Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 91.0% → 95.7%

Time: 8.5s

Alternatives: 11

Speedup: 0.5×

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

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+295} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+256}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-9, t \cdot \frac{z}{y}, x\right)}{a} \cdot \frac{y}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+295) (not (<= (* x y) 5e+256)))
   (* (/ (fma -9.0 (* t (/ z y)) x) a) (/ y 2.0))
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+295) || !((x * y) <= 5e+256)) {
		tmp = (fma(-9.0, (t * (z / y)), x) / a) * (y / 2.0);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+295) || !(Float64(x * y) <= 5e+256))
		tmp = Float64(Float64(fma(-9.0, Float64(t * Float64(z / y)), x) / a) * Float64(y / 2.0));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+295], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+256]], $MachinePrecision]], N[(N[(N[(-9.0 * N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999991e295 or 5.00000000000000015e256 < (*.f64 x y)

   1. Initial program 68.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.0%

      \[\leadsto \frac{\color{blue}{y \cdot \left(x + -9 \cdot \frac{t \cdot z}{y}\right)}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 73.0%

         \[\leadsto \frac{\color{blue}{\left(x + -9 \cdot \frac{t \cdot z}{y}\right) \cdot y}}{a \cdot 2} \]

      2. times-frac 96.0%

         \[\leadsto \color{blue}{\frac{x + -9 \cdot \frac{t \cdot z}{y}}{a} \cdot \frac{y}{2}} \]

      3. +-commutative 96.0%

         \[\leadsto \frac{\color{blue}{-9 \cdot \frac{t \cdot z}{y} + x}}{a} \cdot \frac{y}{2} \]

      4. fma-define 96.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, \frac{t \cdot z}{y}, x\right)}}{a} \cdot \frac{y}{2} \]

      5. associate-/l* 98.0%

         \[\leadsto \frac{\mathsf{fma}\left(-9, \color{blue}{t \cdot \frac{z}{y}}, x\right)}{a} \cdot \frac{y}{2} \]

   5. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-9, t \cdot \frac{z}{y}, x\right)}{a} \cdot \frac{y}{2}} \]

   if -4.99999999999999991e295 < (*.f64 x y) < 5.00000000000000015e256

   1. Initial program 98.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 97.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 97.4%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 98.4%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 98.4%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 98.4%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 98.4%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 98.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      2. associate-*r* 98.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot -9\right) \cdot t}\right)}{a \cdot 2} \]

      3. metadata-eval 98.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \left(z \cdot \color{blue}{\left(-9\right)}\right) \cdot t\right)}{a \cdot 2} \]

      4. distribute-rgt-neg-in 98.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(-z \cdot 9\right)} \cdot t\right)}{a \cdot 2} \]

      5. distribute-lft-neg-in 98.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{-\left(z \cdot 9\right) \cdot t}\right)}{a \cdot 2} \]

      6. fma-neg 98.4%

         \[\leadsto \frac{\color{blue}{x \cdot y - \left(z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      7. associate-*l* 98.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   6. Applied egg-rr 98.3%

      \[\leadsto \frac{\color{blue}{x \cdot y - z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+295} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+256}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-9, t \cdot \frac{z}{y}, x\right)}{a} \cdot \frac{y}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-28}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+34)
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) -2e-28)
     (/ (* z (* t -4.5)) a)
     (if (<= (* x y) -5e-65)
       (/ (* x y) (* a 2.0))
       (if (<= (* x y) 4e-8) (* (* t z) (/ -4.5 a)) (* (/ y 2.0) (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+34) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= -2e-28) {
		tmp = (z * (t * -4.5)) / a;
	} else if ((x * y) <= -5e-65) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 4e-8) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+34)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((x * y) <= (-2d-28)) then
        tmp = (z * (t * (-4.5d0))) / a
    else if ((x * y) <= (-5d-65)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 4d-8) then
        tmp = (t * z) * ((-4.5d0) / a)
    else
        tmp = (y / 2.0d0) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+34) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= -2e-28) {
		tmp = (z * (t * -4.5)) / a;
	} else if ((x * y) <= -5e-65) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 4e-8) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+34:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= -2e-28:
		tmp = (z * (t * -4.5)) / a
	elif (x * y) <= -5e-65:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 4e-8:
		tmp = (t * z) * (-4.5 / a)
	else:
		tmp = (y / 2.0) * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+34)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= -2e-28)
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	elseif (Float64(x * y) <= -5e-65)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 4e-8)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	else
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+34)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= -2e-28)
		tmp = (z * (t * -4.5)) / a;
	elseif ((x * y) <= -5e-65)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 4e-8)
		tmp = (t * z) * (-4.5 / a);
	else
		tmp = (y / 2.0) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+34], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-28], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-65], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-8], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999989e34

