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

Percentage Accurate: 91.2% → 96.8%

Time: 6.9s

Alternatives: 10

Speedup: 0.5×

• 27.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{z}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+272}:\\ \;\;\;\;\mathsf{fma}\left(-1, t_1, \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;t_2 \leq 10^{+288}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - t_1\\ \end{array} \end{array} \]

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 (- (* x y) (* z t))))
   (if (<= t_2 -5e+272)
     (fma -1.0 t_1 (/ y (/ a x)))
     (if (<= t_2 1e+288)
       (* (fma x y (* t (- z))) (/ 1.0 a))
       (- (* x (/ y a)) t_1)))))

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 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+272) {
		tmp = fma(-1.0, t_1, (y / (a / x)));
	} else if (t_2 <= 1e+288) {
		tmp = fma(x, y, (t * -z)) * (1.0 / a);
	} else {
		tmp = (x * (y / a)) - t_1;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / z))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+272)
		tmp = fma(-1.0, t_1, Float64(y / Float64(a / x)));
	elseif (t_2 <= 1e+288)
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) * Float64(1.0 / a));
	else
		tmp = Float64(Float64(x * Float64(y / a)) - t_1);
	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[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+272], N[(-1.0 * t$95$1 + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+288], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.99999999999999973e272

   1. Initial program 69.6%

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

   2. Taylor expanded in x around 0 69.6%

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

      1. fma-def 69.6%

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

      2. associate-/l* 82.2%

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

      3. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   if -4.99999999999999973e272 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e288

   1. Initial program 99.1%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

   3. Applied egg-rr 99.2%

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

   if 1e288 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 71.6%

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

      1. div-inv 71.6%

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

      2. fma-neg 71.6%

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

      3. *-commutative 71.6%

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

      4. distribute-rgt-neg-in 71.6%

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

   3. Applied egg-rr 71.6%

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

      1. *-commutative 71.6%

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

      2. fma-udef 71.6%

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

      3. *-commutative 71.6%

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

      4. distribute-rgt-neg-out 71.6%

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

      5. distribute-lft-neg-out 71.6%

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

      6. distribute-rgt-in 68.9%

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

      7. div-inv 68.8%

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

      8. distribute-lft-neg-out 68.8%

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

      9. distribute-lft-neg-in 68.8%

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

      10. div-inv 68.8%

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

      11. unsub-neg 68.8%

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

      12. associate-/l* 89.4%

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

      13. associate-/r/ 86.7%

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

      14. associate-/l* 91.7%

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

   5. Applied egg-rr 91.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+272}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+288}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 2: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+274} \lor \neg \left(t_1 \leq 10^{+288}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \frac{1}{a}\\ \end{array} \end{array} \]

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+274) (not (<= t_1 1e+288)))
     (- (* x (/ y a)) (/ t (/ a z)))
     (* (fma x y (* t (- z))) (/ 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 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -5e+274) || !(t_1 <= 1e+288)) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else {
		tmp = fma(x, y, (t * -z)) * (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(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -5e+274) || !(t_1 <= 1e+288))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	else
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) * Float64(1.0 / 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+274], N[Not[LessEqual[t$95$1, 1e+288]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.9999999999999998e274 or 1e288 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 70.2%

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

      1. div-inv 70.2%

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

      2. fma-neg 70.2%

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

      3. *-commutative 70.2%

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

      4. distribute-rgt-neg-in 70.2%

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

   3. Applied egg-rr 70.2%

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

      1. *-commutative 70.2%

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

      2. fma-udef 70.2%

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

      3. *-commutative 70.2%

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

      4. distribute-rgt-neg-out 70.2%

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

      5. distribute-lft-neg-out 70.2%

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

      6. distribute-rgt-in 68.8%

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

      7. div-inv 68.8%

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

      8. distribute-lft-neg-out 68.8%

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

      9. distribute-lft-neg-in 68.8%

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

      10. div-inv 68.8%

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

      11. unsub-neg 68.8%

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

      12. associate-/l* 88.1%

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

      13. associate-/r/ 85.4%

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

      14. associate-/l* 94.3%

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

   5. Applied egg-rr 94.3%

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

   if -4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e288

   1. Initial program 99.1%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \frac{1}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+274} \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+288}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \frac{1}{a}\\ \end{array} \]

