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

Percentage Accurate: 91.6% → 97.0%

Time: 8.1s

Alternatives: 12

Speedup: 0.7×

• 28.4% 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: 91.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+261}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-t, z, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{a}, \frac{-z}{\frac{a}{t}}\right)\\ \end{array} \end{array} \]

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 -5e+261)
     (- (/ x (/ a y)) (/ z (/ a t)))
     (if (<= t_1 4e+305)
       (/ (fma (- t) z (* x y)) a)
       (fma y (/ x a) (/ (- 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 <= -5e+261) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else if (t_1 <= 4e+305) {
		tmp = fma(-t, z, (x * y)) / a;
	} else {
		tmp = fma(y, (x / a), (-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 <= -5e+261)
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	elseif (t_1 <= 4e+305)
		tmp = Float64(fma(Float64(-t), z, Float64(x * y)) / a);
	else
		tmp = fma(y, Float64(x / a), Float64(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, -5e+261], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+305], N[(N[((-t) * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $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)) < -5.0000000000000001e261

   1. Initial program 67.6%

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

      1. div-sub 65.3%

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

      2. associate-/l* 86.6%

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

      3. associate-/l* 95.1%

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

   3. Applied egg-rr 95.1%

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

   if -5.0000000000000001e261 < (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999998e305

   1. Initial program 98.5%

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

      1. cancel-sign-sub-inv 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. distribute-rgt-neg-out 98.5%

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

      5. distribute-lft-neg-in 98.5%

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

      6. fma-def 98.6%

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

   3. Applied egg-rr 98.6%

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

   if 3.9999999999999998e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 69.5%

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

      1. div-sub 66.2%

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

      2. *-commutative 66.2%

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

      3. *-un-lft-identity 66.2%

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

      4. times-frac 81.6%

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

      5. fma-neg 81.6%

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

      6. associate-/l* 93.4%

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

   3. Applied egg-rr 93.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+261}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-t, z, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{a}, \frac{-z}{\frac{a}{t}}\right)\\ \end{array} \]

Alternative 2: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+261} \lor \neg \left(t_1 \leq 4 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-t, z, x \cdot y\right)}{a}\\ \end{array} \end{array} \]

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 -5e+261) (not (<= t_1 4e+305)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ (fma (- t) z (* x y)) 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 <= -5e+261) || !(t_1 <= 4e+305)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = fma(-t, z, (x * y)) / 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 <= -5e+261) || !(t_1 <= 4e+305))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(fma(Float64(-t), z, Float64(x * y)) / 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, -5e+261], N[Not[LessEqual[t$95$1, 4e+305]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-t) * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000001e261 or 3.9999999999999998e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 68.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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* 84.5%

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

      3. associate-/l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   if -5.0000000000000001e261 < (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999998e305

   1. Initial program 98.5%

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

      1. cancel-sign-sub-inv 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. distribute-rgt-neg-out 98.5%

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

      5. distribute-lft-neg-in 98.5%

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

      6. fma-def 98.6%

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

   3. Applied egg-rr 98.6%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+261} \lor \neg \left(x \cdot y - z \cdot t \leq 4 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-t, z, x \cdot y\right)}{a}\\ \end{array} \]

Alternative 3: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+261} \lor \neg \left(t_1 \leq 4 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

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 -5e+261) (not (<= t_1 4e+305)))
     (- (/ 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 <= -5e+261) || !(t_1 <= 4e+305)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if ((t_1 <= (-5d+261)) .or. (.not. (t_1 <= 4d+305))) then
        tmp = (x / (a / y)) - (z / (a / t))
    else
        tmp = t_1 / 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 t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -5e+261) || !(t_1 <= 4e+305)) {
		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 <= -5e+261) or not (t_1 <= 4e+305):
		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 <= -5e+261) || !(t_1 <= 4e+305))
		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 <= -5e+261) || ~((t_1 <= 4e+305)))
		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, -5e+261], N[Not[LessEqual[t$95$1, 4e+305]], $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)) < -5.0000000000000001e261 or 3.9999999999999998e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 68.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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* 84.5%