   1. Initial program 87.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 81.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 81.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 81.3%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 81.3%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -1.99999999999999989e34 < (*.f64 x y) < -1.99999999999999994e-28

   1. Initial program 99.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.6%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 68.7%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 60.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 60.2%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 60.2%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 60.1%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 60.1%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{z \cdot \left(-4.5 \cdot t\right)}{a}} \]

      2. *-commutative 68.7%

         \[\leadsto \frac{z \cdot \color{blue}{\left(t \cdot -4.5\right)}}{a} \]

   7. Applied egg-rr 68.7%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4.5\right)}{a}} \]

   if -1.99999999999999994e-28 < (*.f64 x y) < -4.99999999999999983e-65

   1. Initial program 99.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.9%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if -4.99999999999999983e-65 < (*.f64 x y) < 4.0000000000000001e-8

   1. Initial program 97.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 81.0%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 81.0%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 76.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 77.0%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 77.0%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 76.1%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 76.1%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.0%

         \[\leadsto \color{blue}{\frac{z \cdot \left(-4.5 \cdot t\right)}{a}} \]

      2. *-commutative 81.0%

         \[\leadsto \frac{z \cdot \color{blue}{\left(t \cdot -4.5\right)}}{a} \]

   7. Applied egg-rr 81.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4.5\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 76.1%

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -4.5}{a}} \]

      2. associate-*r/ 77.0%

         \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]

      3. associate-*r* 81.1%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   9. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   if 4.0000000000000001e-8 < (*.f64 x y)

   1. Initial program 86.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.7%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 79.7%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 86.8%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 86.8%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-28}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-28}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+34)
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) -2e-28)
     (/ (* t (* z -4.5)) a)
     (if (<= (* x y) -5e-65)
       (/ (* x y) (* a 2.0))
       (if (<= (* x y) 4e-8) (* (* t z) (/ -4.5 a)) (* (/ y 2.0) (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+34) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= -2e-28) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= -5e-65) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 4e-8) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+34)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((x * y) <= (-2d-28)) then
        tmp = (t * (z * (-4.5d0))) / a
    else if ((x * y) <= (-5d-65)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 4d-8) then
        tmp = (t * z) * ((-4.5d0) / a)
    else
        tmp = (y / 2.0d0) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+34) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= -2e-28) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= -5e-65) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 4e-8) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+34:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= -2e-28:
		tmp = (t * (z * -4.5)) / a
	elif (x * y) <= -5e-65:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 4e-8:
		tmp = (t * z) * (-4.5 / a)
	else:
		tmp = (y / 2.0) * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+34)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= -2e-28)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif (Float64(x * y) <= -5e-65)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 4e-8)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	else
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+34)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= -2e-28)
		tmp = (t * (z * -4.5)) / a;
	elseif ((x * y) <= -5e-65)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 4e-8)
		tmp = (t * z) * (-4.5 / a);
	else
		tmp = (y / 2.0) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+34], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-28], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-65], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-8], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999989e34

   1. Initial program 87.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 81.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 81.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 81.3%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 81.3%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -1.99999999999999989e34 < (*.f64 x y) < -1.99999999999999994e-28

   1. Initial program 99.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 99.6%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 99.6%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 99.6%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 99.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 99.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 99.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 99.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      2. associate-*r* 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot -9\right) \cdot t}\right)}{a \cdot 2} \]

      3. metadata-eval 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \left(z \cdot \color{blue}{\left(-9\right)}\right) \cdot t\right)}{a \cdot 2} \]

      4. distribute-rgt-neg-in 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(-z \cdot 9\right)} \cdot t\right)}{a \cdot 2} \]

      5. distribute-lft-neg-in 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{-\left(z \cdot 9\right) \cdot t}\right)}{a \cdot 2} \]

      6. fma-neg 99.6%

         \[\leadsto \frac{\color{blue}{x \cdot y - \left(z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      7. associate-*l* 99.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   6. Applied egg-rr 99.6%

      \[\leadsto \frac{\color{blue}{x \cdot y - z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.6%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - z \cdot \left(9 \cdot t\right)\right)}}{a \cdot 2} \]

