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

Percentage Accurate: 91.2% → 96.9%

Time: 7.7s

Alternatives: 10

Speedup: 0.6×

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{a}, \frac{t}{a} \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - z \cdot \frac{t}{y \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

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 (/ x a) (* (/ t a) (- z)))
     (if (<= t_1 5e+297) (/ t_1 a) (* y (- (/ x a) (* z (/ t (* y a)))))))))

C

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, (x / a), ((t / a) * -z));
	} else if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (z * (t / (y * a))));
	}
	return tmp;
}

Julia

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(y, Float64(x / a), Float64(Float64(t / a) * Float64(-z)));
	elseif (t_1 <= 5e+297)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(z * Float64(t / Float64(y * a)))));
	end
	return tmp
end

Wolfram

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[(y * N[(x / a), $MachinePrecision] + N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+297], N[(t$95$1 / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(z * N[(t / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.0%

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

      1. div-sub 52.9%

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

      2. *-commutative 52.9%

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

      3. associate-/l* 64.6%

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

      4. fma-neg 64.6%

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

      5. associate-/l* 95.6%

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

   4. Applied egg-rr 95.6%

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

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

   1. Initial program 97.8%

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

   if 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

      5. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 96.7%

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

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - z \cdot \frac{t}{y \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

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))
     (- (* x (/ y a)) (/ t (/ a z)))
     (if (<= t_1 5e+297) (/ t_1 a) (* y (- (/ x a) (* z (/ t (* y a)))))))))

C

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 = (x * (y / a)) - (t / (a / z));
	} else if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (z * (t / (y * a))));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (z * (t / (y * a))));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y / a)) - (t / (a / z))
	elif t_1 <= 5e+297:
		tmp = t_1 / a
	else:
		tmp = y * ((x / a) - (z * (t / (y * a))))
	return tmp

Julia

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 = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	elseif (t_1 <= 5e+297)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(z * Float64(t / Float64(y * a)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y / a)) - (t / (a / z));
	elseif (t_1 <= 5e+297)
		tmp = t_1 / a;
	else
		tmp = y * ((x / a) - (z * (t / (y * a))));
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+297], N[(t$95$1 / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(z * N[(t / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.0%

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

      1. div-sub 52.9%

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

      2. associate-/l* 64.7%

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

      3. associate-/l* 95.7%

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

   4. Applied egg-rr 95.7%

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

      1. associate-*r/ 64.7%

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

      2. add-sqr-sqrt 34.5%

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

      3. sqrt-unprod 42.0%

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

      4. sqr-neg 42.0%

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

      5. sqrt-unprod 16.7%

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

      6. add-sqr-sqrt 41.7%

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

      7. associate-*l/ 41.8%

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

      8. *-commutative 41.8%

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

      9. clear-num 41.8%

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

      10. un-div-inv 41.8%

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

      11. add-sqr-sqrt 16.7%

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

      12. sqrt-unprod 46.3%

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

      13. sqr-neg 46.3%

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

      14. sqrt-unprod 45.7%

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

      15. add-sqr-sqrt 95.7%

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

   6. Applied egg-rr 95.7%

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

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

   1. Initial program 97.8%

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

   if 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

      5. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 96.7%

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

Alternative 3: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \frac{z}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