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

      3. associate-/l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   if -5.0000000000000001e261 < (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999998e305

   1. Initial program 98.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+261} \lor \neg \left(x \cdot y - z \cdot t \leq 4 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 4: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{t}{a} \cdot \left(-z\right)\\ t_2 := y \cdot \frac{x}{a}\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* (/ t a) (- z))) (t_2 (* y (/ x a))))
   (if (<= x -1.25e+162)
     (/ y (/ a x))
     (if (<= x -6e+151)
       t_1
       (if (<= x -1.55e+34)
         t_2
         (if (<= x -9e-159) t_1 (if (<= x 2.9e+25) (/ (- t) (/ a z)) t_2)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / a) * -z;
	double t_2 = y * (x / a);
	double tmp;
	if (x <= -1.25e+162) {
		tmp = y / (a / x);
	} else if (x <= -6e+151) {
		tmp = t_1;
	} else if (x <= -1.55e+34) {
		tmp = t_2;
	} else if (x <= -9e-159) {
		tmp = t_1;
	} else if (x <= 2.9e+25) {
		tmp = -t / (a / z);
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t / a) * -z
    t_2 = y * (x / a)
    if (x <= (-1.25d+162)) then
        tmp = y / (a / x)
    else if (x <= (-6d+151)) then
        tmp = t_1
    else if (x <= (-1.55d+34)) then
        tmp = t_2
    else if (x <= (-9d-159)) then
        tmp = t_1
    else if (x <= 2.9d+25) then
        tmp = -t / (a / z)
    else
        tmp = t_2
    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 t_1 = (t / a) * -z;
	double t_2 = y * (x / a);
	double tmp;
	if (x <= -1.25e+162) {
		tmp = y / (a / x);
	} else if (x <= -6e+151) {
		tmp = t_1;
	} else if (x <= -1.55e+34) {
		tmp = t_2;
	} else if (x <= -9e-159) {
		tmp = t_1;
	} else if (x <= 2.9e+25) {
		tmp = -t / (a / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (t / a) * -z
	t_2 = y * (x / a)
	tmp = 0
	if x <= -1.25e+162:
		tmp = y / (a / x)
	elif x <= -6e+151:
		tmp = t_1
	elif x <= -1.55e+34:
		tmp = t_2
	elif x <= -9e-159:
		tmp = t_1
	elif x <= 2.9e+25:
		tmp = -t / (a / z)
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / a) * Float64(-z))
	t_2 = Float64(y * Float64(x / a))
	tmp = 0.0
	if (x <= -1.25e+162)
		tmp = Float64(y / Float64(a / x));
	elseif (x <= -6e+151)
		tmp = t_1;
	elseif (x <= -1.55e+34)
		tmp = t_2;
	elseif (x <= -9e-159)
		tmp = t_1;
	elseif (x <= 2.9e+25)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = t_2;
	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 = (t / a) * -z;
	t_2 = y * (x / a);
	tmp = 0.0;
	if (x <= -1.25e+162)
		tmp = y / (a / x);
	elseif (x <= -6e+151)
		tmp = t_1;
	elseif (x <= -1.55e+34)
		tmp = t_2;
	elseif (x <= -9e-159)
		tmp = t_1;
	elseif (x <= 2.9e+25)
		tmp = -t / (a / z);
	else
		tmp = t_2;
	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[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+162], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e+151], t$95$1, If[LessEqual[x, -1.55e+34], t$95$2, If[LessEqual[x, -9e-159], t$95$1, If[LessEqual[x, 2.9e+25], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2499999999999999e162

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf 67.7%

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

      1. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -1.2499999999999999e162 < x < -5.9999999999999998e151 or -1.54999999999999989e34 < x < -8.99999999999999977e-159

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-/l* 74.1%

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

      3. distribute-neg-frac 74.1%

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

   4. Simplified 74.1%

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

      1. frac-2neg 74.1%

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

      2. associate-/r/ 69.7%

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

      3. frac-2neg 69.7%

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

   6. Applied egg-rr 69.7%

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

   if -5.9999999999999998e151 < x < -1.54999999999999989e34 or 2.8999999999999999e25 < x

