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

Percentage Accurate: 91.5% → 96.3%

Time: 11.0s

Alternatives: 8

Speedup: 0.4×

• 28.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.5% 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: 96.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{\frac{x}{\frac{z}{y}} - t}}\\ t_2 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ a (- (/ x (/ z y)) t)))) (t_2 (/ (- (* x y) (* z t)) a)))
   (if (<= t_2 -2e+301)
     t_1
     (if (<= t_2 2e+295) (- (/ (* x y) a) (/ (* z t) a)) t_1))))

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 = z / (a / ((x / (z / y)) - t));
	double t_2 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_2 <= -2e+301) {
		tmp = t_1;
	} else if (t_2 <= 2e+295) {
		tmp = ((x * y) / a) - ((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.
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 / (a / ((x / (z / y)) - t))
    t_2 = ((x * y) - (z * t)) / a
    if (t_2 <= (-2d+301)) then
        tmp = t_1
    else if (t_2 <= 2d+295) then
        tmp = ((x * y) / a) - ((z * t) / a)
    else
        tmp = t_1
    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 = z / (a / ((x / (z / y)) - t));
	double t_2 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_2 <= -2e+301) {
		tmp = t_1;
	} else if (t_2 <= 2e+295) {
		tmp = ((x * y) / a) - ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = z / (a / ((x / (z / y)) - t))
	t_2 = ((x * y) - (z * t)) / a
	tmp = 0
	if t_2 <= -2e+301:
		tmp = t_1
	elif t_2 <= 2e+295:
		tmp = ((x * y) / a) - ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a / Float64(Float64(x / Float64(z / y)) - t)))
	t_2 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_2 <= -2e+301)
		tmp = t_1;
	elseif (t_2 <= 2e+295)
		tmp = Float64(Float64(Float64(x * y) / a) - Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	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 = z / (a / ((x / (z / y)) - t));
	t_2 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_2 <= -2e+301)
		tmp = t_1;
	elseif (t_2 <= 2e+295)
		tmp = ((x * y) / a) - ((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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a / N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+301], t$95$1, If[LessEqual[t$95$2, 2e+295], N[(N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -2.00000000000000011e301 or 2e295 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(\frac{x \cdot y}{z} - t\right)\right)}, a\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{x \cdot y}{z} - t\right)\right), a\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), t\right)\right), a\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), t\right)\right), a\right) \]

      4. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right)\right), a\right) \]

   5. Simplified 79.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{x \cdot y}{z} - t}{a}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot y}{z} - t\right), a\right), z\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), t\right), a\right), z\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), t\right), a\right), z\right) \]

      7. *-lowering-*.f64 85.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right), a\right), z\right) \]

   7. Applied egg-rr 85.6%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{a}{\frac{x \cdot y}{z} - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{x \cdot y}{z} - t\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{t}\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot \frac{y}{z}\right), t\right)\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot \frac{1}{\frac{z}{y}}\right), t\right)\right)\right) \]

      9. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(\left(\frac{x}{\frac{z}{y}}\right), t\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{z}{y}\right)\right), t\right)\right)\right) \]

      11. /-lowering-/.f64 91.9%

          \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), t\right)\right)\right) \]

   9. Applied egg-rr 91.9%

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

   if -2.00000000000000011e301 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 2e295

   1. Initial program 99.1%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a}\right), \color{blue}{\left(\frac{z \cdot t}{a}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), a\right), \left(\frac{\color{blue}{z \cdot t}}{a}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), \left(\frac{\color{blue}{z} \cdot t}{a}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), \mathsf{/.f64}\left(\left(z \cdot t\right), \color{blue}{a}\right)\right) \]

      6. *-lowering-*.f64 99.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), a\right)\right) \]

   4. Applied egg-rr 99.1%

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

Alternative 2: 96.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{x}{\frac{z}{y}} - t\right) \cdot \frac{z}{a}\\ t_2 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- (/ x (/ z y)) t) (/ z a))) (t_2 (/ (- (* x y) (* z t)) a)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e+295) (- (/ (* x y) a) (/ (* z t) a)) t_1))))

