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

Percentage Accurate: 91.3% → 96.1%

Time: 8.8s

Alternatives: 11

Speedup: 0.6×

• 28.7% 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: 91.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 7 \cdot 10^{+38}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\sqrt{a\_m}}, \frac{x}{\sqrt{a\_m}}, \frac{t}{a\_m} \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

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 (<= a_m 7e+38)
    (/ (fma x y (* z (- t))) a_m)
    (fma (/ y (sqrt a_m)) (/ x (sqrt a_m)) (* (/ t a_m) (- z))))))

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 (a_m <= 7e+38) {
		tmp = fma(x, y, (z * -t)) / a_m;
	} else {
		tmp = fma((y / sqrt(a_m)), (x / sqrt(a_m)), ((t / a_m) * -z));
	}
	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 (a_m <= 7e+38)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a_m);
	else
		tmp = fma(Float64(y / sqrt(a_m)), Float64(x / sqrt(a_m)), Float64(Float64(t / a_m) * Float64(-z)));
	end
	return Float64(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[a$95$m, 7e+38], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(y / N[Sqrt[a$95$m], $MachinePrecision]), $MachinePrecision] * N[(x / N[Sqrt[a$95$m], $MachinePrecision]), $MachinePrecision] + N[(N[(t / a$95$m), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 7.00000000000000003e38

   1. Initial program 93.4%

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

      1. div-sub 91.0%

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

      2. *-commutative 91.0%

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

      3. div-sub 93.4%

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

      4. *-commutative 93.4%

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

      5. fma-neg 93.9%

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

      6. distribute-rgt-neg-out 93.9%

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

   3. Simplified 93.9%

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

   if 7.00000000000000003e38 < a

   1. Initial program 79.0%

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

      1. div-sub 79.0%

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

      2. *-commutative 79.0%

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

      3. add-sqr-sqrt 78.9%

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

      4. times-frac 88.2%

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

      5. fma-neg 88.2%

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

      6. associate-/l* 95.3%

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

   4. Applied egg-rr 95.3%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7 \cdot 10^{+38}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\sqrt{a}}, \frac{x}{\sqrt{a}}, \frac{t}{a} \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 10^{+44}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - z \cdot \frac{t}{a\_m}\\ \end{array} \end{array} \]

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 (<= a_m 1e+44)
    (/ (fma x y (* z (- t))) a_m)
    (- (* x (/ y a_m)) (* 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 (a_m <= 1e+44) {
		tmp = fma(x, y, (z * -t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (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 (a_m <= 1e+44)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(z * Float64(t / a_m)));
	end
	return Float64(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[a$95$m, 1e+44], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 1.0000000000000001e44

   1. Initial program 93.4%

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

      1. div-sub 91.0%

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

      2. *-commutative 91.0%

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

      3. div-sub 93.4%

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

      4. *-commutative 93.4%

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

      5. fma-neg 93.9%

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

      6. distribute-rgt-neg-out 93.9%

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

   3. Simplified 93.9%

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

   if 1.0000000000000001e44 < a

   1. Initial program 79.0%

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

      1. div-sub 79.0%

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

      2. associate-/l* 91.6%

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

      3. associate-/l* 98.7%

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

   4. Applied egg-rr 98.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{+44}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{t}{\frac{a\_m}{-z}}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a\_m}{x}}\\ \end{array} \end{array} \end{array} \]

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 (/ t (/ a_m (- z)))))
   (*
    a_s
    (if (<= (* x y) -4e+72)
      (* y (/ x a_m))
      (if (<= (* x y) 5e-57)
        t_1
        (if (<= (* x y) 1e+79)
          (/ (* x y) a_m)
          (if (<= (* x y) 2e+148) t_1 (/ y (/ a_m x)))))))))

