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

Percentage Accurate: 91.5% → 96.7%

Time: 9.0s

Alternatives: 11

Speedup: 0.6×

• 27.9% 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: 91.5% 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: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+232}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ (/ z x) a))))
     (if (<= t_1 2e+232) (/ t_1 a) (- (* x (/ y a)) (/ 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 = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 2e+232) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (t / (a / z));
	}
	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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 2e+232) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (t / (a / z));
	}
	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):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x * ((y / a) - (t * ((z / x) / a)))
	elif t_1 <= 2e+232:
		tmp = t_1 / a
	else:
		tmp = (x * (y / a)) - (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 = Float64(x * Float64(Float64(y / a) - Float64(t * Float64(Float64(z / x) / a))));
	elseif (t_1 <= 2e+232)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y, 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	elseif (t_1 <= 2e+232)
		tmp = t_1 / a;
	else
		tmp = (x * (y / a)) - (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.
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[(x * N[(N[(y / a), $MachinePrecision] - N[(t * N[(N[(z / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+232], N[(t$95$1 / a), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.4%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. associate-/l* 80.2%

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

      5. *-commutative 80.2%

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

      6. associate-/r* 87.5%

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

   5. Simplified 87.5%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000011e232

   1. Initial program 99.2%

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

   if 2.00000000000000011e232 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 68.8%

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

      1. div-sub 68.8%

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

      2. associate-/l* 90.0%

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

      3. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. associate-*r/ 90.0%

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

      2. add-sqr-sqrt 33.7%

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

      3. sqrt-unprod 71.8%

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

      4. sqr-neg 71.8%

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

      5. sqrt-unprod 43.5%

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

      6. add-sqr-sqrt 58.9%

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

      7. associate-*l/ 58.9%

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

      8. *-commutative 58.9%

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

      9. clear-num 58.9%

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

      10. un-div-inv 58.9%

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

      11. add-sqr-sqrt 43.5%

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

      12. sqrt-unprod 74.3%

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

      13. sqr-neg 74.3%

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

      14. sqrt-unprod 38.3%

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

      15. add-sqr-sqrt 97.3%

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

   6. Applied egg-rr 97.3%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+232}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a}\\ t_2 := y \cdot \frac{x}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (/ (- z) a))) (t_2 (* y (/ x a))))
   (if (<= (* x y) -5e-59)
     t_2
     (if (<= (* x y) 2e-88)
       t_1
       (if (<= (* x y) 1e-15)
         (/ (* x y) a)
         (if (<= (* x y) 1e+47) t_1 t_2))))))

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 = t * (-z / a);
	double t_2 = y * (x / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_2;
	} else if ((x * y) <= 2e-88) {
		tmp = t_1;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (-z / a)
    t_2 = y * (x / a)
    if ((x * y) <= (-5d-59)) then
        tmp = t_2
    else if ((x * y) <= 2d-88) then
        tmp = t_1
    else if ((x * y) <= 1d-15) then
        tmp = (x * y) / a
    else if ((x * y) <= 1d+47) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = t * (-z / a);
	double t_2 = y * (x / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_2;
	} else if ((x * y) <= 2e-88) {
		tmp = t_1;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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):
	t_1 = t * (-z / a)
	t_2 = y * (x / a)
	tmp = 0
	if (x * y) <= -5e-59:
		tmp = t_2
	elif (x * y) <= 2e-88:
		tmp = t_1
	elif (x * y) <= 1e-15:
		tmp = (x * y) / a
	elif (x * y) <= 1e+47:
		tmp = t_1
	else:
		tmp = t_2
	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(t * Float64(Float64(-z) / a))
	t_2 = Float64(y * Float64(x / a))
	tmp = 0.0
	if (Float64(x * y) <= -5e-59)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e-88)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 1e+47)
		tmp = t_1;
	else
		tmp = t_2;
	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)
	t_1 = t * (-z / a);
	t_2 = y * (x / a);
	tmp = 0.0;
	if ((x * y) <= -5e-59)
		tmp = t_2;
	elseif ((x * y) <= 2e-88)
		tmp = t_1;
	elseif ((x * y) <= 1e-15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 1e+47)
		tmp = t_1;
	else
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-59], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e-88], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000001e-59 or 1e47 < (*.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. clear-num 72.1%

