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

Percentage Accurate: 91.4% → 96.7%

Time: 8.6s

Alternatives: 9

Speedup: 0.6×

• 28.9% 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: 91.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+257}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 1e+257)))
     (- (* x (/ y a)) (* z (/ t a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+257)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} 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 <= 1e+257)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[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 <= 1e+257):
		tmp = (x * (y / a)) - (z * (t / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= 1e+257))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= 1e+257)))
		tmp = (x * (y / a)) - (z * (t / a));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 1e+257]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 1.00000000000000003e257 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 78.6%

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

      1. fma-def 78.6%

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

      2. associate-/l* 89.7%

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

      3. associate-*l/ 96.9%

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

   5. Simplified 96.9%

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

      1. fma-udef 96.9%

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

      2. associate-/r/ 96.9%

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

      3. +-commutative 96.9%

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

      4. clear-num 96.9%

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

      5. associate-/r/ 96.9%

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

      6. clear-num 96.9%

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

      7. associate-/r/ 96.9%

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

      8. neg-mul-1 96.9%

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

      9. sub-neg 96.9%

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

      10. clear-num 96.9%

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

      11. associate-/r/ 96.9%

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

      12. clear-num 96.9%

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

      13. *-commutative 96.9%

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

      14. div-inv 96.9%

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

      15. clear-num 96.9%

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

   7. Applied egg-rr 96.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000003e257

   1. Initial program 99.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+257}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.04:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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) -0.04)
   (/ y (/ a x))
   (if (<= (* x y) 2e+26) (/ (- t) (/ a z)) (/ (* 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) {
	double tmp;
	if ((x * y) <= -0.04) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+26) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / 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 ((x * y) <= (-0.04d0)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d+26) then
        tmp = -t / (a / z)
    else
        tmp = (x * y) / 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 ((x * y) <= -0.04) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+26) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / 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) <= -0.04:
		tmp = y / (a / x)
	elif (x * y) <= 2e+26:
		tmp = -t / (a / z)
	else:
		tmp = (x * y) / 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) <= -0.04)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(Float64(x * y) / 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) <= -0.04)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e+26)
		tmp = -t / (a / z);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -0.04], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.0400000000000000008

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 74.3%

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

      1. associate-*l/ 75.7%

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

   5. Simplified 75.7%

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

      1. associate-/r/ 78.1%

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

   7. Applied egg-rr 78.1%

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

   8. Taylor expanded in x around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 76.3%

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

   10. Simplified 76.3%

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

   if -0.0400000000000000008 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if 2.0000000000000001e26 < (*.f64 x y)

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 88.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.04:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.04:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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) -0.04)
   (/ y (/ a x))
   (if (<= (* x y) 2e+26) (* z (/ (- t) a)) (/ (* 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) {
	double tmp;
	if ((x * y) <= -0.04) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+26) {
		tmp = z * (-t / a);
	} else {
		tmp = (x * y) / 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 ((x * y) <= (-0.04d0)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d+26) then
        tmp = z * (-t / a)
    else
        tmp = (x * y) / 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 ((x * y) <= -0.04) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+26) {
		tmp = z * (-t / a);
	} else {
		tmp = (x * y) / 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) <= -0.04:
		tmp = y / (a / x)
	elif (x * y) <= 2e+26:
		tmp = z * (-t / a)
	else:
		tmp = (x * y) / 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) <= -0.04)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e+26)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(Float64(x * y) / 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) <= -0.04)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e+26)
		tmp = z * (-t / a);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -0.04], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+26], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.0400000000000000008