      2. times-frac 99.5%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{2}} \]

   8. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{2}} \]
   9. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{2} \cdot \frac{1}{a}} \]

      2. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{2}{x \cdot y - z \cdot \left(9 \cdot t\right)}}} \cdot \frac{1}{a} \]

      3. frac-times 99.6%

         \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{2}{x \cdot y - z \cdot \left(9 \cdot t\right)} \cdot a}} \]

      4. metadata-eval 99.6%

         \[\leadsto \frac{\color{blue}{1}}{\frac{2}{x \cdot y - z \cdot \left(9 \cdot t\right)} \cdot a} \]

      5. associate-*r* 99.5%

         \[\leadsto \frac{1}{\frac{2}{x \cdot y - \color{blue}{\left(z \cdot 9\right) \cdot t}} \cdot a} \]

   10. Applied egg-rr 99.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{2}{x \cdot y - \left(z \cdot 9\right) \cdot t} \cdot a}} \]

   11. Taylor expanded in x around 0 68.7%

       \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   12. Step-by-step derivation

       1. associate-*r/ 68.6%

          \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

       2. associate-*l* 68.7%

          \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

       3. *-commutative 68.7%

          \[\leadsto \frac{\color{blue}{\left(t \cdot -4.5\right)} \cdot z}{a} \]

       4. associate-*l* 68.8%

          \[\leadsto \frac{\color{blue}{t \cdot \left(-4.5 \cdot z\right)}}{a} \]

   13. Simplified 68.8%

       \[\leadsto \color{blue}{\frac{t \cdot \left(-4.5 \cdot z\right)}{a}} \]

   if -1.99999999999999994e-28 < (*.f64 x y) < -4.99999999999999983e-65

   1. Initial program 99.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.9%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if -4.99999999999999983e-65 < (*.f64 x y) < 4.0000000000000001e-8

   1. Initial program 97.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 81.0%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 81.0%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 76.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 77.0%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 77.0%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 76.1%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 76.1%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.0%

         \[\leadsto \color{blue}{\frac{z \cdot \left(-4.5 \cdot t\right)}{a}} \]

      2. *-commutative 81.0%

         \[\leadsto \frac{z \cdot \color{blue}{\left(t \cdot -4.5\right)}}{a} \]

   7. Applied egg-rr 81.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4.5\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 76.1%

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -4.5}{a}} \]

      2. associate-*r/ 77.0%

         \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]

      3. associate-*r* 81.1%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   9. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   if 4.0000000000000001e-8 < (*.f64 x y)

   1. Initial program 86.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.7%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 79.7%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 86.8%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 86.8%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-28}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+27}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87} \lor \neg \left(y \leq 1.7 \cdot 10^{+155}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= y -1e-131)
     t_1
     (if (<= y 5.6e+27)
       (* -4.5 (/ (* t z) a))
       (if (or (<= y 1.28e+87) (not (<= y 1.7e+155)))
         t_1
         (* -4.5 (* t (/ z a))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if (y <= -1e-131) {
		tmp = t_1;
	} else if (y <= 5.6e+27) {
		tmp = -4.5 * ((t * z) / a);
	} else if ((y <= 1.28e+87) || !(y <= 1.7e+155)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    if (y <= (-1d-131)) then
        tmp = t_1
    else if (y <= 5.6d+27) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if ((y <= 1.28d+87) .or. (.not. (y <= 1.7d+155))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if (y <= -1e-131) {
		tmp = t_1;
	} else if (y <= 5.6e+27) {
		tmp = -4.5 * ((t * z) / a);
	} else if ((y <= 1.28e+87) || !(y <= 1.7e+155)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if y <= -1e-131:
		tmp = t_1
	elif y <= 5.6e+27:
		tmp = -4.5 * ((t * z) / a)
	elif (y <= 1.28e+87) or not (y <= 1.7e+155):
		tmp = t_1
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (y <= -1e-131)
		tmp = t_1;
	elseif (y <= 5.6e+27)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif ((y <= 1.28e+87) || !(y <= 1.7e+155))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y * 0.5) / a);
	tmp = 0.0;
	if (y <= -1e-131)
		tmp = t_1;
	elseif (y <= 5.6e+27)
		tmp = -4.5 * ((t * z) / a);
	elseif ((y <= 1.28e+87) || ~((y <= 1.7e+155)))
		tmp = t_1;
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-131], t$95$1, If[LessEqual[y, 5.6e+27], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.28e+87], N[Not[LessEqual[y, 1.7e+155]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999999e-132 or 5.5999999999999999e27 < y < 1.28e87 or 1.7e155 < y