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 58.9%

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

      1. associate-*r/ 70.2%

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

   4. Simplified 70.2%

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

   if -8.99999999999999977e-159 < x < 2.8999999999999999e25

   1. Initial program 94.3%

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

   2. Taylor expanded in x around 0 78.0%

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

      1. mul-1-neg 78.0%

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

      2. associate-/l* 72.7%

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

      3. distribute-neg-frac 72.7%

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

   4. Simplified 72.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+151}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-t\right)}{a}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -3.85 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (* z (- t)) a)))
   (if (<= x -1.8e+162)
     (/ y (/ a x))
     (if (<= x -3.85e+146)
       t_1
       (if (<= x -3.5e+34)
         (* y (/ x a))
         (if (<= x 3.3e+25) t_1 (* y (* x (/ 1.0 a)))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -t) / a;
	double tmp;
	if (x <= -1.8e+162) {
		tmp = y / (a / x);
	} else if (x <= -3.85e+146) {
		tmp = t_1;
	} else if (x <= -3.5e+34) {
		tmp = y * (x / a);
	} else if (x <= 3.3e+25) {
		tmp = t_1;
	} else {
		tmp = y * (x * (1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (z * -t) / a
    if (x <= (-1.8d+162)) then
        tmp = y / (a / x)
    else if (x <= (-3.85d+146)) then
        tmp = t_1
    else if (x <= (-3.5d+34)) then
        tmp = y * (x / a)
    else if (x <= 3.3d+25) then
        tmp = t_1
    else
        tmp = y * (x * (1.0d0 / 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 t_1 = (z * -t) / a;
	double tmp;
	if (x <= -1.8e+162) {
		tmp = y / (a / x);
	} else if (x <= -3.85e+146) {
		tmp = t_1;
	} else if (x <= -3.5e+34) {
		tmp = y * (x / a);
	} else if (x <= 3.3e+25) {
		tmp = t_1;
	} else {
		tmp = y * (x * (1.0 / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (z * -t) / a
	tmp = 0
	if x <= -1.8e+162:
		tmp = y / (a / x)
	elif x <= -3.85e+146:
		tmp = t_1
	elif x <= -3.5e+34:
		tmp = y * (x / a)
	elif x <= 3.3e+25:
		tmp = t_1
	else:
		tmp = y * (x * (1.0 / 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(z * Float64(-t)) / a)
	tmp = 0.0
	if (x <= -1.8e+162)
		tmp = Float64(y / Float64(a / x));
	elseif (x <= -3.85e+146)
		tmp = t_1;
	elseif (x <= -3.5e+34)
		tmp = Float64(y * Float64(x / a));
	elseif (x <= 3.3e+25)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * Float64(1.0 / 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 = (z * -t) / a;
	tmp = 0.0;
	if (x <= -1.8e+162)
		tmp = y / (a / x);
	elseif (x <= -3.85e+146)
		tmp = t_1;
	elseif (x <= -3.5e+34)
		tmp = y * (x / a);
	elseif (x <= 3.3e+25)
		tmp = t_1;
	else
		tmp = y * (x * (1.0 / 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[(z * (-t)), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[x, -1.8e+162], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.85e+146], t$95$1, If[LessEqual[x, -3.5e+34], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+25], t$95$1, N[(y * N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.79999999999999997e162

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf 67.7%

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

      1. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -1.79999999999999997e162 < x < -3.8500000000000001e146 or -3.49999999999999998e34 < x < 3.3000000000000001e25

