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

Percentage Accurate: 91.8% → 93.6%

Time: 11.5s

Alternatives: 8

Speedup: 0.6×

• 29.2% 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: 91.8% 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: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a\_m}{\frac{x \cdot y}{z} - t}}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z t)) a_m)))
   (* a_s (if (<= t_1 2e+296) t_1 (/ z (/ a_m (- (/ (* x y) z) t)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((x * y) - (z * t)) / a_m;
	double tmp;
	if (t_1 <= 2e+296) {
		tmp = t_1;
	} else {
		tmp = z / (a_m / (((x * y) / z) - t));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) - (z * t)) / a_m
    if (t_1 <= 2d+296) then
        tmp = t_1
    else
        tmp = z / (a_m / (((x * y) / z) - t))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((x * y) - (z * t)) / a_m;
	double tmp;
	if (t_1 <= 2e+296) {
		tmp = t_1;
	} else {
		tmp = z / (a_m / (((x * y) / z) - t));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = ((x * y) - (z * t)) / a_m
	tmp = 0
	if t_1 <= 2e+296:
		tmp = t_1
	else:
		tmp = z / (a_m / (((x * y) / z) - t))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m)
	tmp = 0.0
	if (t_1 <= 2e+296)
		tmp = t_1;
	else
		tmp = Float64(z / Float64(a_m / Float64(Float64(Float64(x * y) / z) - t)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = ((x * y) - (z * t)) / a_m;
	tmp = 0.0;
	if (t_1 <= 2e+296)
		tmp = t_1;
	else
		tmp = z / (a_m / (((x * y) / z) - t));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, 2e+296], t$95$1, N[(z / N[(a$95$m / N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 1.99999999999999996e296

   1. Initial program 97.0%

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

   if 1.99999999999999996e296 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 74.2%

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

   5. Simplified 74.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

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

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

      7. *-lowering-*.f64 82.3%

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

   7. Applied egg-rr 82.3%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 82.4%

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

   9. Applied egg-rr 82.4%

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

Alternative 2: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} - t\right) \cdot \frac{z}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z t)) a_m)))
   (* a_s (if (<= t_1 2e+288) t_1 (* (- (/ (* x y) z) t) (/ z a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((x * y) - (z * t)) / a_m;
	double tmp;
	if (t_1 <= 2e+288) {
		tmp = t_1;
	} else {
		tmp = (((x * y) / z) - t) * (z / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) - (z * t)) / a_m
    if (t_1 <= 2d+288) then
        tmp = t_1
    else
        tmp = (((x * y) / z) - t) * (z / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((x * y) - (z * t)) / a_m;
	double tmp;
	if (t_1 <= 2e+288) {
		tmp = t_1;
	} else {
		tmp = (((x * y) / z) - t) * (z / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = ((x * y) - (z * t)) / a_m
	tmp = 0
	if t_1 <= 2e+288:
		tmp = t_1
	else:
		tmp = (((x * y) / z) - t) * (z / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m)
	tmp = 0.0
	if (t_1 <= 2e+288)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(x * y) / z) - t) * Float64(z / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = ((x * y) - (z * t)) / a_m;
	tmp = 0.0;
	if (t_1 <= 2e+288)
		tmp = t_1;
	else
		tmp = (((x * y) / z) - t) * (z / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, 2e+288], t$95$1, N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] - t), $MachinePrecision] * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 2e288

