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

Percentage Accurate: 91.4% → 97.0%

Time: 7.3s

Alternatives: 9

Speedup: 0.5×

• 28.1% 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: 91.4% 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, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \frac{-t}{\frac{a}{z}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (fma (/ y a) x (* (- t) (/ z a)))
     (if (<= t_1 5e+197) (/ t_1 a) (fma (/ y a) x (/ (- t) (/ a z)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((y / a), x, (-t * (z / a)));
	} else if (t_1 <= 5e+197) {
		tmp = t_1 / a;
	} else {
		tmp = fma((y / a), x, (-t / (a / z)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) * Float64(z / a)));
	elseif (t_1 <= 5e+197)
		tmp = Float64(t_1 / a);
	else
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) / Float64(a / z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / a), $MachinePrecision] * x + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+197], N[(t$95$1 / a), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x + N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.0%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. distribute-lft-neg-in N/A

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

      14. lower-*.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000009e197

   1. Initial program 99.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.00000000000000009e197 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. distribute-lft-neg-in N/A

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

      14. lower-*.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 93.5

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

   4. Applied rewrites 93.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 93.4

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

   6. Applied rewrites 93.4%

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

Alternative 2: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+197}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+197)))
     (fma (/ y a) x (* (- t) (/ z a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+197)) {
		tmp = fma((y / a), x, (-t * (z / a)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+197))
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+197]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * x + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 5.00000000000000009e197 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 75.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. distribute-lft-neg-in N/A

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

      14. lower-*.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 95.7

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

   4. Applied rewrites 95.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000009e197

   1. Initial program 99.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+197}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+197}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+197)))
     (fma (/ x a) y (* (- t) (/ z a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+197)) {
		tmp = fma((x / a), y, (-t * (z / a)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+197))
		tmp = fma(Float64(x / a), y, Float64(Float64(-t) * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+197]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * y + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 5.00000000000000009e197 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 75.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-/l* N/A

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

      14. distribute-lft-neg-in N/A

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

      15. lower-*.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-/.f64 95.7

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

   4. Applied rewrites 95.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000009e197

   1. Initial program 99.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+197}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\left(\frac{-1}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* (* (/ -1.0 a) z) t)
   (if (<= (* z t) 5e+297) (/ (- (* x y) (* z t)) a) (* (/ (- z) a) t))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = ((-1.0 / a) * z) * t;
	} else if ((z * t) <= 5e+297) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (-z / a) * t;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = ((-1.0 / a) * z) * t;
	} else if ((z * t) <= 5e+297) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (-z / a) * t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = ((-1.0 / a) * z) * t
	elif (z * t) <= 5e+297:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (-z / a) * t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-1.0 / a) * z) * t);
	elseif (Float64(z * t) <= 5e+297)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(Float64(-z) / a) * t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = ((-1.0 / a) * z) * t;
	elseif ((z * t) <= 5e+297)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (-z / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(N[(-1.0 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+297], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. distribute-frac-neg2 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. associate-/r* N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 N/A

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

      17. lower-/.f64 70.8

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 70.8

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

   4. Applied rewrites 70.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 99.8

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

   7. Applied rewrites 99.8%

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

   9. Applied rewrites 99.9%

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

   if -inf.0 < (*.f64 z t) < 4.9999999999999998e297

   1. Initial program 96.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 4.9999999999999998e297 < (*.f64 z t)

   1. Initial program 58.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. distribute-frac-neg2 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. associate-/r* N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 N/A

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

      17. lower-/.f64 58.1

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 58.1

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

   4. Applied rewrites 58.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 94.4

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

   7. Applied rewrites 94.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\left(\frac{-1}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} \leq 5 \cdot 10^{+91}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- (* x y) (* z t)) a) 5e+91) (/ (* y x) a) (* (/ x a) y)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((x * y) - (z * t)) / a) <= 5e+91) {
		tmp = (y * x) / a;
	} else {
		tmp = (x / a) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) - (z * t)) / a) <= 5d+91) then
        tmp = (y * x) / a
    else
        tmp = (x / a) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((x * y) - (z * t)) / a) <= 5e+91) {
		tmp = (y * x) / a;
	} else {
		tmp = (x / a) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (((x * y) - (z * t)) / a) <= 5e+91:
		tmp = (y * x) / a
	else:
		tmp = (x / a) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) - Float64(z * t)) / a) <= 5e+91)
		tmp = Float64(Float64(y * x) / a);
	else
		tmp = Float64(Float64(x / a) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((((x * y) - (z * t)) / a) <= 5e+91)
		tmp = (y * x) / a;
	else
		tmp = (x / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], 5e+91], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 5.0000000000000002e91