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 74.3%

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

      1. associate-*l/ 75.7%

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

   5. Simplified 75.7%

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

      1. associate-/r/ 78.1%

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

   7. Applied egg-rr 78.1%

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

   8. Taylor expanded in x around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 76.3%

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

   10. Simplified 76.3%

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

   if -0.0400000000000000008 < (*.f64 x y) < 2.0000000000000001e26

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 93.6%

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

      1. fma-def 93.6%

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

      2. associate-/l* 93.5%

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

      3. associate-*l/ 89.5%

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

   5. Simplified 89.5%

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

      1. fma-udef 89.5%

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

      2. associate-/r/ 92.6%

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

      3. +-commutative 92.6%

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

      4. clear-num 92.5%

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

      5. associate-/r/ 92.6%

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

      6. clear-num 92.6%

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

      7. associate-/r/ 90.3%

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

      8. neg-mul-1 90.3%

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

      9. sub-neg 90.3%

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

      10. clear-num 90.3%

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

      11. associate-/r/ 90.3%

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

      12. clear-num 90.7%

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

      13. *-commutative 90.7%

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

      14. div-inv 90.6%

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

      15. clear-num 91.2%

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

   7. Applied egg-rr 91.2%

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

      1. associate-*r/ 93.2%

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

      2. clear-num 93.0%

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

   9. Applied egg-rr 93.0%

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

   10. Taylor expanded in x around 0 74.6%

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

       1. mul-1-neg 74.6%

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

       2. associate-*l/ 72.7%

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

       3. *-commutative 72.7%

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

       4. distribute-rgt-neg-out 72.7%

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

       5. distribute-neg-frac 72.7%

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

   12. Simplified 72.7%

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

   if 2.0000000000000001e26 < (*.f64 x y)

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 88.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.04:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.04:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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) -0.04)
   (/ y (/ a x))
   (if (<= (* x y) 1e-5) (/ (* z (- t)) a) (/ (* 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) {
	double tmp;
	if ((x * y) <= -0.04) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1e-5) {
		tmp = (z * -t) / a;
	} else {
		tmp = (x * y) / 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 ((x * y) <= (-0.04d0)) then
        tmp = y / (a / x)
    else if ((x * y) <= 1d-5) then
        tmp = (z * -t) / a
    else
        tmp = (x * y) / 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 ((x * y) <= -0.04) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1e-5) {
		tmp = (z * -t) / a;
	} else {
		tmp = (x * y) / 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) <= -0.04:
		tmp = y / (a / x)
	elif (x * y) <= 1e-5:
		tmp = (z * -t) / a
	else:
		tmp = (x * y) / 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) <= -0.04)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 1e-5)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	else
		tmp = Float64(Float64(x * y) / 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) <= -0.04)
		tmp = y / (a / x);
	elseif ((x * y) <= 1e-5)
		tmp = (z * -t) / a;
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -0.04], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-5], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.0400000000000000008

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 74.3%

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

      1. associate-*l/ 75.7%

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

   5. Simplified 75.7%

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

      1. associate-/r/ 78.1%

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

   7. Applied egg-rr 78.1%

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

   8. Taylor expanded in x around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 76.3%

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

   10. Simplified 76.3%

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

   if -0.0400000000000000008 < (*.f64 x y) < 1.00000000000000008e-5

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-rgt-neg-in 76.6%

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

   5. Simplified 76.6%

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

   if 1.00000000000000008e-5 < (*.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 84.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.04:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.2% accurate, 0.6× speedup

Math

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

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 (<= (* z t) (- INFINITY)) (* z (/ (- t) a)) (/ (- (* x y) (* 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 ((z * t) <= -((double) INFINITY)) {
		tmp = z * (-t / a);
	} else {
		tmp = ((x * y) - (z * t)) / 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 ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (-t / a);
	} else {
		tmp = ((x * y) - (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 (z * t) <= -math.inf:
		tmp = z * (-t / a)
	else:
		tmp = ((x * y) - (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 (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * 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 ((z * t) <= -Inf)
		tmp = z * (-t / a);
	else
		tmp = ((x * y) - (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[N[(z * t), $MachinePrecision], (-Infinity)], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 36.7%