   1. Initial program 89.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 70.9%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 70.9%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 70.9%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 70.9%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -9.9999999999999999e-132 < y < 5.5999999999999999e27

   1. Initial program 97.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 1.28e87 < y < 1.7e155

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.1%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+27}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87} \lor \neg \left(y \leq 1.7 \cdot 10^{+155}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.7e-131)
   (* (/ y 2.0) (/ x a))
   (if (<= y 1.7e+27)
     (* (* t z) (/ -4.5 a))
     (if (<= y 1.28e+87)
       (* x (* y (/ 0.5 a)))
       (if (<= y 1.3e+155) (* -4.5 (* t (/ z a))) (* x (/ (* y 0.5) a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e-131) {
		tmp = (y / 2.0) * (x / a);
	} else if (y <= 1.7e+27) {
		tmp = (t * z) * (-4.5 / a);
	} else if (y <= 1.28e+87) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.3e+155) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.7d-131)) then
        tmp = (y / 2.0d0) * (x / a)
    else if (y <= 1.7d+27) then
        tmp = (t * z) * ((-4.5d0) / a)
    else if (y <= 1.28d+87) then
        tmp = x * (y * (0.5d0 / a))
    else if (y <= 1.3d+155) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e-131) {
		tmp = (y / 2.0) * (x / a);
	} else if (y <= 1.7e+27) {
		tmp = (t * z) * (-4.5 / a);
	} else if (y <= 1.28e+87) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.3e+155) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.7e-131:
		tmp = (y / 2.0) * (x / a)
	elif y <= 1.7e+27:
		tmp = (t * z) * (-4.5 / a)
	elif y <= 1.28e+87:
		tmp = x * (y * (0.5 / a))
	elif y <= 1.3e+155:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.7e-131)
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	elseif (y <= 1.7e+27)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	elseif (y <= 1.28e+87)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (y <= 1.3e+155)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.7e-131)
		tmp = (y / 2.0) * (x / a);
	elseif (y <= 1.7e+27)
		tmp = (t * z) * (-4.5 / a);
	elseif (y <= 1.28e+87)
		tmp = x * (y * (0.5 / a));
	elseif (y <= 1.3e+155)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.7e-131], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+27], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e+87], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+155], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.69999999999999998e-131

   1. Initial program 90.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.8%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 58.8%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 64.6%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 64.6%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   if -1.69999999999999998e-131 < y < 1.7e27

   1. Initial program 97.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 66.6%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 66.6%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 62.4%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 63.3%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 63.3%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 62.4%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 62.4%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 66.6%

         \[\leadsto \color{blue}{\frac{z \cdot \left(-4.5 \cdot t\right)}{a}} \]

      2. *-commutative 66.6%

         \[\leadsto \frac{z \cdot \color{blue}{\left(t \cdot -4.5\right)}}{a} \]

   7. Applied egg-rr 66.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4.5\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 62.4%

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -4.5}{a}} \]

      2. associate-*r/ 63.3%

         \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]

      3. associate-*r* 66.7%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   9. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   if 1.7e27 < y < 1.28e87

   1. Initial program 86.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. associate-/l* 81.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a \cdot 2}} \]

      2. *-un-lft-identity 81.4%

         \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{a \cdot 2} \]

      3. *-commutative 81.4%

         \[\leadsto x \cdot \frac{1 \cdot y}{\color{blue}{2 \cdot a}} \]

      4. times-frac 81.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{y}{a}\right)} \]

      5. metadata-eval 81.4%

         \[\leadsto x \cdot \left(\color{blue}{0.5} \cdot \frac{y}{a}\right) \]

      6. metadata-eval 81.4%

         \[\leadsto x \cdot \left(\color{blue}{\frac{0.5}{1}} \cdot \frac{y}{a}\right) \]

      7. times-frac 81.4%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{1 \cdot a}} \]

      8. *-commutative 81.4%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 0.5}}{1 \cdot a} \]

      9. *-un-lft-identity 81.4%

         \[\leadsto x \cdot \frac{y \cdot 0.5}{\color{blue}{a}} \]