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 = t / (a_m / -z);
	double tmp;
	if ((x * y) <= -4e+72) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e-57) {
		tmp = t_1;
	} else if ((x * y) <= 1e+79) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e+148) {
		tmp = t_1;
	} else {
		tmp = y / (a_m / x);
	}
	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 = t / (a_m / -z)
    if ((x * y) <= (-4d+72)) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d-57) then
        tmp = t_1
    else if ((x * y) <= 1d+79) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 2d+148) then
        tmp = t_1
    else
        tmp = y / (a_m / x)
    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 = t / (a_m / -z);
	double tmp;
	if ((x * y) <= -4e+72) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e-57) {
		tmp = t_1;
	} else if ((x * y) <= 1e+79) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e+148) {
		tmp = t_1;
	} else {
		tmp = y / (a_m / x);
	}
	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 = t / (a_m / -z)
	tmp = 0
	if (x * y) <= -4e+72:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e-57:
		tmp = t_1
	elif (x * y) <= 1e+79:
		tmp = (x * y) / a_m
	elif (x * y) <= 2e+148:
		tmp = t_1
	else:
		tmp = y / (a_m / x)
	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(t / Float64(a_m / Float64(-z)))
	tmp = 0.0
	if (Float64(x * y) <= -4e+72)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e-57)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+79)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 2e+148)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a_m / x));
	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 = t / (a_m / -z);
	tmp = 0.0;
	if ((x * y) <= -4e+72)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e-57)
		tmp = t_1;
	elseif ((x * y) <= 1e+79)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 2e+148)
		tmp = t_1;
	else
		tmp = y / (a_m / x);
	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[(t / N[(a$95$m / (-z)), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -4e+72], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+79], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+148], t$95$1, N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.99999999999999978e72

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.0%

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

      1. associate-*r/ 78.7%

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

   5. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 78.8%

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

   7. Applied egg-rr 78.8%

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

      1. associate-/r/ 79.1%

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

   9. Simplified 79.1%

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

   if -3.99999999999999978e72 < (*.f64 x y) < 5.0000000000000002e-57 or 9.99999999999999967e78 < (*.f64 x y) < 2.0000000000000001e148

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-/l* 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

      4. distribute-neg-frac2 80.8%

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

   5. Simplified 80.8%

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

      1. distribute-frac-neg2 80.8%

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

      2. distribute-rgt-neg-out 80.8%

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

      3. add-sqr-sqrt 38.6%

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

      4. sqrt-unprod 36.3%

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

      5. sqr-neg 36.3%

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

      6. sqrt-unprod 5.6%

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

      7. add-sqr-sqrt 9.1%

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

      8. clear-num 9.1%

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

      9. un-div-inv 9.1%

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

      10. add-sqr-sqrt 5.6%

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

      11. sqrt-unprod 36.4%

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

      12. sqr-neg 36.4%

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

      13. sqrt-unprod 38.7%

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

      14. add-sqr-sqrt 80.7%

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

   7. Applied egg-rr 80.7%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 9.99999999999999967e78

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 63.0%

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

   if 2.0000000000000001e148 < (*.f64 x y)

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. associate-*r/ 89.3%

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

   5. Simplified 89.3%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. add-sqr-sqrt 37.6%

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

      4. frac-times 48.7%

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

      5. clear-num 48.6%

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

      6. un-div-inv 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. associate-/r* 48.8%

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

      2. associate-*r/ 48.8%

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

      3. rem-square-sqrt 89.4%

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

   9. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{a}{-z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{t}{\frac{a}{-z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{a\_m}{-z}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{t}{a\_m} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a\_m}{x}}\\ \end{array} \end{array} \]

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 y) -4e+72)
    (* y (/ x a_m))
    (if (<= (* x y) 5e-57)
      (/ t (/ a_m (- z)))
      (if (<= (* x y) 2e+44)
        (/ (* x y) a_m)
        (if (<= (* x y) 2e+148) (* (/ t a_m) (- z)) (/ y (/ a_m x))))))))

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 * y) <= -4e+72) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e-57) {
		tmp = t / (a_m / -z);
	} else if ((x * y) <= 2e+44) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e+148) {
		tmp = (t / a_m) * -z;
	} else {
		tmp = y / (a_m / x);
	}
	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 * y) <= (-4d+72)) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d-57) then
        tmp = t / (a_m / -z)
    else if ((x * y) <= 2d+44) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 2d+148) then
        tmp = (t / a_m) * -z
    else
        tmp = y / (a_m / x)
    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 * y) <= -4e+72) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e-57) {
		tmp = t / (a_m / -z);
	} else if ((x * y) <= 2e+44) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e+148) {
		tmp = (t / a_m) * -z;
	} else {
		tmp = y / (a_m / x);
	}
	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 * y) <= -4e+72:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e-57:
		tmp = t / (a_m / -z)
	elif (x * y) <= 2e+44:
		tmp = (x * y) / a_m
	elif (x * y) <= 2e+148:
		tmp = (t / a_m) * -z
	else:
		tmp = y / (a_m / x)
	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(x * y) <= -4e+72)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e-57)
		tmp = Float64(t / Float64(a_m / Float64(-z)));
	elseif (Float64(x * y) <= 2e+44)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 2e+148)
		tmp = Float64(Float64(t / a_m) * Float64(-z));
	else
		tmp = Float64(y / Float64(a_m / x));
	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 * y) <= -4e+72)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e-57)
		tmp = t / (a_m / -z);
	elseif ((x * y) <= 2e+44)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 2e+148)
		tmp = (t / a_m) * -z;
	else
		tmp = y / (a_m / x);
	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[(x * y), $MachinePrecision], -4e+72], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], N[(t / N[(a$95$m / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+44], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+148], N[(N[(t / a$95$m), $MachinePrecision] * (-z)), $MachinePrecision], N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -3.99999999999999978e72