   1. Initial program 97.0%

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

   if 2e288 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 74.2%

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

   5. Simplified 74.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      7. /-lowering-/.f64 84.3%

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

   7. Applied egg-rr 84.3%

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

Alternative 3: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-68}:\\ \;\;\;\;\frac{z}{a\_m} \cdot \left(0 - t\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z \cdot t}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* z t) -1e-68)
    (* (/ z a_m) (- 0.0 t))
    (if (<= (* z t) 5e-35) (/ (* x y) a_m) (- 0.0 (/ (* z t) a_m))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= -1e-68) {
		tmp = (z / a_m) * (0.0 - t);
	} else if ((z * t) <= 5e-35) {
		tmp = (x * y) / a_m;
	} else {
		tmp = 0.0 - ((z * t) / a_m);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((z * t) <= (-1d-68)) then
        tmp = (z / a_m) * (0.0d0 - t)
    else if ((z * t) <= 5d-35) then
        tmp = (x * y) / a_m
    else
        tmp = 0.0d0 - ((z * t) / a_m)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= -1e-68) {
		tmp = (z / a_m) * (0.0 - t);
	} else if ((z * t) <= 5e-35) {
		tmp = (x * y) / a_m;
	} else {
		tmp = 0.0 - ((z * t) / a_m);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (z * t) <= -1e-68:
		tmp = (z / a_m) * (0.0 - t)
	elif (z * t) <= 5e-35:
		tmp = (x * y) / a_m
	else:
		tmp = 0.0 - ((z * t) / a_m)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(z * t) <= -1e-68)
		tmp = Float64(Float64(z / a_m) * Float64(0.0 - t));
	elseif (Float64(z * t) <= 5e-35)
		tmp = Float64(Float64(x * y) / a_m);
	else
		tmp = Float64(0.0 - Float64(Float64(z * t) / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((z * t) <= -1e-68)
		tmp = (z / a_m) * (0.0 - t);
	elseif ((z * t) <= 5e-35)
		tmp = (x * y) / a_m;
	else
		tmp = 0.0 - ((z * t) / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(z * t), $MachinePrecision], -1e-68], N[(N[(z / a$95$m), $MachinePrecision] * N[(0.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-35], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], N[(0.0 - N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000007e-68

   1. Initial program 86.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 61.2%

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

   7. Simplified 61.2%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. *-lowering-*.f64 61.2%

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

   9. Applied egg-rr 61.2%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 63.0%

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

   11. Applied egg-rr 63.0%

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

   if -1.00000000000000007e-68 < (*.f64 z t) < 4.99999999999999964e-35

   1. Initial program 97.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 88.3%

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

   5. Simplified 88.3%

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

   if 4.99999999999999964e-35 < (*.f64 z t)

   1. Initial program 90.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 80.8%

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

   7. Simplified 80.8%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. *-lowering-*.f64 80.8%

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

   9. Applied egg-rr 80.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-68}:\\ \;\;\;\;\frac{z}{a} \cdot \left(0 - t\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{z}{a\_m} \cdot \left(0 - t\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (/ z a_m) (- 0.0 t))))
   (* a_s (if (<= z -3.4e+107) t_1 (if (<= z 1.6e-145) (/ (* x y) a_m) t_1)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (z / a_m) * (0.0 - t);
	double tmp;
	if (z <= -3.4e+107) {
		tmp = t_1;
	} else if (z <= 1.6e-145) {
		tmp = (x * y) / a_m;
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / a_m) * (0.0d0 - t)
    if (z <= (-3.4d+107)) then
        tmp = t_1
    else if (z <= 1.6d-145) then
        tmp = (x * y) / a_m
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (z / a_m) * (0.0 - t);
	double tmp;
	if (z <= -3.4e+107) {
		tmp = t_1;
	} else if (z <= 1.6e-145) {
		tmp = (x * y) / a_m;
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (z / a_m) * (0.0 - t)
	tmp = 0
	if z <= -3.4e+107:
		tmp = t_1
	elif z <= 1.6e-145:
		tmp = (x * y) / a_m
	else:
		tmp = t_1
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(z / a_m) * Float64(0.0 - t))
	tmp = 0.0
	if (z <= -3.4e+107)
		tmp = t_1;
	elseif (z <= 1.6e-145)
		tmp = Float64(Float64(x * y) / a_m);
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (z / a_m) * (0.0 - t);
	tmp = 0.0;
	if (z <= -3.4e+107)
		tmp = t_1;
	elseif (z <= 1.6e-145)
		tmp = (x * y) / a_m;
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(z / a$95$m), $MachinePrecision] * N[(0.0 - t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[z, -3.4e+107], t$95$1, If[LessEqual[z, 1.6e-145], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999997e107 or 1.60000000000000004e-145 < z