      10. *-commutative 81.4%

          \[\leadsto \color{blue}{\frac{y \cdot 0.5}{a} \cdot x} \]

      11. associate-/l* 81.1%

          \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right)} \cdot x \]

   5. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right) \cdot x} \]

   if 1.28e87 < y < 1.3000000000000001e155

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.1%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

   if 1.3000000000000001e155 < y

   1. Initial program 87.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 78.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 84.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 84.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 84.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 84.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 84.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= y -1.45e-131)
     t_1
     (if (<= y 6.5e+27)
       (* (* t z) (/ -4.5 a))
       (if (<= y 1.28e+87)
         (* x (* y (/ 0.5 a)))
         (if (<= y 1.3e+155) (* -4.5 (* t (/ z a))) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if (y <= -1.45e-131) {
		tmp = t_1;
	} else if (y <= 6.5e+27) {
		tmp = (t * z) * (-4.5 / a);
	} else if (y <= 1.28e+87) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.3e+155) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    if (y <= (-1.45d-131)) then
        tmp = t_1
    else if (y <= 6.5d+27) then
        tmp = (t * z) * ((-4.5d0) / a)
    else if (y <= 1.28d+87) then
        tmp = x * (y * (0.5d0 / a))
    else if (y <= 1.3d+155) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if (y <= -1.45e-131) {
		tmp = t_1;
	} else if (y <= 6.5e+27) {
		tmp = (t * z) * (-4.5 / a);
	} else if (y <= 1.28e+87) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.3e+155) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if y <= -1.45e-131:
		tmp = t_1
	elif y <= 6.5e+27:
		tmp = (t * z) * (-4.5 / a)
	elif y <= 1.28e+87:
		tmp = x * (y * (0.5 / a))
	elif y <= 1.3e+155:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (y <= -1.45e-131)
		tmp = t_1;
	elseif (y <= 6.5e+27)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	elseif (y <= 1.28e+87)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (y <= 1.3e+155)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y * 0.5) / a);
	tmp = 0.0;
	if (y <= -1.45e-131)
		tmp = t_1;
	elseif (y <= 6.5e+27)
		tmp = (t * z) * (-4.5 / a);
	elseif (y <= 1.28e+87)
		tmp = x * (y * (0.5 / a));
	elseif (y <= 1.3e+155)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-131], t$95$1, If[LessEqual[y, 6.5e+27], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e+87], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+155], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4500000000000001e-131 or 1.3000000000000001e155 < y

   1. Initial program 89.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 63.6%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 69.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 69.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 69.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -1.4500000000000001e-131 < y < 6.5000000000000005e27

   1. Initial program 97.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 66.6%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 66.6%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 62.4%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 63.3%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 63.3%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 62.4%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 62.4%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 66.6%

         \[\leadsto \color{blue}{\frac{z \cdot \left(-4.5 \cdot t\right)}{a}} \]

      2. *-commutative 66.6%

         \[\leadsto \frac{z \cdot \color{blue}{\left(t \cdot -4.5\right)}}{a} \]

   7. Applied egg-rr 66.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4.5\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 62.4%

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -4.5}{a}} \]

      2. associate-*r/ 63.3%

         \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]

      3. associate-*r* 66.7%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   9. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

   if 6.5000000000000005e27 < y < 1.28e87

   1. Initial program 86.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. associate-/l* 81.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a \cdot 2}} \]

      2. *-un-lft-identity 81.4%

         \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{a \cdot 2} \]

      3. *-commutative 81.4%

         \[\leadsto x \cdot \frac{1 \cdot y}{\color{blue}{2 \cdot a}} \]

      4. times-frac 81.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{y}{a}\right)} \]

      5. metadata-eval 81.4%

         \[\leadsto x \cdot \left(\color{blue}{0.5} \cdot \frac{y}{a}\right) \]

      6. metadata-eval 81.4%

         \[\leadsto x \cdot \left(\color{blue}{\frac{0.5}{1}} \cdot \frac{y}{a}\right) \]

      7. times-frac 81.4%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{1 \cdot a}} \]

      8. *-commutative 81.4%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 0.5}}{1 \cdot a} \]

      9. *-un-lft-identity 81.4%

         \[\leadsto x \cdot \frac{y \cdot 0.5}{\color{blue}{a}} \]

      10. *-commutative 81.4%

          \[\leadsto \color{blue}{\frac{y \cdot 0.5}{a} \cdot x} \]