Alternative 3: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+274} \lor \neg \left(t_1 \leq 10^{+288}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

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+274) (not (<= t_1 1e+288)))
     (- (* x (/ y a)) (/ t (/ a z)))
     (/ 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+274) || !(t_1 <= 1e+288)) {
		tmp = (x * (y / a)) - (t / (a / z));
	} 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+274)) .or. (.not. (t_1 <= 1d+288))) then
        tmp = (x * (y / a)) - (t / (a / z))
    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+274) || !(t_1 <= 1e+288)) {
		tmp = (x * (y / a)) - (t / (a / z));
	} 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+274) or not (t_1 <= 1e+288):
		tmp = (x * (y / a)) - (t / (a / z))
	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+274) || !(t_1 <= 1e+288))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	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+274) || ~((t_1 <= 1e+288)))
		tmp = (x * (y / a)) - (t / (a / z));
	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+274], N[Not[LessEqual[t$95$1, 1e+288]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $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)) < -4.9999999999999998e274 or 1e288 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 70.2%

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

      1. div-inv 70.2%

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

      2. fma-neg 70.2%

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

      3. *-commutative 70.2%

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

      4. distribute-rgt-neg-in 70.2%

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

   3. Applied egg-rr 70.2%

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

      1. *-commutative 70.2%

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

      2. fma-udef 70.2%

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

      3. *-commutative 70.2%

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

      4. distribute-rgt-neg-out 70.2%

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

      5. distribute-lft-neg-out 70.2%

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

      6. distribute-rgt-in 68.8%

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

      7. div-inv 68.8%

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

      8. distribute-lft-neg-out 68.8%

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

      9. distribute-lft-neg-in 68.8%

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

      10. div-inv 68.8%

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

      11. unsub-neg 68.8%

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

      12. associate-/l* 88.1%

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

      13. associate-/r/ 85.4%

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

      14. associate-/l* 94.3%

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

   5. Applied egg-rr 94.3%

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

   if -4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e288

   1. Initial program 99.1%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+274} \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+288}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 4: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+255}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_1 \leq 10^{+288}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

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+255)
     (- (/ x (/ a y)) (/ z (/ a t)))
     (if (<= t_1 1e+288) (/ t_1 a) (- (* x (/ y a)) (/ t (/ a z)))))))

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+255) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else if (t_1 <= 1e+288) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (t / (a / z));
	}
	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+255)) then
        tmp = (x / (a / y)) - (z / (a / t))
    else if (t_1 <= 1d+288) then
        tmp = t_1 / a
    else
        tmp = (x * (y / a)) - (t / (a / z))
    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+255) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else if (t_1 <= 1e+288) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (t / (a / z));
	}
	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+255:
		tmp = (x / (a / y)) - (z / (a / t))
	elif t_1 <= 1e+288:
		tmp = t_1 / a
	else:
		tmp = (x * (y / a)) - (t / (a / z))
	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+255)
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	elseif (t_1 <= 1e+288)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	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+255)
		tmp = (x / (a / y)) - (z / (a / t));
	elseif (t_1 <= 1e+288)
		tmp = t_1 / a;
	else
		tmp = (x * (y / a)) - (t / (a / z));
	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[LessEqual[t$95$1, -5e+255], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+288], N[(t$95$1 / a), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000002e255

   1. Initial program 72.5%

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

      1. div-sub 72.5%

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

      2. associate-/l* 85.9%

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

      3. associate-/l* 97.4%

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

   3. Applied egg-rr 97.4%

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

   if -5.0000000000000002e255 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e288