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. associate-*r* 75.4%

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

      3. neg-mul-1 75.4%

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

   4. Simplified 75.4%

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

   if -3.8500000000000001e146 < x < -3.49999999999999998e34

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 60.2%

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

      1. associate-*r/ 71.2%

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

   4. Simplified 71.2%

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

   if 3.3000000000000001e25 < x

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf 59.7%

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

      1. associate-*r/ 70.0%

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

   4. Simplified 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-/r/ 64.8%

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

   6. Applied egg-rr 64.8%

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

      1. *-un-lft-identity 64.8%

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

      2. div-inv 64.9%

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

      3. frac-times 59.7%

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

      4. associate-/r/ 59.7%

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

      5. /-rgt-identity 59.7%

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

      6. associate-*r* 70.0%

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

   8. Applied egg-rr 70.0%

      \[\leadsto \color{blue}{\left(\frac{1}{a} \cdot x\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -3.85 \cdot 10^{+146}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternative 6: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-8} \lor \neg \left(x \leq -9.5 \cdot 10^{-50}\right) \land x \leq 3.6 \cdot 10^{+40}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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 (<= x -2.1e+34)
   (/ y (/ a x))
   (if (or (<= x -9e-8) (and (not (<= x -9.5e-50)) (<= x 3.6e+40)))
     (* (- t) (/ z a))
     (* y (/ x a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.1e+34) {
		tmp = y / (a / x);
	} else if ((x <= -9e-8) || (!(x <= -9.5e-50) && (x <= 3.6e+40))) {
		tmp = -t * (z / a);
	} else {
		tmp = y * (x / 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 (x <= (-2.1d+34)) then
        tmp = y / (a / x)
    else if ((x <= (-9d-8)) .or. (.not. (x <= (-9.5d-50))) .and. (x <= 3.6d+40)) then
        tmp = -t * (z / a)
    else
        tmp = y * (x / 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 (x <= -2.1e+34) {
		tmp = y / (a / x);
	} else if ((x <= -9e-8) || (!(x <= -9.5e-50) && (x <= 3.6e+40))) {
		tmp = -t * (z / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.1e+34:
		tmp = y / (a / x)
	elif (x <= -9e-8) or (not (x <= -9.5e-50) and (x <= 3.6e+40)):
		tmp = -t * (z / a)
	else:
		tmp = y * (x / 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 (x <= -2.1e+34)
		tmp = Float64(y / Float64(a / x));
	elseif ((x <= -9e-8) || (!(x <= -9.5e-50) && (x <= 3.6e+40)))
		tmp = Float64(Float64(-t) * Float64(z / a));
	else
		tmp = Float64(y * Float64(x / 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 (x <= -2.1e+34)
		tmp = y / (a / x);
	elseif ((x <= -9e-8) || (~((x <= -9.5e-50)) && (x <= 3.6e+40)))
		tmp = -t * (z / a);
	else
		tmp = y * (x / 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[x, -2.1e+34], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -9e-8], And[N[Not[LessEqual[x, -9.5e-50]], $MachinePrecision], LessEqual[x, 3.6e+40]]], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000017e34

   1. Initial program 78.0%

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

   2. Taylor expanded in x around inf 63.4%

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

      1. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   if -2.10000000000000017e34 < x < -8.99999999999999986e-8 or -9.4999999999999993e-50 < x < 3.59999999999999996e40

   1. Initial program 95.7%

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

   2. Taylor expanded in x around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*l/ 72.9%

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

      4. *-commutative 72.9%

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

      5. distribute-lft-neg-in 72.9%

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

   4. Simplified 72.9%

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

   if -8.99999999999999986e-8 < x < -9.4999999999999993e-50 or 3.59999999999999996e40 < x

