% 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 2023275 
(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))