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

Percentage Accurate: 91.3% → 96.9%

Time: 6.6s

Alternatives: 10

Speedup: 0.5×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.3% 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: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+270}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \end{array} \end{array} \]

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))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (if (<= t_1 5e+270)
       (/ (fma (- z) t (* x y)) a)
       (fma -1.0 (/ t (/ a z)) (/ y (/ a x)))))))

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 = (x / (a / y)) - (z / (a / t));
	} else if (t_1 <= 5e+270) {
		tmp = fma(-z, t, (x * y)) / a;
	} else {
		tmp = fma(-1.0, (t / (a / z)), (y / (a / x)));
	}
	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 = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	elseif (t_1 <= 5e+270)
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	else
		tmp = fma(-1.0, Float64(t / Float64(a / z)), Float64(y / Float64(a / x)));
	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[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+270], N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(-1.0 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.4%

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

      1. div-sub 54.2%

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

      2. associate-/l* 69.2%

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

      3. associate-/l* 93.3%

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

   3. Applied egg-rr 93.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.99999999999999976e270

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. +-commutative 98.9%

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

      3. distribute-lft-neg-in 98.9%

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

      4. fma-def 98.9%

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

   3. Applied egg-rr 98.9%

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

   if 4.99999999999999976e270 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 75.7%

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

   2. Taylor expanded in x around 0 70.5%

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

      1. fma-def 70.5%

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

      2. associate-/l* 77.8%

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

      3. associate-/l* 92.2%

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

   4. Simplified 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+270}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1 - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1 - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ x (/ a y))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 (- INFINITY))
     (- t_1 (/ z (/ a t)))
     (if (<= t_2 5e+294) (/ (fma (- z) t (* x y)) a) (- t_1 (* 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 / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 5e+294) {
		tmp = fma(-z, t, (x * y)) / a;
	} else {
		tmp = t_1 - (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(x / Float64(a / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	elseif (t_2 <= 5e+294)
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	else
		tmp = Float64(t_1 - 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[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+294], N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(t$95$1 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.4%

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

      1. div-sub 54.2%

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

      2. associate-/l* 69.2%

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

      3. associate-/l* 93.3%

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

   3. Applied egg-rr 93.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e294

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. +-commutative 98.9%

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

      3. distribute-lft-neg-in 98.9%

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

      4. fma-def 99.0%

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

   3. Applied egg-rr 99.0%

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

   if 4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.6%

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

      1. div-sub 68.1%

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

      2. associate-/l* 86.4%

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

      3. associate-/l* 91.4%

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

   3. Applied egg-rr 91.4%

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

      1. associate-/r/ 94.3%

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

   5. Applied egg-rr 94.3%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \end{array} \]

Alternative 3: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+294}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

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 5e+294)))
     (- (/ x (/ a y)) (* t (/ z a)))
     (/ 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 <= 5e+294)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} 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 <= 5e+294)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} 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 <= 5e+294):
		tmp = (x / (a / y)) - (t * (z / a))
	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 <= 5e+294))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	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 <= 5e+294)))
		tmp = (x / (a / y)) - (t * (z / a));
	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, 5e+294]], $MachinePrecision]], N[(N[(x / N[(a / y), $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)) < -inf.0 or 4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.1%

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

      1. div-sub 61.7%

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

      2. associate-/l* 78.5%

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

      3. associate-/l* 92.3%

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

   3. Applied egg-rr 92.3%

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

      1. associate-/r/ 92.4%

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

   5. Applied egg-rr 92.4%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e294

   1. Initial program 98.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+294}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 4: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1 - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{t_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1 - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ x (/ a y))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 (- INFINITY))
     (- t_1 (/ z (/ a t)))
     (if (<= t_2 5e+294) (/ t_2 a) (- t_1 (* 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 / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 5e+294) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (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 t_1 = x / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 - (z / (a / t));
	} else if (t_2 <= 5e+294) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (t * (z / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 - (z / (a / t))
	elif t_2 <= 5e+294:
		tmp = t_2 / a
	else:
		tmp = t_1 - (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(x / Float64(a / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	elseif (t_2 <= 5e+294)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(t * 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)
	t_1 = x / (a / y);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 - (z / (a / t));
	elseif (t_2 <= 5e+294)
		tmp = t_2 / a;
	else
		tmp = t_1 - (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_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+294], N[(t$95$2 / a), $MachinePrecision], N[(t$95$1 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.4%

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

      1. div-sub 54.2%

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

      2. associate-/l* 69.2%

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

      3. associate-/l* 93.3%

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

   3. Applied egg-rr 93.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e294

   1. Initial program 98.9%

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

   if 4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.6%

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

      1. div-sub 68.1%

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

      2. associate-/l* 86.4%

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

      3. associate-/l* 91.4%

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

   3. Applied egg-rr 91.4%

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

      1. associate-/r/ 94.3%

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

   5. Applied egg-rr 94.3%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \end{array} \]

Alternative 5: 95.2% accurate, 0.5× speedup

Math

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

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 (<= (* x y) (- INFINITY))
   (* y (/ x a))
   (if (<= (* x y) 5e+260) (/ (- (* x y) (* z t)) a) (/ y (/ a x)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e+260) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y / (a / x);
	}
	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 ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e+260) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y * (x / a)
	elif (x * y) <= 5e+260:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = y / (a / x)
	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(x * y) <= Float64(-Inf))
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 5e+260)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(y / Float64(a / x));
	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 ((x * y) <= -Inf)
		tmp = y * (x / a);
	elseif ((x * y) <= 5e+260)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = y / (a / x);
	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[(x * y), $MachinePrecision], (-Infinity)], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+260], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.4%