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

      2. associate-/r* 79.5%

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

      3. associate-/r/ 79.5%

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

      4. clear-num 79.6%

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

   5. Applied egg-rr 79.6%

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

   if -5.0000000000000001e-59 < (*.f64 x y) < 1.99999999999999987e-88 or 1.0000000000000001e-15 < (*.f64 x y) < 1e47

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. associate-/l* 83.9%

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

      3. distribute-rgt-neg-in 83.9%

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

      4. distribute-neg-frac2 83.9%

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

   5. Simplified 83.9%

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

   if 1.99999999999999987e-88 < (*.f64 x y) < 1.0000000000000001e-15

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf 73.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ t_2 := y \cdot \frac{x}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* z (/ (- t) a))) (t_2 (* y (/ x a))))
   (if (<= (* x y) -5e-59)
     t_2
     (if (<= (* x y) 2e-88)
       t_1
       (if (<= (* x y) 1e-15)
         (/ (* x y) a)
         (if (<= (* x y) 1e+47) t_1 t_2))))))

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 = z * (-t / a);
	double t_2 = y * (x / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_2;
	} else if ((x * y) <= 2e-88) {
		tmp = t_1;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (-t / a)
    t_2 = y * (x / a)
    if ((x * y) <= (-5d-59)) then
        tmp = t_2
    else if ((x * y) <= 2d-88) then
        tmp = t_1
    else if ((x * y) <= 1d-15) then
        tmp = (x * y) / a
    else if ((x * y) <= 1d+47) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = z * (-t / a);
	double t_2 = y * (x / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_2;
	} else if ((x * y) <= 2e-88) {
		tmp = t_1;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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):
	t_1 = z * (-t / a)
	t_2 = y * (x / a)
	tmp = 0
	if (x * y) <= -5e-59:
		tmp = t_2
	elif (x * y) <= 2e-88:
		tmp = t_1
	elif (x * y) <= 1e-15:
		tmp = (x * y) / a
	elif (x * y) <= 1e+47:
		tmp = t_1
	else:
		tmp = t_2
	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(z * Float64(Float64(-t) / a))
	t_2 = Float64(y * Float64(x / a))
	tmp = 0.0
	if (Float64(x * y) <= -5e-59)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e-88)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 1e+47)
		tmp = t_1;
	else
		tmp = t_2;
	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)
	t_1 = z * (-t / a);
	t_2 = y * (x / a);
	tmp = 0.0;
	if ((x * y) <= -5e-59)
		tmp = t_2;
	elseif ((x * y) <= 2e-88)
		tmp = t_1;
	elseif ((x * y) <= 1e-15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 1e+47)
		tmp = t_1;
	else
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-59], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e-88], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000001e-59 or 1e47 < (*.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. clear-num 72.1%

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

      2. associate-/r* 79.5%

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

      3. associate-/r/ 79.5%

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

      4. clear-num 79.6%

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

   5. Applied egg-rr 79.6%

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

   if -5.0000000000000001e-59 < (*.f64 x y) < 1.99999999999999987e-88 or 1.0000000000000001e-15 < (*.f64 x y) < 1e47

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*r/ 83.0%

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

      3. neg-mul-1 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. distribute-frac-neg 83.0%

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

   5. Simplified 83.0%

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

   if 1.99999999999999987e-88 < (*.f64 x y) < 1.0000000000000001e-15

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf 73.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* y (/ x a))))
   (if (<= (* x y) -5e-59)
     t_1
     (if (<= (* x y) 2e-88)
       (/ (* z (- t)) a)
       (if (<= (* x y) 1e-15)
         (/ (* x y) a)
         (if (<= (* x y) 1e+47) (* z (/ (- t) a)) t_1))))))