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 (* (- t) (/ z a))))
   (if (<= (* x y) -1e-87)
     (* x (/ y a))
     (if (<= (* x y) 1e-13)
       t_1
       (if (<= (* x y) 1e+24)
         (/ x (/ a y))
         (if (<= (* x y) 5e+32) t_1 (* y (/ x a))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -t * (z / a);
	double tmp;
	if ((x * y) <= -1e-87) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e-13) {
		tmp = t_1;
	} else if ((x * y) <= 1e+24) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+32) {
		tmp = t_1;
	} 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.
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 = -t * (z / a)
    if ((x * y) <= (-1d-87)) then
        tmp = x * (y / a)
    else if ((x * y) <= 1d-13) then
        tmp = t_1
    else if ((x * y) <= 1d+24) then
        tmp = x / (a / y)
    else if ((x * y) <= 5d+32) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t * (z / a);
	double tmp;
	if ((x * y) <= -1e-87) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e-13) {
		tmp = t_1;
	} else if ((x * y) <= 1e+24) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+32) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -t * (z / a)
	tmp = 0
	if (x * y) <= -1e-87:
		tmp = x * (y / a)
	elif (x * y) <= 1e-13:
		tmp = t_1
	elif (x * y) <= 1e+24:
		tmp = x / (a / y)
	elif (x * y) <= 5e+32:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) * Float64(z / a))
	tmp = 0.0
	if (Float64(x * y) <= -1e-87)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 1e-13)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+24)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 5e+32)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -t * (z / a);
	tmp = 0.0;
	if ((x * y) <= -1e-87)
		tmp = x * (y / a);
	elseif ((x * y) <= 1e-13)
		tmp = t_1;
	elseif ((x * y) <= 1e+24)
		tmp = x / (a / y);
	elseif ((x * y) <= 5e+32)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e-87], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-13], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+24], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+32], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.00000000000000002e-87

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf 77.1%

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

      1. associate-*r/ 78.9%

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

   5. Simplified 78.9%

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

   if -1.00000000000000002e-87 < (*.f64 x y) < 1e-13 or 9.9999999999999998e23 < (*.f64 x y) < 4.9999999999999997e32

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 79.3%

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

      3. distribute-rgt-neg-in 79.3%

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

      4. distribute-neg-frac2 79.3%

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

   5. Simplified 79.3%

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

   if 1e-13 < (*.f64 x y) < 9.9999999999999998e23

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 77.4%

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

      1. associate-*r/ 63.6%

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

   5. Simplified 63.6%

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

      1. clear-num 63.6%

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

      2. un-div-inv 63.8%

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

   7. Applied egg-rr 63.8%

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

   if 4.9999999999999997e32 < (*.f64 x y)

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 77.8%

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

      1. associate-*l/ 85.2%

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

   5. Applied egg-rr 76.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+260}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+260)))
     (- (* x (/ y a)) (* z (/ t a)))
     (/ t_1 a))))

C

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 <= 4e+260)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+260)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+260):
		tmp = (x * (y / a)) - (z * (t / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

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 <= 4e+260))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+260)))
		tmp = (x * (y / a)) - (z * (t / a));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

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, 4e+260]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 4.00000000000000026e260 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.4%

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

      1. div-sub 65.7%

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

      2. associate-/l* 75.5%

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

      3. associate-/l* 93.0%

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

   4. Applied egg-rr 93.0%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.00000000000000026e260

   1. Initial program 97.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 4 \cdot 10^{+260}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t\_1 \leq 10^{+151}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

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))
     (- (* x (/ y a)) (/ t (/ a z)))
     (if (<= t_1 1e+151) (/ t_1 a) (- (* y (/ x a)) (* z (/ t a)))))))

C

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 = (x * (y / a)) - (t / (a / z));
	} else if (t_1 <= 1e+151) {
		tmp = t_1 / a;
	} else {
		tmp = (y * (x / a)) - (z * (t / a));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else if (t_1 <= 1e+151) {
		tmp = t_1 / a;
	} else {
		tmp = (y * (x / a)) - (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y / a)) - (t / (a / z))
	elif t_1 <= 1e+151:
		tmp = t_1 / a
	else:
		tmp = (y * (x / a)) - (z * (t / a))
	return tmp

Julia

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 = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	elseif (t_1 <= 1e+151)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(y * Float64(x / a)) - Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y / a)) - (t / (a / z));
	elseif (t_1 <= 1e+151)
		tmp = t_1 / a;
	else
		tmp = (y * (x / a)) - (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+151], N[(t$95$1 / a), $MachinePrecision], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.0%