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

   2. Taylor expanded in x around inf 68.4%

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

      1. associate-*r/ 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (*.f64 x y) < 4.9999999999999996e260

   1. Initial program 94.4%

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

   if 4.9999999999999996e260 < (*.f64 x y)

   1. Initial program 63.0%

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

   2. Taylor expanded in x around inf 63.0%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 95.2%

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

Alternative 6: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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
 (if (<= (* x y) -4e+123)
   (* y (/ x a))
   (if (<= (* x y) 5e+29) (* t (/ (- z) a)) (/ x (/ a y)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e+29) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((x * y) <= (-4d+123)) then
        tmp = y * (x / a)
    else if ((x * y) <= 5d+29) then
        tmp = t * (-z / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e+29) {
		tmp = t * (-z / 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):
	tmp = 0
	if (x * y) <= -4e+123:
		tmp = y * (x / a)
	elif (x * y) <= 5e+29:
		tmp = t * (-z / 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)
	tmp = 0.0
	if (Float64(x * y) <= -4e+123)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 5e+29)
		tmp = Float64(t * Float64(Float64(-z) / 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)
	tmp = 0.0;
	if ((x * y) <= -4e+123)
		tmp = y * (x / a);
	elseif ((x * y) <= 5e+29)
		tmp = t * (-z / 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_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+123], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+29], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999991e123

   1. Initial program 85.2%

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

   2. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 87.1%

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

   4. Simplified 87.1%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 5.0000000000000001e29

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 74.2%

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

      1. associate-*r/ 74.2%

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

      2. mul-1-neg 74.2%

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

      3. distribute-rgt-neg-out 74.2%

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

      4. *-commutative 74.2%

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

      5. associate-/l* 75.8%

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

      6. associate-/r/ 73.1%

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

   4. Simplified 73.1%

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

   if 5.0000000000000001e29 < (*.f64 x y)

   1. Initial program 85.0%

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

   2. Taylor expanded in x around inf 77.8%

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

      1. associate-*r/ 85.3%

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

   4. Simplified 85.3%

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

      1. associate-*r/ 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-/l* 81.4%

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

   6. Applied egg-rr 81.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-143} \lor \neg \left(y \leq 4.9 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \end{array} \end{array} \]

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 (or (<= y -6.5e-143) (not (<= y 4.9e+70)))
   (/ x (/ a y))
   (* z (- (/ t a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.5e-143) || !(y <= 4.9e+70)) {
		tmp = x / (a / y);
	} else {
		tmp = z * -(t / a);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y <= (-6.5d-143)) .or. (.not. (y <= 4.9d+70))) then
        tmp = x / (a / y)
    else
        tmp = z * -(t / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.5e-143) || !(y <= 4.9e+70)) {
		tmp = x / (a / y);
	} else {
		tmp = z * -(t / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.5e-143) or not (y <= 4.9e+70):
		tmp = x / (a / y)
	else:
		tmp = z * -(t / 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 ((y <= -6.5e-143) || !(y <= 4.9e+70))
		tmp = Float64(x / Float64(a / y));
	else
		tmp = Float64(z * Float64(-Float64(t / 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 ((y <= -6.5e-143) || ~((y <= 4.9e+70)))
		tmp = x / (a / y);
	else
		tmp = z * -(t / 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[Or[LessEqual[y, -6.5e-143], N[Not[LessEqual[y, 4.9e+70]], $MachinePrecision]], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(z * (-N[(t / a), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999999e-143 or 4.90000000000000028e70 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in x around inf 57.6%

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

      1. associate-*r/ 63.5%

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

   4. Simplified 63.5%

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

      1. associate-*r/ 57.6%

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

      2. *-commutative 57.6%

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

      3. associate-/l* 62.9%

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

   6. Applied egg-rr 62.9%

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

   if -6.4999999999999999e-143 < y < 4.90000000000000028e70

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. +-commutative 93.5%

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

      3. distribute-lft-neg-in 93.5%

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

      4. fma-def 93.5%

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

   3. Applied egg-rr 93.5%

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

   4. Taylor expanded in z around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-*l/ 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-143} \lor \neg \left(y \leq 4.9 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \end{array} \]

Alternative 8: 51.1% 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 90.4%

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

2. Taylor expanded in x around inf 47.1%

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

   1. associate-*r/ 49.6%

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

4. Simplified 49.6%

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

5. Final simplification 49.6%

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

Alternative 9: 51.0% accurate, 1.8× speedup

Math

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

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 90.4%

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

2. Taylor expanded in x around inf 47.1%

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

   1. associate-/l* 49.4%

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

   2. associate-/r/ 47.9%

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

4. Applied egg-rr 47.9%

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

5. Final simplification 47.9%

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

Alternative 10: 50.9% accurate, 1.8× speedup

Math

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

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 (/ a y)))

C

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

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 / (a / y)
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 / (a / y);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 90.4%

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

2. Taylor expanded in x around inf 47.1%

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

   1. associate-*r/ 49.6%

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

4. Simplified 49.6%

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

   1. associate-*r/ 47.1%

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

   2. *-commutative 47.1%

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

   3. associate-/l* 47.8%

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

6. Applied egg-rr 47.8%

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

7. Final simplification 47.8%

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

Developer target: 91.9% 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 2023196 
(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))