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 63.5%

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

      1. associate-*r/ 73.8%

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

   4. Simplified 73.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-8} \lor \neg \left(x \leq -9.5 \cdot 10^{-50}\right) \land x \leq 3.6 \cdot 10^{+40}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 7: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+151}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+35} \lor \neg \left(x \leq 3.5 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 (<= x -1.8e+162)
   (/ y (/ a x))
   (if (<= x -6e+151)
     (* (/ t a) (- z))
     (if (or (<= x -3.6e+35) (not (<= x 3.5e+38)))
       (* y (/ x 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 (x <= -1.8e+162) {
		tmp = y / (a / x);
	} else if (x <= -6e+151) {
		tmp = (t / a) * -z;
	} else if ((x <= -3.6e+35) || !(x <= 3.5e+38)) {
		tmp = y * (x / a);
	} else {
		tmp = -t * (z / 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 (x <= (-1.8d+162)) then
        tmp = y / (a / x)
    else if (x <= (-6d+151)) then
        tmp = (t / a) * -z
    else if ((x <= (-3.6d+35)) .or. (.not. (x <= 3.5d+38))) then
        tmp = y * (x / a)
    else
        tmp = -t * (z / 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 (x <= -1.8e+162) {
		tmp = y / (a / x);
	} else if (x <= -6e+151) {
		tmp = (t / a) * -z;
	} else if ((x <= -3.6e+35) || !(x <= 3.5e+38)) {
		tmp = y * (x / 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 x <= -1.8e+162:
		tmp = y / (a / x)
	elif x <= -6e+151:
		tmp = (t / a) * -z
	elif (x <= -3.6e+35) or not (x <= 3.5e+38):
		tmp = y * (x / 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 (x <= -1.8e+162)
		tmp = Float64(y / Float64(a / x));
	elseif (x <= -6e+151)
		tmp = Float64(Float64(t / a) * Float64(-z));
	elseif ((x <= -3.6e+35) || !(x <= 3.5e+38))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(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)
	tmp = 0.0;
	if (x <= -1.8e+162)
		tmp = y / (a / x);
	elseif (x <= -6e+151)
		tmp = (t / a) * -z;
	elseif ((x <= -3.6e+35) || ~((x <= 3.5e+38)))
		tmp = y * (x / 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[x, -1.8e+162], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e+151], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision], If[Or[LessEqual[x, -3.6e+35], N[Not[LessEqual[x, 3.5e+38]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.79999999999999997e162

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf 67.7%

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

      1. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -1.79999999999999997e162 < x < -5.9999999999999998e151

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. associate-/l* 50.3%

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

      3. distribute-neg-frac 50.3%

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

   4. Simplified 50.3%

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

      1. frac-2neg 50.3%

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

      2. associate-/r/ 28.0%

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

      3. frac-2neg 28.0%

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

   6. Applied egg-rr 28.0%

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

   if -5.9999999999999998e151 < x < -3.6e35 or 3.50000000000000002e38 < x

   1. Initial program 86.2%

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

   2. Taylor expanded in x around inf 61.6%

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

      1. associate-*r/ 73.7%

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

   4. Simplified 73.7%

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

   if -3.6e35 < x < 3.50000000000000002e38

   1. Initial program 95.2%

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

   2. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*l/ 72.5%

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

      4. *-commutative 72.5%

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

      5. distribute-lft-neg-in 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+151}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+35} \lor \neg \left(x \leq 3.5 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+145} \lor \neg \left(x \leq -8.6 \cdot 10^{+36}\right) \land x \leq 3.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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 (<= x -1.25e+162)
   (/ y (/ a x))
   (if (or (<= x -8e+145) (and (not (<= x -8.6e+36)) (<= x 3.8e+25)))
     (/ (* z (- t)) a)
     (* y (/ x a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.25e+162) {
		tmp = y / (a / x);
	} else if ((x <= -8e+145) || (!(x <= -8.6e+36) && (x <= 3.8e+25))) {
		tmp = (z * -t) / a;
	} else {
		tmp = y * (x / 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 (x <= (-1.25d+162)) then
        tmp = y / (a / x)
    else if ((x <= (-8d+145)) .or. (.not. (x <= (-8.6d+36))) .and. (x <= 3.8d+25)) then
        tmp = (z * -t) / a
    else
        tmp = y * (x / 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 (x <= -1.25e+162) {
		tmp = y / (a / x);
	} else if ((x <= -8e+145) || (!(x <= -8.6e+36) && (x <= 3.8e+25))) {
		tmp = (z * -t) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.25e+162:
		tmp = y / (a / x)
	elif (x <= -8e+145) or (not (x <= -8.6e+36) and (x <= 3.8e+25)):
		tmp = (z * -t) / a
	else:
		tmp = y * (x / 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 (x <= -1.25e+162)
		tmp = Float64(y / Float64(a / x));
	elseif ((x <= -8e+145) || (!(x <= -8.6e+36) && (x <= 3.8e+25)))
		tmp = Float64(Float64(z * Float64(-t)) / a);
	else
		tmp = Float64(y * Float64(x / 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 (x <= -1.25e+162)
		tmp = y / (a / x);
	elseif ((x <= -8e+145) || (~((x <= -8.6e+36)) && (x <= 3.8e+25)))
		tmp = (z * -t) / a;
	else
		tmp = y * (x / 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[x, -1.25e+162], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -8e+145], And[N[Not[LessEqual[x, -8.6e+36]], $MachinePrecision], LessEqual[x, 3.8e+25]]], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2499999999999999e162