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 / (z / y)) - t) * (z / a);
	double t_2 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+295) {
		tmp = ((x * y) / a) - ((z * t) / a);
	} else {
		tmp = t_1;
	}
	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 / (z / y)) - t) * (z / a);
	double t_2 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+295) {
		tmp = ((x * y) / a) - ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = ((x / (z / y)) - t) * (z / a)
	t_2 = ((x * y) - (z * t)) / a
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+295:
		tmp = ((x * y) / a) - ((z * t) / a)
	else:
		tmp = t_1
	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(Float64(x / Float64(z / y)) - t) * Float64(z / a))
	t_2 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+295)
		tmp = Float64(Float64(Float64(x * y) / a) - Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	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 / (z / y)) - t) * (z / a);
	t_2 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+295)
		tmp = ((x * y) / a) - ((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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+295], N[(N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -inf.0 or 2e295 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(\frac{x \cdot y}{z} - t\right)\right)}, a\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{x \cdot y}{z} - t\right)\right), a\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), t\right)\right), a\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), t\right)\right), a\right) \]

      4. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right)\right), a\right) \]

   5. Simplified 79.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot y}{z} - t\right), \color{blue}{\left(\frac{z}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), t\right), \left(\frac{\color{blue}{z}}{a}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), t\right), \left(\frac{z}{a}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right), \left(\frac{z}{a}\right)\right) \]

      7. /-lowering-/.f64 84.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right), \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 84.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \frac{y}{z}\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \frac{1}{\frac{z}{y}}\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{x}{\frac{z}{y}}\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{z}{y}\right)\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      5. /-lowering-/.f64 90.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

   9. Applied egg-rr 90.7%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 2e295

   1. Initial program 99.1%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a}\right), \color{blue}{\left(\frac{z \cdot t}{a}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), a\right), \left(\frac{\color{blue}{z \cdot t}}{a}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), \left(\frac{\color{blue}{z} \cdot t}{a}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), \mathsf{/.f64}\left(\left(z \cdot t\right), \color{blue}{a}\right)\right) \]

      6. *-lowering-*.f64 99.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), a\right)\right) \]

   4. Applied egg-rr 99.1%

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

Alternative 3: 96.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{x}{\frac{z}{y}} - t\right) \cdot \frac{z}{a}\\ t_2 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- (/ x (/ z y)) t) (/ z a))) (t_2 (/ (- (* x y) (* z t)) a)))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 2e+295) t_2 t_1))))

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 / (z / y)) - t) * (z / a);
	double t_2 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+295) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 / (z / y)) - t) * (z / a);
	double t_2 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+295) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = ((x / (z / y)) - t) * (z / a)
	t_2 = ((x * y) - (z * t)) / a
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+295:
		tmp = t_2
	else:
		tmp = t_1
	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(Float64(x / Float64(z / y)) - t) * Float64(z / a))
	t_2 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+295)
		tmp = t_2;
	else
		tmp = t_1;
	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 / (z / y)) - t) * (z / a);
	t_2 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+295)
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+295], t$95$2, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -inf.0 or 2e295 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(\frac{x \cdot y}{z} - t\right)\right)}, a\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{x \cdot y}{z} - t\right)\right), a\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), t\right)\right), a\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), t\right)\right), a\right) \]

      4. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right)\right), a\right) \]

   5. Simplified 79.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot y}{z} - t\right), \color{blue}{\left(\frac{z}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{x \cdot y}{z}\right), t\right), \left(\frac{\color{blue}{z}}{a}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), t\right), \left(\frac{z}{a}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right), \left(\frac{z}{a}\right)\right) \]

      7. /-lowering-/.f64 84.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), t\right), \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 84.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \frac{y}{z}\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \frac{1}{\frac{z}{y}}\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{x}{\frac{z}{y}}\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{z}{y}\right)\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

      5. /-lowering-/.f64 90.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), t\right), \mathsf{/.f64}\left(z, a\right)\right) \]