   1. Initial program 99.1%

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

   if 1e288 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 71.6%

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

      1. div-inv 71.6%

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

      2. fma-neg 71.6%

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

      3. *-commutative 71.6%

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

      4. distribute-rgt-neg-in 71.6%

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

   3. Applied egg-rr 71.6%

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

      1. *-commutative 71.6%

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

      2. fma-udef 71.6%

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

      3. *-commutative 71.6%

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

      4. distribute-rgt-neg-out 71.6%

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

      5. distribute-lft-neg-out 71.6%

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

      6. distribute-rgt-in 68.9%

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

      7. div-inv 68.8%

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

      8. distribute-lft-neg-out 68.8%

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

      9. distribute-lft-neg-in 68.8%

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

      10. div-inv 68.8%

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

      11. unsub-neg 68.8%

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

      12. associate-/l* 89.4%

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

      13. associate-/r/ 86.7%

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

      14. associate-/l* 91.7%

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

   5. Applied egg-rr 91.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+255}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+288}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+269}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+207}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+269)
   (/ y (/ a x))
   (if (<= (* x y) 5e+207) (/ (- (* x y) (* z t)) a) (/ x (/ a y)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+269) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e+207) {
		tmp = ((x * y) - (z * t)) / 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) <= (-2d+269)) then
        tmp = y / (a / x)
    else if ((x * y) <= 5d+207) then
        tmp = ((x * y) - (z * t)) / 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) <= -2e+269) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e+207) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+269:
		tmp = y / (a / x)
	elif (x * y) <= 5e+207:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+269)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 5e+207)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+269)
		tmp = y / (a / x);
	elseif ((x * y) <= 5e+207)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+269], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+207], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e269

   1. Initial program 70.2%

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

   2. Taylor expanded in x around inf 70.2%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   if -2.0000000000000001e269 < (*.f64 x y) < 4.9999999999999999e207

   1. Initial program 95.6%

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

   if 4.9999999999999999e207 < (*.f64 x y)

   1. Initial program 70.5%

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

      1. div-inv 70.6%

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

      2. fma-neg 70.6%

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

      3. *-commutative 70.6%

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

      4. distribute-rgt-neg-in 70.6%

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

   3. Applied egg-rr 70.6%

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

   4. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+269}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+207}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 (<= y -1.3e-67)
   (/ x (/ a y))
   (if (<= y 5.8e+39) (/ (- t) (/ a z)) (* 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 (y <= -1.3e-67) {
		tmp = x / (a / y);
	} else if (y <= 5.8e+39) {
		tmp = -t / (a / z);
	} 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 (y <= (-1.3d-67)) then
        tmp = x / (a / y)
    else if (y <= 5.8d+39) then
        tmp = -t / (a / z)
    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 (y <= -1.3e-67) {
		tmp = x / (a / y);
	} else if (y <= 5.8e+39) {
		tmp = -t / (a / z);
	} 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 y <= -1.3e-67:
		tmp = x / (a / y)
	elif y <= 5.8e+39:
		tmp = -t / (a / z)
	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 (y <= -1.3e-67)
		tmp = Float64(x / Float64(a / y));
	elseif (y <= 5.8e+39)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(x * Float64(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 (y <= -1.3e-67)
		tmp = x / (a / y);
	elseif (y <= 5.8e+39)
		tmp = -t / (a / z);
	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[y, -1.3e-67], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+39], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e-67

   1. Initial program 86.7%

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

      1. div-inv 86.8%

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

      2. fma-neg 86.8%

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

      3. *-commutative 86.8%

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

      4. distribute-rgt-neg-in 86.8%

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

   3. Applied egg-rr 86.8%

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

   4. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   if -1.2999999999999999e-67 < y < 5.80000000000000059e39

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 73.0%

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

      1. associate-*r/ 73.0%

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

      2. associate-*r* 73.0%

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

      3. neg-mul-1 73.0%

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

   4. Simplified 73.0%

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

      1. associate-/l* 73.2%

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

      2. distribute-frac-neg 73.2%

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

   6. Applied egg-rr 73.2%

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

   if 5.80000000000000059e39 < y

   1. Initial program 85.8%

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

   2. Taylor expanded in x around inf 62.2%

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

      1. associate-/l* 72.3%

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

      2. associate-/r/ 74.3%

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

   4. Applied egg-rr 74.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 (<= y -1.3e-67)
   (/ x (/ a y))
   (if (<= y 1.35e+40) (* z (/ (- t) 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 (y <= -1.3e-67) {
		tmp = x / (a / y);
	} else if (y <= 1.35e+40) {
		tmp = z * (-t / 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 (y <= (-1.3d-67)) then
        tmp = x / (a / y)
    else if (y <= 1.35d+40) then
        tmp = z * (-t / 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 (y <= -1.3e-67) {
		tmp = x / (a / y);
	} else if (y <= 1.35e+40) {
		tmp = z * (-t / 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 y <= -1.3e-67:
		tmp = x / (a / y)
	elif y <= 1.35e+40:
		tmp = z * (-t / 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 (y <= -1.3e-67)
		tmp = Float64(x / Float64(a / y));
	elseif (y <= 1.35e+40)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(x * Float64(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 (y <= -1.3e-67)
		tmp = x / (a / y);
	elseif (y <= 1.35e+40)
		tmp = z * (-t / 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[y, -1.3e-67], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+40], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e-67