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

      1. div-sub 52.9%

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

      2. associate-/l* 64.7%

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

      3. associate-/l* 95.7%

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

   4. Applied egg-rr 95.7%

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

      1. associate-*r/ 64.7%

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

      2. add-sqr-sqrt 34.5%

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

      3. sqrt-unprod 42.0%

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

      4. sqr-neg 42.0%

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

      5. sqrt-unprod 16.7%

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

      6. add-sqr-sqrt 41.7%

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

      7. associate-*l/ 41.8%

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

      8. *-commutative 41.8%

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

      9. clear-num 41.8%

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

      10. un-div-inv 41.8%

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

      11. add-sqr-sqrt 16.7%

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

      12. sqrt-unprod 46.3%

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

      13. sqr-neg 46.3%

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

      14. sqrt-unprod 45.7%

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

      15. add-sqr-sqrt 95.7%

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

   6. Applied egg-rr 95.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000002e151

   1. Initial program 97.5%

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

   if 1.00000000000000002e151 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 83.9%

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

      1. div-sub 83.9%

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

      2. associate-/l* 89.2%

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

      3. associate-/l* 94.3%

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

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in x around 0 89.0%

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

      1. associate-*l/ 90.7%

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

   7. Applied egg-rr 90.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+151}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1 - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+260}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

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 a))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 (- INFINITY))
     (- t_1 (/ t (/ a z)))
     (if (<= t_2 4e+260) (/ t_2 a) (- t_1 (* z (/ t a)))))))

C

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 / a);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 - (t / (a / z));
	} else if (t_2 <= 4e+260) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z * (t / a));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 - (t / (a / z));
	} else if (t_2 <= 4e+260) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * (y / a)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 - (t / (a / z))
	elif t_2 <= 4e+260:
		tmp = t_2 / a
	else:
		tmp = t_1 - (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / a))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 - Float64(t / Float64(a / z)));
	elseif (t_2 <= 4e+260)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / a);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 - (t / (a / z));
	elseif (t_2 <= 4e+260)
		tmp = t_2 / a;
	else
		tmp = t_1 - (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+260], N[(t$95$2 / a), $MachinePrecision], N[(t$95$1 - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 57.0%

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

      1. div-sub 52.9%

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

      2. associate-/l* 64.7%

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

      3. associate-/l* 95.7%

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

   4. Applied egg-rr 95.7%

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

      1. associate-*r/ 64.7%

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

      2. add-sqr-sqrt 34.5%

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

      3. sqrt-unprod 42.0%

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

      4. sqr-neg 42.0%

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

      5. sqrt-unprod 16.7%

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

      6. add-sqr-sqrt 41.7%

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

      7. associate-*l/ 41.8%

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

      8. *-commutative 41.8%

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

      9. clear-num 41.8%

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

      10. un-div-inv 41.8%

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

      11. add-sqr-sqrt 16.7%

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

      12. sqrt-unprod 46.3%

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

      13. sqr-neg 46.3%

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

      14. sqrt-unprod 45.7%

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

      15. add-sqr-sqrt 95.7%

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

   6. Applied egg-rr 95.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.00000000000000026e260

   1. Initial program 97.7%

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

   if 4.00000000000000026e260 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 74.7%

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

      1. div-sub 74.7%

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

      2. associate-/l* 83.1%

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

      3. associate-/l* 91.1%

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

   4. Applied egg-rr 91.1%

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

Alternative 7: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

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) -1e+49)
   (* (- t) (/ z a))
   (if (<= (* z t) 5e-26) (/ (* x y) a) (* (/ t a) (- z)))))

C

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) <= -1e+49) {
		tmp = -t * (z / a);
	} else if ((z * t) <= 5e-26) {
		tmp = (x * y) / a;
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Fortran

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) <= (-1d+49)) then
        tmp = -t * (z / a)
    else if ((z * t) <= 5d-26) then
        tmp = (x * y) / a
    else
        tmp = (t / a) * -z
    end if
    code = tmp
end function

Java

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) <= -1e+49) {
		tmp = -t * (z / a);
	} else if ((z * t) <= 5e-26) {
		tmp = (x * y) / a;
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -1e+49:
		tmp = -t * (z / a)
	elif (z * t) <= 5e-26:
		tmp = (x * y) / a
	else:
		tmp = (t / a) * -z
	return tmp