   9. Applied egg-rr 90.7%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 2e295

   1. Initial program 99.1%

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

Alternative 4: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+263}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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) (- INFINITY))
   (* x (/ y a))
   (if (<= (* x y) 1e+263) (/ (- (* x y) (* z t)) a) (/ x (/ a y)))))

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) <= -((double) INFINITY)) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e+263) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x / (a / y);
	}
	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 tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e+263) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x / (a / y);
	}
	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) <= -math.inf:
		tmp = x * (y / a)
	elif (x * y) <= 1e+263:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x / (a / y)
	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) <= Float64(-Inf))
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 1e+263)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x / Float64(a / y));
	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) <= -Inf)
		tmp = x * (y / a);
	elseif ((x * y) <= 1e+263)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+263], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.0%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 71.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 71.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 94.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), x\right) \]

   7. Applied egg-rr 94.0%

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

   if -inf.0 < (*.f64 x y) < 1.00000000000000002e263

   1. Initial program 96.2%

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

   if 1.00000000000000002e263 < (*.f64 x y)

   1. Initial program 59.3%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 63.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 63.1%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. associate-/r/ N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{a}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 88.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   7. Applied egg-rr 88.6%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{a}{y}\right)}\right) \]

      6. /-lowering-/.f64 91.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 91.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+263}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-41}:\\ \;\;\;\;\frac{z \cdot t}{0 - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) -5e-48)
   (* y (/ x a))
   (if (<= (* x y) 4e-41) (/ (* z t) (- 0.0 a)) (/ y (/ a x)))))

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) <= -5e-48) {
		tmp = y * (x / a);
	} else if ((x * y) <= 4e-41) {
		tmp = (z * t) / (0.0 - a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-5d-48)) then
        tmp = y * (x / a)
    else if ((x * y) <= 4d-41) then
        tmp = (z * t) / (0.0d0 - a)
    else
        tmp = y / (a / x)
    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) <= -5e-48) {
		tmp = y * (x / a);
	} else if ((x * y) <= 4e-41) {
		tmp = (z * t) / (0.0 - a);
	} else {
		tmp = y / (a / x);
	}
	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) <= -5e-48:
		tmp = y * (x / a)
	elif (x * y) <= 4e-41:
		tmp = (z * t) / (0.0 - a)
	else:
		tmp = y / (a / x)
	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) <= -5e-48)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 4e-41)
		tmp = Float64(Float64(z * t) / Float64(0.0 - a));
	else
		tmp = Float64(y / Float64(a / x));
	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) <= -5e-48)
		tmp = y * (x / a);
	elseif ((x * y) <= 4e-41)
		tmp = (z * t) / (0.0 - a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e-48], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-41], N[(N[(z * t), $MachinePrecision] / N[(0.0 - a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999999e-48

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 69.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 69.8%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. associate-/r/ N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{a}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 73.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   7. Applied egg-rr 73.8%

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

   if -4.9999999999999999e-48 < (*.f64 x y) < 4.00000000000000002e-41

   1. Initial program 95.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a}\right), \color{blue}{\left(x \cdot y - z \cdot t\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\color{blue}{x \cdot y} - z \cdot t\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot t\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z} \cdot t\right)\right)\right) \]

      7. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\mathsf{neg}\left(t \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(t \cdot \left(-1 \cdot \color{blue}{z}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \left(0 - \color{blue}{z}\right)\right)\right) \]

      7. --lowering--.f64 88.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(0, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 88.4%

      \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(t \cdot \left(0 - z\right)\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-neg-out N/A

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

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(\frac{1}{a} \cdot t\right) \cdot z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{a} \cdot t\right), z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(t \cdot \frac{1}{a}\right), z\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(\frac{t}{a}\right), z\right)\right) \]

      8. /-lowering-/.f64 87.7%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), z\right)\right) \]

   9. Applied egg-rr 87.7%

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

       1. associate-*l/ N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{t \cdot z}{a}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(t \cdot z\right), a\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), a\right)\right) \]

       4. *-lowering-*.f64 88.5%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), a\right)\right) \]

   11. Applied egg-rr 88.5%

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

   if 4.00000000000000002e-41 < (*.f64 x y)

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 70.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 70.4%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{x}\right)}\right) \]