   1. Initial program 86.7%

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

      1. div-inv 86.8%

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

      2. fma-neg 86.8%

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

      3. *-commutative 86.8%

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

      4. distribute-rgt-neg-in 86.8%

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

   3. Applied egg-rr 86.8%

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

   4. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   if -1.2999999999999999e-67 < y < 1.35000000000000005e40

   1. Initial program 95.8%

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

      1. div-sub 95.0%

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

      2. associate-/l* 91.9%

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

      3. associate-/l* 88.8%

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

   3. Applied egg-rr 88.8%

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

      1. add-sqr-sqrt 47.9%

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

      2. sqrt-unprod 49.0%

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

      3. sqr-neg 49.0%

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

      4. sqrt-unprod 14.6%

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

      5. add-sqr-sqrt 32.4%

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

      6. distribute-neg-frac 32.4%

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

      7. associate-/r/ 33.2%

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

      8. distribute-lft-neg-in 33.2%

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

      9. distribute-frac-neg 33.2%

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

      10. div-inv 33.2%

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

      11. associate-*l* 32.4%

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

      12. add-sqr-sqrt 14.6%

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

      13. sqrt-unprod 49.0%

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

      14. sqr-neg 49.0%

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

      15. sqrt-unprod 47.9%

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

      16. add-sqr-sqrt 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in x around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-*l/ 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   8. Simplified 70.7%

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

   if 1.35000000000000005e40 < y

   1. Initial program 85.8%

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

   2. Taylor expanded in x around inf 62.2%

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

      1. associate-/l* 72.3%

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

      2. associate-/r/ 74.3%

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

   4. Applied egg-rr 74.3%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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 (<= z -5.2e-72) (* x (/ y 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 (z <= -5.2e-72) {
		tmp = x * (y / 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 (z <= (-5.2d-72)) then
        tmp = x * (y / 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 (z <= -5.2e-72) {
		tmp = x * (y / 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 z <= -5.2e-72:
		tmp = x * (y / 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 (z <= -5.2e-72)
		tmp = Float64(x * Float64(y / 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 (z <= -5.2e-72)
		tmp = x * (y / 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[z, -5.2e-72], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999992e-72

   1. Initial program 88.8%

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

   2. Taylor expanded in x around inf 33.5%

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

      1. associate-/l* 42.0%

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

      2. associate-/r/ 35.9%

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

   4. Applied egg-rr 35.9%

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

   if -5.19999999999999992e-72 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 56.9%

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

      1. associate-*r/ 58.4%

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

   4. Simplified 58.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 9: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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 (<= z -5e-68) (* x (/ y 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 (z <= -5e-68) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	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 (z <= (-5d-68)) then
        tmp = x * (y / a)
    else
        tmp = y / (a / x)
    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 (z <= -5e-68) {
		tmp = x * (y / 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 z <= -5e-68:
		tmp = x * (y / 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 (z <= -5e-68)
		tmp = Float64(x * Float64(y / 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 (z <= -5e-68)
		tmp = x * (y / 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[z, -5e-68], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999971e-68

   1. Initial program 88.6%

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

   2. Taylor expanded in x around inf 32.6%

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

      1. associate-/l* 41.2%

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

      2. associate-/r/ 35.1%

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

   4. Applied egg-rr 35.1%

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

   if -4.99999999999999971e-68 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 57.1%

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

      1. associate-/l* 58.8%

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

   4. Simplified 58.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 10: 52.1% 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 90.9%

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

2. Taylor expanded in x around inf 49.9%

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

   1. associate-*r/ 53.5%

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

4. Simplified 53.5%

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

5. Final simplification 53.5%

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

Developer target: 91.4% 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 2023200 
(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))