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

Percentage Accurate: 91.5% → 95.0%

Time: 16.0s

Alternatives: 6

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: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+247} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+198}\right):\\ \;\;\;\;\left(\frac{x \cdot y}{t} - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* z t) -5e+247) (not (<= (* z t) 5e+198)))
   (* (- (/ (* x y) t) z) (/ t a))
   (/ (- (* x y) (* z t)) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -5e+247) || !((z * t) <= 5e+198)) {
		tmp = (((x * y) / t) - z) * (t / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z * t) <= (-5d+247)) .or. (.not. ((z * t) <= 5d+198))) then
        tmp = (((x * y) / t) - z) * (t / a)
    else
        tmp = ((x * y) - (z * t)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -5e+247) || !((z * t) <= 5e+198)) {
		tmp = (((x * y) / t) - z) * (t / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * t) <= -5e+247) or not ((z * t) <= 5e+198):
		tmp = (((x * y) / t) - z) * (t / a)
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+247) || !(Float64(z * t) <= 5e+198))
		tmp = Float64(Float64(Float64(Float64(x * y) / t) - z) * 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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z * t) <= -5e+247) || ~(((z * t) <= 5e+198)))
		tmp = (((x * y) / t) - 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.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+247], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+198]], $MachinePrecision]], N[(N[(N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision] - z), $MachinePrecision] * 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) < -5.00000000000000023e247 or 5.00000000000000049e198 < (*.f64 z t)

   1. Initial program 72.1%

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

   3. Taylor expanded in t around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 74.0%

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

   5. Simplified 74.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      7. /-lowering-/.f64 96.1%

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

   7. Applied egg-rr 96.1%

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

   if -5.00000000000000023e247 < (*.f64 z t) < 5.00000000000000049e198

   1. Initial program 96.1%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+247} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+198}\right):\\ \;\;\;\;\left(\frac{x \cdot y}{t} - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(0 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+223}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* t (- 0.0 (/ z a)))
   (if (<= (* z t) 2e+223) (/ (- (* x y) (* z t)) a) (- 0.0 (/ z (/ a t))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = t * (0.0 - (z / a));
	} else if ((z * t) <= 2e+223) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = 0.0 - (z / (a / t));
	}
	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 ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = t * (0.0 - (z / a));
	} else if ((z * t) <= 2e+223) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = 0.0 - (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = t * (0.0 - (z / a))
	elif (z * t) <= 2e+223:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = 0.0 - (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(t * Float64(0.0 - Float64(z / a)));
	elseif (Float64(z * t) <= 2e+223)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(0.0 - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = t * (0.0 - (z / a));
	elseif ((z * t) <= 2e+223)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = 0.0 - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(t * N[(0.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+223], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.0 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 72.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 72.4%

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

   4. Applied egg-rr 72.4%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. neg-mul-1 N/A

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

      4. associate-/r* N/A

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

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

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

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

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

      7. *-lowering-*.f64 72.4%

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

   7. Simplified 72.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. metadata-eval N/A

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

      5. times-frac N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. /-rgt-identity N/A

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

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

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

      11. *-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. neg-sub0 N/A

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

      15. --lowering--.f64 100.0%

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

   9. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{z}{0 - a} \cdot t} \]
   10. Step-by-step derivation

       1. sub0-neg N/A

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

       2. neg-lowering-neg.f64 100.0%

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

   11. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 z t) < 2.00000000000000009e223

   1. Initial program 95.8%

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

   if 2.00000000000000009e223 < (*.f64 z t)

   1. Initial program 62.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 62.8%

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

   4. Applied egg-rr 62.8%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. neg-mul-1 N/A

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

      4. associate-/r* N/A

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

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

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

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

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

      7. *-lowering-*.f64 62.8%

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

   7. Simplified 62.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-neg-frac2 N/A

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

      5. associate-/l* N/A

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. distribute-neg-frac N/A

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

      9. /-lowering-/.f64 N/A

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

      10. neg-sub0 N/A

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

      11. --lowering--.f64 N/A

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

      12. /-lowering-/.f64 95.4%

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

   9. Applied egg-rr 95.4%

      \[\leadsto \color{blue}{\frac{0 - z}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(0 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+223}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10:\\ \;\;\;\;\frac{0 - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e-24)
   (* y (/ x a))
   (if (<= (* x y) 10.0) (/ (- 0.0 (* z t)) a) (* x (/ y a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-24) {
		tmp = y * (x / a);
	} else if ((x * y) <= 10.0) {
		tmp = (0.0 - (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.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d-24)) then
        tmp = y * (x / a)
    else if ((x * y) <= 10.0d0) then
        tmp = (0.0d0 - (z * t)) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-24) {
		tmp = y * (x / a);
	} else if ((x * y) <= 10.0) {
		tmp = (0.0 - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e-24:
		tmp = y * (x / a)
	elif (x * y) <= 10.0:
		tmp = (0.0 - (z * t)) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e-24)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 10.0)
		tmp = Float64(Float64(0.0 - Float64(z * t)) / 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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e-24)
		tmp = y * (x / a);
	elseif ((x * y) <= 10.0)
		tmp = (0.0 - (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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-24], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 10.0], N[(N[(0.0 - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999924e-25