      11. associate-/l* 81.1%

          \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right)} \cdot x \]

   5. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right) \cdot x} \]

   if 1.28e87 < y < 1.3000000000000001e155

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.1%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= y -1.7e-131)
     t_1
     (if (<= y 1.8e+27)
       (* -4.5 (/ (* t z) a))
       (if (<= y 1.28e+87)
         (* x (* y (/ 0.5 a)))
         (if (<= y 1.3e+155) (* -4.5 (* t (/ z a))) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if (y <= -1.7e-131) {
		tmp = t_1;
	} else if (y <= 1.8e+27) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 1.28e+87) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.3e+155) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    if (y <= (-1.7d-131)) then
        tmp = t_1
    else if (y <= 1.8d+27) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (y <= 1.28d+87) then
        tmp = x * (y * (0.5d0 / a))
    else if (y <= 1.3d+155) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if (y <= -1.7e-131) {
		tmp = t_1;
	} else if (y <= 1.8e+27) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 1.28e+87) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.3e+155) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if y <= -1.7e-131:
		tmp = t_1
	elif y <= 1.8e+27:
		tmp = -4.5 * ((t * z) / a)
	elif y <= 1.28e+87:
		tmp = x * (y * (0.5 / a))
	elif y <= 1.3e+155:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (y <= -1.7e-131)
		tmp = t_1;
	elseif (y <= 1.8e+27)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (y <= 1.28e+87)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (y <= 1.3e+155)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y * 0.5) / a);
	tmp = 0.0;
	if (y <= -1.7e-131)
		tmp = t_1;
	elseif (y <= 1.8e+27)
		tmp = -4.5 * ((t * z) / a);
	elseif (y <= 1.28e+87)
		tmp = x * (y * (0.5 / a));
	elseif (y <= 1.3e+155)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-131], t$95$1, If[LessEqual[y, 1.8e+27], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e+87], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+155], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999998e-131 or 1.3000000000000001e155 < y

   1. Initial program 89.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 63.6%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 69.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 69.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 69.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -1.69999999999999998e-131 < y < 1.79999999999999991e27

   1. Initial program 97.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 1.79999999999999991e27 < y < 1.28e87

   1. Initial program 86.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. associate-/l* 81.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a \cdot 2}} \]

      2. *-un-lft-identity 81.4%

         \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{a \cdot 2} \]

      3. *-commutative 81.4%

         \[\leadsto x \cdot \frac{1 \cdot y}{\color{blue}{2 \cdot a}} \]

      4. times-frac 81.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{y}{a}\right)} \]

      5. metadata-eval 81.4%

         \[\leadsto x \cdot \left(\color{blue}{0.5} \cdot \frac{y}{a}\right) \]

      6. metadata-eval 81.4%

         \[\leadsto x \cdot \left(\color{blue}{\frac{0.5}{1}} \cdot \frac{y}{a}\right) \]

      7. times-frac 81.4%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{1 \cdot a}} \]

      8. *-commutative 81.4%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 0.5}}{1 \cdot a} \]

      9. *-un-lft-identity 81.4%

         \[\leadsto x \cdot \frac{y \cdot 0.5}{\color{blue}{a}} \]

      10. *-commutative 81.4%

          \[\leadsto \color{blue}{\frac{y \cdot 0.5}{a} \cdot x} \]

      11. associate-/l* 81.1%

          \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right)} \cdot x \]

   5. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right) \cdot x} \]

   if 1.28e87 < y < 1.3000000000000001e155

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.1%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+295}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+238}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+295)
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 1e+238)
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
     (* x (* y (/ 0.5 a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+295) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 1e+238) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+295)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((x * y) <= 1d+238) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = x * (y * (0.5d0 / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+295) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 1e+238) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+295:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= 1e+238:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+295)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 1e+238)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+295)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= 1e+238)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = x * (y * (0.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+295], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+238], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999991e295

   1. Initial program 65.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 95.4%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 95.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 95.4%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 95.4%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 95.4%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -4.99999999999999991e295 < (*.f64 x y) < 1e238

   1. Initial program 98.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 97.3%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 97.3%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 98.3%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 98.3%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 98.3%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 98.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      2. associate-*r* 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot -9\right) \cdot t}\right)}{a \cdot 2} \]

      3. metadata-eval 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \left(z \cdot \color{blue}{\left(-9\right)}\right) \cdot t\right)}{a \cdot 2} \]