      5. /-lowering-/.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 80.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-41}:\\ \;\;\;\;\frac{z \cdot t}{0 - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-41}:\\ \;\;\;\;0 - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) -5e-48)
   (* y (/ x a))
   (if (<= (* x y) 4e-41) (- 0.0 (* z (/ t a))) (/ y (/ a x)))))

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) <= -5e-48) {
		tmp = y * (x / a);
	} else if ((x * y) <= 4e-41) {
		tmp = 0.0 - (z * (t / a));
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-5d-48)) then
        tmp = y * (x / a)
    else if ((x * y) <= 4d-41) then
        tmp = 0.0d0 - (z * (t / a))
    else
        tmp = y / (a / x)
    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) <= -5e-48) {
		tmp = y * (x / a);
	} else if ((x * y) <= 4e-41) {
		tmp = 0.0 - (z * (t / a));
	} else {
		tmp = y / (a / x);
	}
	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) <= -5e-48:
		tmp = y * (x / a)
	elif (x * y) <= 4e-41:
		tmp = 0.0 - (z * (t / a))
	else:
		tmp = y / (a / x)
	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) <= -5e-48)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 4e-41)
		tmp = Float64(0.0 - Float64(z * Float64(t / a)));
	else
		tmp = Float64(y / Float64(a / x));
	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) <= -5e-48)
		tmp = y * (x / a);
	elseif ((x * y) <= 4e-41)
		tmp = 0.0 - (z * (t / a));
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e-48], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-41], N[(0.0 - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999999e-48

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 69.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 69.8%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. associate-/r/ N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{a}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 73.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   7. Applied egg-rr 73.8%

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

   if -4.9999999999999999e-48 < (*.f64 x y) < 4.00000000000000002e-41

   1. Initial program 95.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a}\right), \color{blue}{\left(x \cdot y - z \cdot t\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\color{blue}{x \cdot y} - z \cdot t\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot t\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z} \cdot t\right)\right)\right) \]

      7. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\mathsf{neg}\left(t \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(t \cdot \left(-1 \cdot \color{blue}{z}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \left(0 - \color{blue}{z}\right)\right)\right) \]

      7. --lowering--.f64 88.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(0, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 88.4%

      \[\leadsto \frac{1}{a} \cdot \color{blue}{\left(t \cdot \left(0 - z\right)\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-neg-out N/A

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

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(\frac{1}{a} \cdot t\right) \cdot z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{a} \cdot t\right), z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(t \cdot \frac{1}{a}\right), z\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(\frac{t}{a}\right), z\right)\right) \]

      8. /-lowering-/.f64 87.7%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), z\right)\right) \]

   9. Applied egg-rr 87.7%

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

   if 4.00000000000000002e-41 < (*.f64 x y)

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 70.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 70.4%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{x}\right)}\right) \]

      5. /-lowering-/.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 80.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-41}:\\ \;\;\;\;0 - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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.
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;
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])
def code(x, y, z, t, a):
	return y / (a / x)

Julia

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])){:}
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.
code[x_, y_, z_, t_, a_] := N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in x around inf

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

   2. *-lowering-*.f64 49.7%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

5. Simplified 49.7%

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

   1. clear-num N/A

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

   2. associate-/r* N/A

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

   3. clear-num N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{x}\right)}\right) \]

   5. /-lowering-/.f64 53.7%

      \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{x}\right)\right) \]

7. Applied egg-rr 53.7%

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

Alternative 8: 51.5% accurate, 1.8× speedup

Math

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

FPCore

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

Python

[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])
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])){:}
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.
code[x_, y_, z_, t_, a_] := N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in x around inf

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

   2. *-lowering-*.f64 49.7%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

5. Simplified 49.7%

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

   1. clear-num N/A

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

   2. associate-/r* N/A

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

   3. associate-/r/ N/A

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

   4. clear-num N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{a}\right), \color{blue}{y}\right) \]

   6. /-lowering-/.f64 53.4%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

7. Applied egg-rr 53.4%

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

8. Final simplification 53.4%

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

Developer Target 1: 91.6% 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 2024155 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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