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.0%

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

      1. associate-*r/ 78.7%

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

   5. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 78.8%

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

   7. Applied egg-rr 78.8%

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

      1. associate-/r/ 79.1%

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

   9. Simplified 79.1%

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

   if -3.99999999999999978e72 < (*.f64 x y) < 5.0000000000000002e-57

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. associate-/l* 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

      4. distribute-neg-frac2 80.7%

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

   5. Simplified 80.7%

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

      1. distribute-frac-neg2 80.7%

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

      2. distribute-rgt-neg-out 80.7%

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

      3. add-sqr-sqrt 38.1%

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

      4. sqrt-unprod 36.4%

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

      5. sqr-neg 36.4%

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

      6. sqrt-unprod 5.8%

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

      7. add-sqr-sqrt 9.4%

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

      8. clear-num 9.5%

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

      9. un-div-inv 9.5%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 36.4%

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

      12. sqr-neg 36.4%

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

      13. sqrt-unprod 38.2%

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

      14. add-sqr-sqrt 80.6%

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

   7. Applied egg-rr 80.6%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 2.0000000000000002e44

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 65.6%

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

   if 2.0000000000000002e44 < (*.f64 x y) < 2.0000000000000001e148

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-*r/ 71.0%

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

      3. neg-mul-1 71.0%

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

      4. distribute-rgt-neg-in 71.0%

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

      5. distribute-frac-neg 71.0%

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

   5. Simplified 71.0%

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

   if 2.0000000000000001e148 < (*.f64 x y)

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. associate-*r/ 89.3%

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

   5. Simplified 89.3%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. add-sqr-sqrt 37.6%

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

      4. frac-times 48.7%

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

      5. clear-num 48.6%

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

      6. un-div-inv 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. associate-/r* 48.8%

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

      2. associate-*r/ 48.8%

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

      3. rem-square-sqrt 89.4%

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

   9. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{a}{-z}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot y}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{t}{a\_m} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a\_m}{x}}\\ \end{array} \end{array} \]

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 y) -4e+72)
    (* y (/ x a_m))
    (if (<= (* x y) 5e-57)
      (/ (* z (- t)) a_m)
      (if (<= (* x y) 2e+44)
        (/ (* x y) a_m)
        (if (<= (* x y) 2e+148) (* (/ t a_m) (- z)) (/ y (/ a_m x))))))))

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 * y) <= -4e+72) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e-57) {
		tmp = (z * -t) / a_m;
	} else if ((x * y) <= 2e+44) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e+148) {
		tmp = (t / a_m) * -z;
	} else {
		tmp = y / (a_m / x);
	}
	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 * y) <= (-4d+72)) then
        tmp = y * (x / a_m)
    else if ((x * y) <= 5d-57) then
        tmp = (z * -t) / a_m
    else if ((x * y) <= 2d+44) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 2d+148) then
        tmp = (t / a_m) * -z
    else
        tmp = y / (a_m / x)
    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 * y) <= -4e+72) {
		tmp = y * (x / a_m);
	} else if ((x * y) <= 5e-57) {
		tmp = (z * -t) / a_m;
	} else if ((x * y) <= 2e+44) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e+148) {
		tmp = (t / a_m) * -z;
	} else {
		tmp = y / (a_m / x);
	}
	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 * y) <= -4e+72:
		tmp = y * (x / a_m)
	elif (x * y) <= 5e-57:
		tmp = (z * -t) / a_m
	elif (x * y) <= 2e+44:
		tmp = (x * y) / a_m
	elif (x * y) <= 2e+148:
		tmp = (t / a_m) * -z
	else:
		tmp = y / (a_m / x)
	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(x * y) <= -4e+72)
		tmp = Float64(y * Float64(x / a_m));
	elseif (Float64(x * y) <= 5e-57)
		tmp = Float64(Float64(z * Float64(-t)) / a_m);
	elseif (Float64(x * y) <= 2e+44)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 2e+148)
		tmp = Float64(Float64(t / a_m) * Float64(-z));
	else
		tmp = Float64(y / Float64(a_m / x));
	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 * y) <= -4e+72)
		tmp = y * (x / a_m);
	elseif ((x * y) <= 5e-57)
		tmp = (z * -t) / a_m;
	elseif ((x * y) <= 2e+44)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 2e+148)
		tmp = (t / a_m) * -z;
	else
		tmp = y / (a_m / x);
	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[(x * y), $MachinePrecision], -4e+72], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], N[(N[(z * (-t)), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+44], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+148], N[(N[(t / a$95$m), $MachinePrecision] * (-z)), $MachinePrecision], N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -3.99999999999999978e72