   1. Initial program 86.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 86.6%

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

   4. Applied egg-rr 86.6%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 58.1%

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

   7. Simplified 58.1%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. *-lowering-*.f64 58.1%

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

   9. Applied egg-rr 58.1%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 62.5%

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

   11. Applied egg-rr 62.5%

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

   if -3.3999999999999997e107 < z < 1.60000000000000004e-145

   1. Initial program 97.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;\frac{z}{a} \cdot \left(0 - t\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(0 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+234}:\\ \;\;\;\;0 - \frac{z}{\frac{a\_m}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* z t) -1e+234)
    (- 0.0 (/ z (/ a_m t)))
    (/ (- (* x y) (* z t)) a_m))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= -1e+234) {
		tmp = 0.0 - (z / (a_m / t));
	} else {
		tmp = ((x * y) - (z * t)) / a_m;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((z * t) <= (-1d+234)) then
        tmp = 0.0d0 - (z / (a_m / t))
    else
        tmp = ((x * y) - (z * t)) / a_m
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((z * t) <= -1e+234) {
		tmp = 0.0 - (z / (a_m / t));
	} else {
		tmp = ((x * y) - (z * t)) / a_m;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (z * t) <= -1e+234:
		tmp = 0.0 - (z / (a_m / t))
	else:
		tmp = ((x * y) - (z * t)) / a_m
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(z * t) <= -1e+234)
		tmp = Float64(0.0 - Float64(z / Float64(a_m / t)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((z * t) <= -1e+234)
		tmp = 0.0 - (z / (a_m / t));
	else
		tmp = ((x * y) - (z * t)) / a_m;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(z * t), $MachinePrecision], -1e+234], N[(0.0 - N[(z / N[(a$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000002e234

   1. Initial program 58.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 58.6%

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

   4. Applied egg-rr 58.6%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 58.6%

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

   7. Simplified 58.6%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. *-lowering-*.f64 58.5%

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

   9. Applied egg-rr 58.5%

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

       1. distribute-neg-frac N/A

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

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

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

       3. sub0-neg N/A

          \[\leadsto \frac{z \cdot \left(0 - t\right)}{a} \]

       4. associate-*r/ N/A

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

       5. clear-num N/A

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

       6. un-div-inv N/A

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

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

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

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

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

       9. --lowering--.f64 99.9%

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

   11. Applied egg-rr 99.9%

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

   if -1.00000000000000002e234 < (*.f64 z t)

   1. Initial program 94.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+234}:\\ \;\;\;\;0 - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= x -6e+54) (* x (/ y a_m)) (/ (* x y) a_m))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (x <= -6e+54) {
		tmp = x * (y / a_m);
	} else {
		tmp = (x * y) / a_m;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (x <= (-6d+54)) then
        tmp = x * (y / a_m)
    else
        tmp = (x * y) / a_m
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (x <= -6e+54) {
		tmp = x * (y / a_m);
	} else {
		tmp = (x * y) / a_m;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if x <= -6e+54:
		tmp = x * (y / a_m)
	else:
		tmp = (x * y) / a_m
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (x <= -6e+54)
		tmp = Float64(x * Float64(y / a_m));
	else
		tmp = Float64(Float64(x * y) / a_m);
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (x <= -6e+54)
		tmp = x * (y / a_m);
	else
		tmp = (x * y) / a_m;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[x, -6e+54], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999998e54

   1. Initial program 86.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 67.1%

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

   5. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   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 70.4%

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

   7. Applied egg-rr 70.4%

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

   if -5.9999999999999998e54 < x

   1. Initial program 94.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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 53.5%

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

   5. Simplified 53.5%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(x \cdot \frac{y}{a\_m}\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* x (/ y a_m))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * (x * (y / a_m))
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (x * (y / a_m))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(x * Float64(y / a_m)))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (x * (y / a_m));
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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 56.5%

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

5. Simplified 56.5%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
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 55.8%

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

7. Applied egg-rr 55.8%

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

8. Final simplification 55.8%

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

Alternative 8: 51.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(y \cdot \frac{x}{a\_m}\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* y (/ x a_m))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (y * (x / a_m));
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * (y * (x / a_m))
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (y * (x / a_m));
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (y * (x / a_m))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(y * Float64(x / a_m)))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (y * (x / a_m));
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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 56.5%

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

5. Simplified 56.5%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
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 53.3%

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

7. Applied egg-rr 53.3%

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

Developer Target 1: 92.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024161 
(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))