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf 67.7%

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

      1. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -1.2499999999999999e162 < x < -7.9999999999999999e145 or -8.6000000000000001e36 < x < 3.8e25

   1. Initial program 93.9%

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

   2. Taylor expanded in x around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. associate-*r* 74.4%

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

      3. neg-mul-1 74.4%

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

   4. Simplified 74.4%

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

   if -7.9999999999999999e145 < x < -8.6000000000000001e36 or 3.8e25 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around inf 60.0%

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

      1. associate-*r/ 69.5%

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

   4. Simplified 69.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+145} \lor \neg \left(x \leq -8.6 \cdot 10^{+36}\right) \land x \leq 3.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 9: 93.6% accurate, 0.7× speedup

Math

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

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 (<= (* x y) (- INFINITY))
   (* y (* x (/ 1.0 a)))
   (/ (- (* x 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 ((x * y) <= -((double) INFINITY)) {
		tmp = y * (x * (1.0 / a));
	} else {
		tmp = ((x * y) - (z * t)) / 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 ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x * (1.0 / a));
	} else {
		tmp = ((x * y) - (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 (x * y) <= -math.inf:
		tmp = y * (x * (1.0 / a))
	else:
		tmp = ((x * y) - (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 (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y * Float64(x * Float64(1.0 / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * 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 ((x * y) <= -Inf)
		tmp = y * (x * (1.0 / a));
	else
		tmp = ((x * y) - (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[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y * N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 55.9%

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

   2. Taylor expanded in x around inf 55.9%

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

      1. associate-*r/ 99.8%

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

   4. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. *-un-lft-identity 99.6%

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

      2. div-inv 99.6%

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

      3. frac-times 55.9%

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

      4. associate-/r/ 55.9%

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

      5. /-rgt-identity 55.9%

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

      6. associate-*r* 99.8%

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

   8. Applied egg-rr 99.8%

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

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

   1. Initial program 92.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 10: 50.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 (<= a 1.25e-68) (* x (/ y a)) (/ (* x y) a)))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.25e-68) {
		tmp = x * (y / a);
	} else {
		tmp = (x * y) / 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 (a <= 1.25d-68) then
        tmp = x * (y / a)
    else
        tmp = (x * y) / 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 (a <= 1.25e-68) {
		tmp = x * (y / a);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.25e-68:
		tmp = x * (y / a)
	else:
		tmp = (x * y) / 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 (a <= 1.25e-68)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(x * y) / 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 (a <= 1.25e-68)
		tmp = x * (y / a);
	else
		tmp = (x * y) / 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[a, 1.25e-68], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.24999999999999993e-68

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 42.2%

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

      1. associate-/l* 48.4%

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

      2. associate-/r/ 50.2%

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

   4. Applied egg-rr 50.2%

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

   if 1.24999999999999993e-68 < a

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 56.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 11: 50.9% 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 89.8%

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

2. Taylor expanded in x around inf 46.6%

   \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
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 12: 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 89.8%

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

2. Taylor expanded in x around inf 46.6%

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

   1. associate-/l* 49.8%

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

   2. associate-/r/ 50.7%

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

4. Applied egg-rr 50.7%

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

5. Final simplification 50.7%

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

Developer target: 91.7% 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 2023263 
(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))