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.0%

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

      1. associate-*r/ 78.7%

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

   5. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 78.8%

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

   7. Applied egg-rr 78.8%

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

      1. associate-/r/ 79.1%

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

   9. Simplified 79.1%

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

   if -3.99999999999999978e72 < (*.f64 x y) < 5.0000000000000002e-57

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. associate-*r* 81.2%

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

      2. mul-1-neg 81.2%

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

   5. Simplified 81.2%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 2.0000000000000002e44

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 65.6%

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

   if 2.0000000000000002e44 < (*.f64 x y) < 2.0000000000000001e148

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-*r/ 71.0%

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

      3. neg-mul-1 71.0%

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

      4. distribute-rgt-neg-in 71.0%

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

      5. distribute-frac-neg 71.0%

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

   5. Simplified 71.0%

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

   if 2.0000000000000001e148 < (*.f64 x y)

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. associate-*r/ 89.3%

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

   5. Simplified 89.3%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. add-sqr-sqrt 37.6%

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

      4. frac-times 48.7%

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

      5. clear-num 48.6%

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

      6. un-div-inv 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. associate-/r* 48.8%

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

      2. associate-*r/ 48.8%

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

      3. rem-square-sqrt 89.4%

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

   9. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{t\_1}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - \frac{z \cdot t}{y}}{a\_m}\\ \end{array} \end{array} \end{array} \]

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_s (if (<= t_1 2e+286) (/ t_1 a_m) (* y (/ (- x (/ (* z t) 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 2e+286) {
		tmp = t_1 / a_m;
	} else {
		tmp = y * ((x - ((z * t) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= 2d+286) then
        tmp = t_1 / a_m
    else
        tmp = y * ((x - ((z * t) / 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 2e+286) {
		tmp = t_1 / a_m;
	} else {
		tmp = y * ((x - ((z * t) / 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):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= 2e+286:
		tmp = t_1 / a_m
	else:
		tmp = y * ((x - ((z * t) / 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)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= 2e+286)
		tmp = Float64(t_1 / a_m);
	else
		tmp = Float64(y * Float64(Float64(x - Float64(Float64(z * t) / 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 2e+286)
		tmp = t_1 / a_m;
	else
		tmp = y * ((x - ((z * t) / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, 2e+286], N[(t$95$1 / a$95$m), $MachinePrecision], N[(y * N[(N[(x - N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000007e286

   1. Initial program 95.0%

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

   if 2.00000000000000007e286 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 62.3%

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

      1. div-sub 59.5%

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

      2. *-commutative 59.5%

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

      3. add-sqr-sqrt 32.5%

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

      4. times-frac 45.8%

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

      5. fma-neg 45.8%

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

      6. associate-/l* 48.5%

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

   4. Applied egg-rr 48.5%

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

   5. Taylor expanded in y around inf 91.5%

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

      1. +-commutative 91.5%

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

      2. mul-1-neg 91.5%

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

      3. *-commutative 91.5%

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

      4. times-frac 91.4%

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

      5. sub-neg 91.4%

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

      6. associate-*l/ 97.1%

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

      7. /-rgt-identity 97.1%

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

      8. times-frac 94.5%

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

      9. *-commutative 94.5%

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

      10. *-lft-identity 94.5%

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

      11. div-sub 94.5%

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

   7. Simplified 94.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - \frac{z \cdot t}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a\_m}{y}}\\ \end{array} \end{array} \]

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 y) 2e+277) (/ (- (* x y) (* z t)) a_m) (/ x (/ a_m y)))))

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 * y) <= 2e+277) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = x / (a_m / y);
	}
	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 * y) <= 2d+277) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = x / (a_m / y)
    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 * y) <= 2e+277) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = x / (a_m / y);
	}
	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 * y) <= 2e+277:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = x / (a_m / y)
	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(x * y) <= 2e+277)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(x / Float64(a_m / y));
	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 * y) <= 2e+277)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = x / (a_m / y);
	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[(x * y), $MachinePrecision], 2e+277], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 2.00000000000000001e277