      4. distribute-rgt-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(-z \cdot 9\right)} \cdot t\right)}{a \cdot 2} \]

      5. distribute-lft-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{-\left(z \cdot 9\right) \cdot t}\right)}{a \cdot 2} \]

      6. fma-neg 98.3%

         \[\leadsto \frac{\color{blue}{x \cdot y - \left(z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      7. associate-*l* 98.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   6. Applied egg-rr 98.3%

      \[\leadsto \frac{\color{blue}{x \cdot y - z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   if 1e238 < (*.f64 x y)

   1. Initial program 76.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. associate-/l* 93.6%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a \cdot 2}} \]

      2. *-un-lft-identity 93.6%

         \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{a \cdot 2} \]

      3. *-commutative 93.6%

         \[\leadsto x \cdot \frac{1 \cdot y}{\color{blue}{2 \cdot a}} \]

      4. times-frac 93.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{y}{a}\right)} \]

      5. metadata-eval 93.6%

         \[\leadsto x \cdot \left(\color{blue}{0.5} \cdot \frac{y}{a}\right) \]

      6. metadata-eval 93.6%

         \[\leadsto x \cdot \left(\color{blue}{\frac{0.5}{1}} \cdot \frac{y}{a}\right) \]

      7. times-frac 93.6%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{1 \cdot a}} \]

      8. *-commutative 93.6%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 0.5}}{1 \cdot a} \]

      9. *-un-lft-identity 93.6%

         \[\leadsto x \cdot \frac{y \cdot 0.5}{\color{blue}{a}} \]

      10. *-commutative 93.6%

          \[\leadsto \color{blue}{\frac{y \cdot 0.5}{a} \cdot x} \]

      11. associate-/l* 93.6%

          \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right)} \cdot x \]

   5. Applied egg-rr 93.6%

      \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+295}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+238}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+238}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+225)
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 1e+238)
     (* (/ 0.5 a) (+ (* x y) (* -9.0 (* t z))))
     (* x (* y (/ 0.5 a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+225) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 1e+238) {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (t * z)));
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+225)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((x * y) <= 1d+238) then
        tmp = (0.5d0 / a) * ((x * y) + ((-9.0d0) * (t * z)))
    else
        tmp = x * (y * (0.5d0 / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+225) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 1e+238) {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (t * z)));
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+225:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= 1e+238:
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (t * z)))
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+225)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 1e+238)
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(-9.0 * Float64(t * z))));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+225)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= 1e+238)
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (t * z)));
	else
		tmp = x * (y * (0.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+225], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+238], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999986e225

   1. Initial program 72.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 96.4%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 96.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 96.4%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 96.4%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 96.4%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -1.99999999999999986e225 < (*.f64 x y) < 1e238

   1. Initial program 98.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 97.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 97.2%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 98.3%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 98.3%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 98.3%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 98.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 98.3%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      2. associate-*r* 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot -9\right) \cdot t}\right)}{a \cdot 2} \]

      3. metadata-eval 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \left(z \cdot \color{blue}{\left(-9\right)}\right) \cdot t\right)}{a \cdot 2} \]

      4. distribute-rgt-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(-z \cdot 9\right)} \cdot t\right)}{a \cdot 2} \]

      5. distribute-lft-neg-in 98.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{-\left(z \cdot 9\right) \cdot t}\right)}{a \cdot 2} \]

      6. fma-neg 98.3%

         \[\leadsto \frac{\color{blue}{x \cdot y - \left(z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      7. associate-*l* 98.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   6. Applied egg-rr 98.3%

      \[\leadsto \frac{\color{blue}{x \cdot y - z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]
   7. Step-by-step derivation

      1. *-un-lft-identity 98.3%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - z \cdot \left(9 \cdot t\right)\right)}}{a \cdot 2} \]

      2. times-frac 98.2%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{2}} \]

   8. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{2}} \]
   9. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{2} \cdot \frac{1}{a}} \]

      2. clear-num 98.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{2}{x \cdot y - z \cdot \left(9 \cdot t\right)}}} \cdot \frac{1}{a} \]

      3. frac-times 97.7%

         \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{2}{x \cdot y - z \cdot \left(9 \cdot t\right)} \cdot a}} \]

      4. metadata-eval 97.7%

         \[\leadsto \frac{\color{blue}{1}}{\frac{2}{x \cdot y - z \cdot \left(9 \cdot t\right)} \cdot a} \]