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 = y * (x / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_1;
	} else if ((x * y) <= 2e-88) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+47) {
		tmp = z * (-t / a);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / a)
    if ((x * y) <= (-5d-59)) then
        tmp = t_1
    else if ((x * y) <= 2d-88) then
        tmp = (z * -t) / a
    else if ((x * y) <= 1d-15) then
        tmp = (x * y) / a
    else if ((x * y) <= 1d+47) then
        tmp = z * (-t / a)
    else
        tmp = t_1
    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 t_1 = y * (x / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_1;
	} else if ((x * y) <= 2e-88) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+47) {
		tmp = z * (-t / a);
	} else {
		tmp = t_1;
	}
	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):
	t_1 = y * (x / a)
	tmp = 0
	if (x * y) <= -5e-59:
		tmp = t_1
	elif (x * y) <= 2e-88:
		tmp = (z * -t) / a
	elif (x * y) <= 1e-15:
		tmp = (x * y) / a
	elif (x * y) <= 1e+47:
		tmp = z * (-t / a)
	else:
		tmp = t_1
	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(y * Float64(x / a))
	tmp = 0.0
	if (Float64(x * y) <= -5e-59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-88)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	elseif (Float64(x * y) <= 1e-15)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 1e+47)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = t_1;
	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)
	t_1 = y * (x / a);
	tmp = 0.0;
	if ((x * y) <= -5e-59)
		tmp = t_1;
	elseif ((x * y) <= 2e-88)
		tmp = (z * -t) / a;
	elseif ((x * y) <= 1e-15)
		tmp = (x * y) / a;
	elseif ((x * y) <= 1e+47)
		tmp = z * (-t / a);
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-88], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-15], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+47], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.0000000000000001e-59 or 1e47 < (*.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. clear-num 72.1%

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

      2. associate-/r* 79.5%

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

      3. associate-/r/ 79.5%

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

      4. clear-num 79.6%

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

   5. Applied egg-rr 79.6%

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

   if -5.0000000000000001e-59 < (*.f64 x y) < 1.99999999999999987e-88

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. associate-*r* 91.9%

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

      2. mul-1-neg 91.9%

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

   5. Simplified 91.9%

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

   if 1.99999999999999987e-88 < (*.f64 x y) < 1.0000000000000001e-15

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf 73.0%

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

   if 1.0000000000000001e-15 < (*.f64 x y) < 1e47

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*r/ 76.2%

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

      3. neg-mul-1 76.2%

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

      4. distribute-rgt-neg-in 76.2%

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

      5. distribute-frac-neg 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+232}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

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 2e+232)))
     (- (* x (/ y a)) (/ t (/ a z)))
     (/ 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 <= 2e+232)) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else {
		tmp = t_1 / a;
	}
	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 t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+232)) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else {
		tmp = t_1 / 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):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+232):
		tmp = (x * (y / a)) - (t / (a / z))
	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 <= 2e+232))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+232)))
		tmp = (x * (y / a)) - (t / (a / z));
	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.
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, 2e+232]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 2.00000000000000011e232 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 68.6%

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

      1. div-sub 62.8%

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

      2. associate-/l* 78.9%

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

      3. associate-/l* 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. associate-*r/ 78.9%

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

      2. add-sqr-sqrt 33.6%

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

      3. sqrt-unprod 60.9%

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

      4. sqr-neg 60.9%

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

      5. sqrt-unprod 31.8%

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

      6. add-sqr-sqrt 50.7%

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

      7. associate-*l/ 50.7%

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

      8. *-commutative 50.7%

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

      9. clear-num 50.7%

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

      10. un-div-inv 50.7%

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

      11. add-sqr-sqrt 31.8%

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

      12. sqrt-unprod 62.4%

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

      13. sqr-neg 62.4%

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

      14. sqrt-unprod 39.0%

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

      15. add-sqr-sqrt 89.7%

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

   6. Applied egg-rr 89.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000011e232

   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 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+232}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{z \cdot t}{x}\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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)) a)))
   (if (<= t_1 5e+294) t_1 (* (- y (/ (* z t) x)) (/ 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 t_1 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= 5e+294) {
		tmp = t_1;
	} else {
		tmp = (y - ((z * t) / x)) * (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) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) - (z * t)) / a
    if (t_1 <= 5d+294) then
        tmp = t_1
    else
        tmp = (y - ((z * t) / x)) * (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 t_1 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= 5e+294) {
		tmp = t_1;
	} else {
		tmp = (y - ((z * t) / x)) * (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):
	t_1 = ((x * y) - (z * t)) / a
	tmp = 0
	if t_1 <= 5e+294:
		tmp = t_1
	else:
		tmp = (y - ((z * t) / x)) * (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)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_1 <= 5e+294)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(Float64(z * t) / x)) * Float64(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)
	t_1 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_1 <= 5e+294)
		tmp = t_1;
	else
		tmp = (y - ((z * t) / x)) * (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_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+294], t$95$1, N[(N[(y - N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.0%

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

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

   1. Initial program 75.8%

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

      1. div-sub 71.1%

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

      2. associate-/l* 75.6%

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

      3. associate-/l* 88.8%

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

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in x around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. +-commutative 75.0%