   1. Initial program 94.1%

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

   if 2.00000000000000001e277 < (*.f64 x y)

   1. Initial program 50.9%

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

   3. Taylor expanded in x around inf 50.9%

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

      1. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m} - z \cdot \frac{t}{a\_m}\\ \end{array} \end{array} \]

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 (<= a_m 2e+37)
    (/ (- (* x y) (* z t)) a_m)
    (- (* x (/ y a_m)) (* 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 (a_m <= 2e+37) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (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 (a_m <= 2d+37) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = (x * (y / a_m)) - (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 (a_m <= 2e+37) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = (x * (y / a_m)) - (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 a_m <= 2e+37:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = (x * (y / a_m)) - (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 (a_m <= 2e+37)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) - Float64(z * Float64(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 (a_m <= 2e+37)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = (x * (y / a_m)) - (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[a$95$m, 2e+37], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < 1.99999999999999991e37

   1. Initial program 93.4%

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

   if 1.99999999999999991e37 < a

   1. Initial program 79.0%

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

      1. div-sub 79.0%

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

      2. associate-/l* 91.6%

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

      3. associate-/l* 98.7%

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

   4. Applied egg-rr 98.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5000:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a\_m}\\ \end{array} \end{array} \]

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 -5000.0) (* x (/ y a_m)) (* 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) {
	double tmp;
	if (z <= -5000.0) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / 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 <= (-5000.0d0)) then
        tmp = x * (y / a_m)
    else
        tmp = y * (x / 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 <= -5000.0) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / 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 <= -5000.0:
		tmp = x * (y / a_m)
	else:
		tmp = y * (x / 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 (z <= -5000.0)
		tmp = Float64(x * Float64(y / a_m));
	else
		tmp = Float64(y * Float64(x / 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 <= -5000.0)
		tmp = x * (y / a_m);
	else
		tmp = y * (x / 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[z, -5000.0], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5e3

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf 31.7%

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

      1. associate-*r/ 34.5%

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

   5. Simplified 34.5%

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

   if -5e3 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 48.4%

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

      1. associate-*r/ 53.8%

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

   5. Simplified 53.8%

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

      1. clear-num 53.5%

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

      2. un-div-inv 53.5%

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

   7. Applied egg-rr 53.5%

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

      1. associate-/r/ 51.0%

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

   9. Simplified 51.0%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -205000:\\ \;\;\;\;x \cdot \frac{y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a\_m}{x}}\\ \end{array} \end{array} \]

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 -205000.0) (* x (/ y a_m)) (/ y (/ a_m x)))))

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 <= -205000.0) {
		tmp = x * (y / a_m);
	} else {
		tmp = y / (a_m / x);
	}
	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 <= (-205000.0d0)) then
        tmp = x * (y / a_m)
    else
        tmp = y / (a_m / x)
    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 <= -205000.0) {
		tmp = x * (y / a_m);
	} else {
		tmp = y / (a_m / x);
	}
	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 <= -205000.0:
		tmp = x * (y / a_m)
	else:
		tmp = y / (a_m / x)
	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 (z <= -205000.0)
		tmp = Float64(x * Float64(y / a_m));
	else
		tmp = Float64(y / Float64(a_m / x));
	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 <= -205000.0)
		tmp = x * (y / a_m);
	else
		tmp = y / (a_m / x);
	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[z, -205000.0], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(y / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -205000

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf 31.7%

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

      1. associate-*r/ 34.5%

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

   5. Simplified 34.5%

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

   if -205000 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 48.4%

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

      1. associate-*r/ 53.8%

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

   5. Simplified 53.8%

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

      1. associate-*r/ 48.4%

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

      2. *-commutative 48.4%

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

      3. add-sqr-sqrt 24.6%

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

      4. frac-times 26.5%

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

      5. clear-num 26.5%

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

      6. un-div-inv 26.5%

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

   7. Applied egg-rr 26.5%

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

      1. associate-/r* 25.6%

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

      2. associate-*r/ 25.6%

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

      3. rem-square-sqrt 51.0%

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

   9. Simplified 51.0%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -205000:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.5% 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 90.6%

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

3. Taylor expanded in x around inf 44.2%

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

   1. associate-*r/ 48.9%

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

5. Simplified 48.9%

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

6. Final simplification 48.9%

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

Developer target: 91.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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