      5. associate-*r* 97.7%

         \[\leadsto \frac{1}{\frac{2}{x \cdot y - \color{blue}{\left(z \cdot 9\right) \cdot t}} \cdot a} \]

   10. Applied egg-rr 97.7%

       \[\leadsto \color{blue}{\frac{1}{\frac{2}{x \cdot y - \left(z \cdot 9\right) \cdot t} \cdot a}} \]
   11. Step-by-step derivation

       1. *-un-lft-identity 97.7%

          \[\leadsto \color{blue}{1 \cdot \frac{1}{\frac{2}{x \cdot y - \left(z \cdot 9\right) \cdot t} \cdot a}} \]

       2. associate-*l/ 97.7%

          \[\leadsto 1 \cdot \frac{1}{\color{blue}{\frac{2 \cdot a}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

       3. associate-*l* 97.8%

          \[\leadsto 1 \cdot \frac{1}{\frac{2 \cdot a}{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}} \]

   12. Applied egg-rr 97.8%

       \[\leadsto \color{blue}{1 \cdot \frac{1}{\frac{2 \cdot a}{x \cdot y - z \cdot \left(9 \cdot t\right)}}} \]
   13. Step-by-step derivation

       1. *-lft-identity 97.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{x \cdot y - z \cdot \left(9 \cdot t\right)}}} \]

       2. associate-/r/ 98.2%

          \[\leadsto \color{blue}{\frac{1}{2 \cdot a} \cdot \left(x \cdot y - z \cdot \left(9 \cdot t\right)\right)} \]

       3. associate-/r* 98.2%

          \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \left(x \cdot y - z \cdot \left(9 \cdot t\right)\right) \]

       4. metadata-eval 98.2%

          \[\leadsto \frac{\color{blue}{0.5}}{a} \cdot \left(x \cdot y - z \cdot \left(9 \cdot t\right)\right) \]

       5. *-commutative 98.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y - \color{blue}{\left(9 \cdot t\right) \cdot z}\right) \]

       6. associate-*r* 98.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y - \color{blue}{9 \cdot \left(t \cdot z\right)}\right) \]

       7. cancel-sign-sub-inv 98.2%

          \[\leadsto \frac{0.5}{a} \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)} \]

       8. metadata-eval 98.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right) \]

   14. Simplified 98.2%

       \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(t \cdot z\right)\right)} \]

   if 1e238 < (*.f64 x y)

   1. Initial program 76.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. associate-/l* 93.6%

         \[\leadsto \color{blue}{x \cdot \frac{y}{a \cdot 2}} \]

      2. *-un-lft-identity 93.6%

         \[\leadsto x \cdot \frac{\color{blue}{1 \cdot y}}{a \cdot 2} \]

      3. *-commutative 93.6%

         \[\leadsto x \cdot \frac{1 \cdot y}{\color{blue}{2 \cdot a}} \]

      4. times-frac 93.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{y}{a}\right)} \]

      5. metadata-eval 93.6%

         \[\leadsto x \cdot \left(\color{blue}{0.5} \cdot \frac{y}{a}\right) \]

      6. metadata-eval 93.6%

         \[\leadsto x \cdot \left(\color{blue}{\frac{0.5}{1}} \cdot \frac{y}{a}\right) \]

      7. times-frac 93.6%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{1 \cdot a}} \]

      8. *-commutative 93.6%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 0.5}}{1 \cdot a} \]

      9. *-un-lft-identity 93.6%

         \[\leadsto x \cdot \frac{y \cdot 0.5}{\color{blue}{a}} \]

      10. *-commutative 93.6%

          \[\leadsto \color{blue}{\frac{y \cdot 0.5}{a} \cdot x} \]

      11. associate-/l* 93.6%

          \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right)} \cdot x \]

   5. Applied egg-rr 93.6%

      \[\leadsto \color{blue}{\left(y \cdot \frac{0.5}{a}\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+238}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \frac{t \cdot z}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (/ (* t z) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((t * z) / a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * ((t * z) / a)
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((t * z) / a);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * ((t * z) / a)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(Float64(t * z) / a))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * ((t * z) / a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 47.4%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Add Preprocessing

Alternative 11: 50.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (t * (z / a))
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * (t * (z / a))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t * Float64(z / a)))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 47.4%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. associate-/l* 46.6%

      \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

5. Simplified 46.6%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Add Preprocessing

Developer target: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	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) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))