Julia

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) <= -1e+49)
		tmp = Float64(Float64(-t) * Float64(z / a));
	elseif (Float64(z * t) <= 5e-26)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(Float64(t / a) * Float64(-z));
	end
	return tmp
end

MATLAB

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) <= -1e+49)
		tmp = -t * (z / a);
	elseif ((z * t) <= 5e-26)
		tmp = (x * y) / a;
	else
		tmp = (t / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

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], -1e+49], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-26], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -9.99999999999999946e48

   1. Initial program 86.1%

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

   3. Taylor expanded in x around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. associate-/l* 87.7%

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

      3. distribute-rgt-neg-in 87.7%

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

      4. distribute-neg-frac2 87.7%

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

   5. Simplified 87.7%

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

   if -9.99999999999999946e48 < (*.f64 z t) < 5.00000000000000019e-26

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 79.7%

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

   if 5.00000000000000019e-26 < (*.f64 z t)

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-*r/ 80.4%

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

      3. neg-mul-1 80.4%

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

      4. distribute-rgt-neg-in 80.4%

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

      5. distribute-frac-neg 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.1% accurate, 0.6× speedup

Math

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

FPCore

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) 1e+294) (/ (- (* x y) (* z t)) a) (/ t (- (/ a z)))))

C

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) <= 1e+294) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t / -(a / z);
	}
	return tmp;
}

Fortran

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) <= 1d+294) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t / -(a / z)
    end if
    code = tmp
end function

Java

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) <= 1e+294) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t / -(a / z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= 1e+294:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t / -(a / z)
	return tmp

Julia

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) <= 1e+294)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(t / Float64(-Float64(a / z)));
	end
	return tmp
end

MATLAB

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) <= 1e+294)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t / -(a / z);
	end
	tmp_2 = tmp;
end

Wolfram

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], 1e+294], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(t / (-N[(a / z), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1.00000000000000007e294

   1. Initial program 93.4%

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

   if 1.00000000000000007e294 < (*.f64 z t)

   1. Initial program 50.3%

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

   3. Taylor expanded in x around 0 50.3%

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

      1. associate-*r* 50.3%

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

      2. mul-1-neg 50.3%

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

   5. Simplified 50.3%

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

      1. add-sqr-sqrt 21.9%

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

      2. sqrt-unprod 20.6%

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

      3. sqr-neg 20.6%

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

      4. sqrt-unprod 0.1%

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

      5. add-sqr-sqrt 0.2%

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

      6. associate-*l/ 0.3%

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

      7. frac-2neg 0.3%

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

   7. Applied egg-rr 0.3%

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

      1. add-sqr-sqrt 0.1%

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

      2. sqrt-unprod 20.8%

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

      3. sqr-neg 20.8%

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

      4. sqrt-unprod 33.3%

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

      5. add-sqr-sqrt 99.9%

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

      6. distribute-rgt-neg-out 99.9%

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

      7. associate-/r/ 99.9%

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

      8. distribute-neg-frac 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 93.8%

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

Alternative 9: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

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) -1e-129) (* x (/ y a)) (* y (/ x a))))

C

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) <= -1e-129) {
		tmp = x * (y / 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.
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) <= (-1d-129)) then
        tmp = x * (y / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

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) <= -1e-129) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e-129:
		tmp = x * (y / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e-129)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

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) <= -1e-129)
		tmp = x * (y / 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-129], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999993e-130

   1. Initial program 89.2%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. associate-*r/ 75.0%

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

   5. Simplified 75.0%

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

   if -9.9999999999999993e-130 < (*.f64 x y)

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf 44.0%

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

      1. associate-*l/ 86.8%

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

   5. Applied egg-rr 41.4%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.2% accurate, 1.8× speedup

Math

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

FPCore

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 (/ y a)))

C

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

Fortran

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 * (y / a)
end function

Java

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 * (y / a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in x around inf 53.4%

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

   1. associate-*r/ 55.1%

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

5. Simplified 55.1%

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

Developer target: 91.0% accurate, 0.4× 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 2024084 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (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))