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

      3. mul-1-neg 75.0%

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

      4. sub-neg 75.0%

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

      5. *-commutative 75.0%

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

      6. associate-/l/ 77.9%

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

      7. div-sub 80.2%

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

      8. associate-*l/ 73.8%

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

      9. associate-/l* 77.9%

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

      10. *-commutative 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 91.3%

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

Alternative 7: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) (- INFINITY))
   (/ x (/ a y))
   (if (<= (* x y) 2e+220) (/ (- (* x y) (* 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 ((x * y) <= -((double) INFINITY)) {
		tmp = x / (a / y);
	} else if ((x * y) <= 2e+220) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	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 ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = x / (a / y);
	} else if ((x * y) <= 2e+220) {
		tmp = ((x * y) - (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 (x * y) <= -math.inf:
		tmp = x / (a / y)
	elif (x * y) <= 2e+220:
		tmp = ((x * y) - (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(x * y) <= Float64(-Inf))
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 2e+220)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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])){:}
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) <= -Inf)
		tmp = x / (a / y);
	elseif ((x * y) <= 2e+220)
		tmp = ((x * y) - (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[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+220], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 63.0%

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

   3. Taylor expanded in x around inf 70.7%

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

      1. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -inf.0 < (*.f64 x y) < 2e220

   1. Initial program 95.4%

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

   if 2e220 < (*.f64 x y)

   1. Initial program 65.3%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. clear-num 65.3%

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

      2. associate-/r* 99.9%

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

      3. associate-/r/ 99.9%

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

      4. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= a 3.2e+105)
   (/ (- (* x y) (* z t)) a)
   (- (* x (/ y a)) (* z (/ t 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 (a <= 3.2e+105) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x * (y / a)) - (z * (t / 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 (a <= 3.2d+105) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = (x * (y / a)) - (z * (t / 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 (a <= 3.2e+105) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x * (y / a)) - (z * (t / 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 a <= 3.2e+105:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (x * (y / a)) - (z * (t / 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 (a <= 3.2e+105)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / 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 (a <= 3.2e+105)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (x * (y / 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.
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[a, 3.2e+105], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.2e105

   1. Initial program 92.4%

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

   if 3.2e105 < a

   1. Initial program 83.5%

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

      1. div-sub 83.5%

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

      2. associate-/l* 85.7%

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

      3. associate-/l* 87.7%

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

   4. Applied egg-rr 87.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.2% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 91.0%

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

3. Taylor expanded in x around inf 50.7%

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

   1. associate-*r/ 53.0%

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

5. Simplified 53.0%

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

6. Final simplification 53.0%

   \[\leadsto x \cdot \frac{y}{a} \]
7. Add Preprocessing

Alternative 10: 51.9% accurate, 1.8× speedup

Math

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

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 (* 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) {
	return y * (x / a);
}

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 = y * (x / a)
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 y * (x / a);
}

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 y * (x / a)

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(y * Float64(x / a))
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 = y * (x / a);
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[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

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

3. Taylor expanded in x around inf 50.7%

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

   1. clear-num 50.6%

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

   2. associate-/r* 54.2%

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

   3. associate-/r/ 54.5%

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

   4. clear-num 54.6%

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

5. Applied egg-rr 54.6%

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

6. Final simplification 54.6%

   \[\leadsto y \cdot \frac{x}{a} \]
7. Add Preprocessing

Alternative 11: 51.9% accurate, 1.8× speedup

Math

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

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 (/ 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) {
	return y / (a / x);
}

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 = y / (a / x)
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 y / (a / x);
}

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 y / (a / x)

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(y / Float64(a / x))
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 = y / (a / x);
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[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

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

3. Taylor expanded in x around inf 50.7%

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

   1. clear-num 50.6%

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

   2. associate-/r* 54.2%

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

   3. associate-/r/ 54.5%

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

   4. clear-num 54.6%

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

5. Applied egg-rr 54.6%

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

   1. *-commutative 54.6%

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

   2. clear-num 54.5%

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

   3. div-inv 54.2%

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

7. Applied egg-rr 54.2%

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

8. Final simplification 54.2%

   \[\leadsto \frac{y}{\frac{a}{x}} \]
9. Add Preprocessing

Developer target: 91.8% 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 2024055 
(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))