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 68.7%

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

   5. Simplified 68.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 70.1%

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

   7. Applied egg-rr 70.1%

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

   if -9.99999999999999924e-25 < (*.f64 x y) < 10

   1. Initial program 92.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 92.4%

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

   4. Applied egg-rr 92.4%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. neg-mul-1 N/A

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

      4. associate-/r* N/A

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

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

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

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

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

      7. *-lowering-*.f64 79.1%

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

   7. Simplified 79.1%

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

      1. frac-2neg N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. /-rgt-identity N/A

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

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

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

      6. *-lowering-*.f64 79.1%

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

   9. Applied egg-rr 79.1%

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

   if 10 < (*.f64 x y)

   1. Initial program 91.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 75.2%

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

   5. Simplified 75.2%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   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 75.1%

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

   7. Applied egg-rr 75.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10:\\ \;\;\;\;\frac{0 - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;0 - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) -1e-24)
   (* y (/ x a))
   (if (<= (* x y) 2e+144) (- 0.0 (/ t (/ a z))) (/ 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) <= -1e-24) {
		tmp = y * (x / a);
	} else if ((x * y) <= 2e+144) {
		tmp = 0.0 - (t / (a / z));
	} 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) <= (-1d-24)) then
        tmp = y * (x / a)
    else if ((x * y) <= 2d+144) then
        tmp = 0.0d0 - (t / (a / z))
    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) <= -1e-24) {
		tmp = y * (x / a);
	} else if ((x * y) <= 2e+144) {
		tmp = 0.0 - (t / (a / z));
	} 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) <= -1e-24:
		tmp = y * (x / a)
	elif (x * y) <= 2e+144:
		tmp = 0.0 - (t / (a / z))
	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) <= -1e-24)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 2e+144)
		tmp = Float64(0.0 - Float64(t / Float64(a / z)));
	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) <= -1e-24)
		tmp = y * (x / a);
	elseif ((x * y) <= 2e+144)
		tmp = 0.0 - (t / (a / z));
	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], -1e-24], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+144], N[(0.0 - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999924e-25

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 68.7%

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

   5. Simplified 68.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 70.1%

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

   7. Applied egg-rr 70.1%

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

   if -9.99999999999999924e-25 < (*.f64 x y) < 2.00000000000000005e144

   1. Initial program 92.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 92.1%

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. neg-mul-1 N/A

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

      4. associate-/r* N/A

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

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

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

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

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

      7. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. metadata-eval N/A

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

      5. times-frac N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. /-rgt-identity N/A

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

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

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

      11. *-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. neg-sub0 N/A

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

      15. --lowering--.f64 74.8%

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

   9. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{\frac{z}{0 - a} \cdot t} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto t \cdot \color{blue}{\frac{z}{0 - a}} \]

       2. clear-num N/A

          \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{0 - a}{z}}} \]

       3. un-div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{\frac{0 - a}{z}}} \]

       4. sub0-neg N/A

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

       5. distribute-frac-neg N/A

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

       6. distribute-frac-neg2 N/A

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

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

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

       8. /-lowering-/.f64 N/A

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

       9. /-lowering-/.f64 75.0%

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

   11. Applied egg-rr 75.0%

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

   if 2.00000000000000005e144 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 89.4%

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

   5. Simplified 89.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 89.6%

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

   7. Applied egg-rr 89.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 89.7%

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

   9. Applied egg-rr 89.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;0 - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.1% 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 91.3%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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 48.0%

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

5. Simplified 48.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

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

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

   4. /-lowering-/.f64 47.4%

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

7. Applied egg-rr 47.4%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

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

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

   4. /-lowering-/.f64 47.3%

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

9. Applied egg-rr 47.3%

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

Alternative 6: 51.1% 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 91.3%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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 48.0%

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

5. Simplified 48.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

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

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

   4. /-lowering-/.f64 47.4%

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

7. Applied egg-rr 47.4%

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

Developer Target 1: 91.3% 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 2024125 
(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))