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

   3. Taylor expanded in x around 0 36.7%

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

      1. fma-def 36.7%

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

      2. associate-/l* 75.2%

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

      3. associate-*l/ 83.2%

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

   5. Simplified 83.2%

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

      1. fma-udef 83.2%

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

      2. associate-/r/ 83.2%

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

      3. +-commutative 83.2%

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

      4. clear-num 83.2%

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

      5. associate-/r/ 83.1%

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

      6. clear-num 83.3%

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

      7. associate-/r/ 83.2%

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

      8. neg-mul-1 83.2%

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

      9. sub-neg 83.2%

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

      10. clear-num 83.2%

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

      11. associate-/r/ 83.2%

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

      12. clear-num 83.2%

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

      13. *-commutative 83.2%

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

      14. div-inv 83.1%

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

      15. clear-num 83.2%

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

   7. Applied egg-rr 83.2%

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

      1. associate-*r/ 36.7%

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

      2. clear-num 36.7%

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

   9. Applied egg-rr 36.7%

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

   10. Taylor expanded in x around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-*l/ 83.8%

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

       3. *-commutative 83.8%

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

       4. distribute-rgt-neg-out 83.8%

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

       5. distribute-neg-frac 83.8%

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

   12. Simplified 83.8%

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

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

   1. Initial program 96.6%

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

4. Final simplification 96.0%

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

Alternative 6: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 (<= y 1.18e+128) (* y (/ x a)) (* 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) {
	double tmp;
	if (y <= 1.18e+128) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / 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 (y <= 1.18d+128) then
        tmp = y * (x / a)
    else
        tmp = x * (y / 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 (y <= 1.18e+128) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / 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 y <= 1.18e+128:
		tmp = y * (x / a)
	else:
		tmp = x * (y / 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 (y <= 1.18e+128)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x * Float64(y / 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 (y <= 1.18e+128)
		tmp = y * (x / a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.18e+128], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.18000000000000009e128

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 54.0%

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

      1. associate-*l/ 54.6%

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

   5. Simplified 54.6%

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

   if 1.18000000000000009e128 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf 88.7%

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

      1. associate-*r/ 91.4%

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

      2. *-commutative 91.4%

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

   5. Applied egg-rr 91.4%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 (<= y 8.8e+129) (/ y (/ a x)) (* 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) {
	double tmp;
	if (y <= 8.8e+129) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / 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 (y <= 8.8d+129) then
        tmp = y / (a / x)
    else
        tmp = x * (y / 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 (y <= 8.8e+129) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / 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 y <= 8.8e+129:
		tmp = y / (a / x)
	else:
		tmp = x * (y / 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 (y <= 8.8e+129)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(x * Float64(y / 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 (y <= 8.8e+129)
		tmp = y / (a / x);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 8.8e+129], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.7999999999999997e129

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 54.0%

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

      1. associate-*l/ 54.6%

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

   5. Simplified 54.6%

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

      1. associate-/r/ 53.7%

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

   7. Applied egg-rr 53.7%

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

   8. Taylor expanded in x around 0 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 54.8%

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

   10. Simplified 54.8%

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

   if 8.7999999999999997e129 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf 88.7%

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

      1. associate-*r/ 91.4%

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

      2. *-commutative 91.4%

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

   5. Applied egg-rr 91.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 -6.5e-220) (/ y (/ a x)) (/ (* 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) {
	double tmp;
	if (x <= -6.5e-220) {
		tmp = y / (a / x);
	} else {
		tmp = (x * y) / 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 (x <= (-6.5d-220)) then
        tmp = y / (a / x)
    else
        tmp = (x * y) / 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 (x <= -6.5e-220) {
		tmp = y / (a / x);
	} else {
		tmp = (x * y) / 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 <= -6.5e-220:
		tmp = y / (a / x)
	else:
		tmp = (x * y) / 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 (x <= -6.5e-220)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(Float64(x * y) / 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 <= -6.5e-220)
		tmp = y / (a / x);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[x, -6.5e-220], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000005e-220

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. associate-*l/ 67.0%

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

   5. Simplified 67.0%

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

      1. associate-/r/ 63.3%

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

   7. Applied egg-rr 63.3%

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

   8. Taylor expanded in x around 0 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-/l* 67.5%

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

   10. Simplified 67.5%

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

   if -6.50000000000000005e-220 < x

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 55.6%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.8% 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 93.8%

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

3. Taylor expanded in x around inf 59.3%

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

   1. associate-*l/ 58.7%

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

5. Simplified 58.7%

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

6. Final simplification 58.7%

   \[\leadsto y \cdot \frac{x}{a} \]
7. 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 2024020 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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