   1. Initial program 94.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.9

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

   5. Applied rewrites 49.9%

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

   if 5.0000000000000002e91 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 88.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.7

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

   5. Applied rewrites 51.7%

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

   7. Applied rewrites 56.3%

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

Alternative 6: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+55} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+56}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* z t) -2e+55) (not (<= (* z t) 4e+56)))
   (* (- z) (/ t a))
   (/ (* y x) a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -2e+55) || !((z * t) <= 4e+56)) {
		tmp = -z * (t / a);
	} else {
		tmp = (y * x) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 * t) <= (-2d+55)) .or. (.not. ((z * t) <= 4d+56))) then
        tmp = -z * (t / a)
    else
        tmp = (y * x) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -2e+55) || !((z * t) <= 4e+56)) {
		tmp = -z * (t / a);
	} else {
		tmp = (y * x) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * t) <= -2e+55) or not ((z * t) <= 4e+56):
		tmp = -z * (t / a)
	else:
		tmp = (y * x) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+55) || !(Float64(z * t) <= 4e+56))
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(Float64(y * x) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z * t) <= -2e+55) || ~(((z * t) <= 4e+56)))
		tmp = -z * (t / a);
	else
		tmp = (y * x) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -2e+55], N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e+56]], $MachinePrecision]], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000002e55 or 4.00000000000000037e56 < (*.f64 z t)

   1. Initial program 86.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 84.0

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

   5. Applied rewrites 84.0%

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

   if -2.00000000000000002e55 < (*.f64 z t) < 4.00000000000000037e56

   1. Initial program 97.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 74.2

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

   5. Applied rewrites 74.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+55} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+56}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+55} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* z t) -2e+55) (not (<= (* z t) 4e+56)))
   (* (/ (- z) a) t)
   (/ (* y x) a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -2e+55) || !((z * t) <= 4e+56)) {
		tmp = (-z / a) * t;
	} else {
		tmp = (y * x) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 * t) <= (-2d+55)) .or. (.not. ((z * t) <= 4d+56))) then
        tmp = (-z / a) * t
    else
        tmp = (y * x) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -2e+55) || !((z * t) <= 4e+56)) {
		tmp = (-z / a) * t;
	} else {
		tmp = (y * x) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * t) <= -2e+55) or not ((z * t) <= 4e+56):
		tmp = (-z / a) * t
	else:
		tmp = (y * x) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+55) || !(Float64(z * t) <= 4e+56))
		tmp = Float64(Float64(Float64(-z) / a) * t);
	else
		tmp = Float64(Float64(y * x) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z * t) <= -2e+55) || ~(((z * t) <= 4e+56)))
		tmp = (-z / a) * t;
	else
		tmp = (y * x) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -2e+55], N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e+56]], $MachinePrecision]], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000002e55 or 4.00000000000000037e56 < (*.f64 z t)

   1. Initial program 86.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. distribute-frac-neg2 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. associate-/r* N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 N/A

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

      17. lower-/.f64 86.1

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 86.1

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

   4. Applied rewrites 86.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 84.6

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

   7. Applied rewrites 84.6%

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

   if -2.00000000000000002e55 < (*.f64 z t) < 4.00000000000000037e56

   1. Initial program 97.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 74.2

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

   5. Applied rewrites 74.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+55} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.3e-52) (* (/ x a) y) (* (/ y a) x)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.3e-52) {
		tmp = (x / a) * y;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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-52) then
        tmp = (x / a) * y
    else
        tmp = (y / a) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.3e-52) {
		tmp = (x / a) * y;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.3e-52:
		tmp = (x / a) * y
	else:
		tmp = (y / a) * x
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.3e-52)
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(Float64(y / a) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.3e-52)
		tmp = (x / a) * y;
	else
		tmp = (y / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.3e-52], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2999999999999999e-52

   1. Initial program 92.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 46.4

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

   5. Applied rewrites 46.4%

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

   7. Applied rewrites 45.3%

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

   if 1.2999999999999999e-52 < y

   1. Initial program 92.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 60.7

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

   5. Applied rewrites 60.7%

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

   7. Applied rewrites 63.3%

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

Alternative 9: 51.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x / a) * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 50.4

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

5. Applied rewrites 50.4%

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

7. Applied rewrites 48.1%

   \[\leadsto \frac{x}{a} \cdot \color{blue}{y} \]
8. Add Preprocessing

Developer Target 1: 91.2% accurate, 0.5× 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 2024322 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

  (/ (- (* x y) (* z t)) a))