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

Percentage Accurate: 91.4% → 94.2%

Time: 10.4s

Alternatives: 11

Speedup: 0.8×

• 27.8% 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: 91.4% 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: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a} + \left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) 1e+272)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (+ (* (* z -4.5) (/ t a)) (* (* x 0.5) (/ y a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= 1e+272) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((z * -4.5) * (t / a)) + ((x * 0.5) * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x and y 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) - ((z * 9.0d0) * t)) <= 1d+272) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((z * (-4.5d0)) * (t / a)) + ((x * 0.5d0) * (y / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= 1e+272) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((z * -4.5) * (t / a)) + ((x * 0.5) * (y / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) - ((z * 9.0) * t)) <= 1e+272:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((z * -4.5) * (t / a)) + ((x * 0.5) * (y / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= 1e+272)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(z * -4.5) * Float64(t / a)) + Float64(Float64(x * 0.5) * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) - ((z * 9.0) * t)) <= 1e+272)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((z * -4.5) * (t / a)) + ((x * 0.5) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 1e+272], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * -4.5), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 1.0000000000000001e272

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   if 1.0000000000000001e272 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*l* 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around 0 72.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   5. Step-by-step derivation

      1. fma-def 72.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 82.4%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/r/ 79.7%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{a} \cdot z}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      4. associate-*r/ 94.4%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)}\right) \]

   6. Simplified 94.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)} \]
   7. Step-by-step derivation

      1. fma-udef 94.4%

         \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right) + 0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

      2. *-commutative 94.4%

         \[\leadsto -4.5 \cdot \color{blue}{\left(z \cdot \frac{t}{a}\right)} + 0.5 \cdot \left(x \cdot \frac{y}{a}\right) \]

      3. associate-*r* 94.4%

         \[\leadsto \color{blue}{\left(-4.5 \cdot z\right) \cdot \frac{t}{a}} + 0.5 \cdot \left(x \cdot \frac{y}{a}\right) \]

      4. associate-*r* 94.4%

         \[\leadsto \left(-4.5 \cdot z\right) \cdot \frac{t}{a} + \color{blue}{\left(0.5 \cdot x\right) \cdot \frac{y}{a}} \]

   8. Applied egg-rr 94.4%

      \[\leadsto \color{blue}{\left(-4.5 \cdot z\right) \cdot \frac{t}{a} + \left(0.5 \cdot x\right) \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a} + \left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 2: 93.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+262}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + t \cdot \left(z \cdot -9\right)}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 1e+262)
   (/ 0.5 (/ a (+ (* x y) (* t (* z -9.0)))))
   (* 0.5 (* x (/ y a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+262) {
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= 1d+262) then
        tmp = 0.5d0 / (a / ((x * y) + (t * (z * (-9.0d0)))))
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+262) {
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 1e+262:
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))))
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 1e+262)
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) + Float64(t * Float64(z * -9.0)))));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 1e+262)
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))));
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 1e+262], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 1e262

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 95.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 95.6%

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

      2. cancel-sign-sub-inv 95.6%

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

      3. metadata-eval 95.6%

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

      4. +-commutative 95.6%

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

      5. associate-/l* 95.6%

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

      6. +-commutative 95.6%

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

      7. metadata-eval 95.6%

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

      8. cancel-sign-sub-inv 95.6%

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

      9. fma-neg 96.0%

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

      10. *-commutative 96.0%

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

      11. distribute-lft-neg-in 96.0%

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

      12. metadata-eval 96.0%

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

      13. *-commutative 96.0%

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

      14. *-commutative 96.0%

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

      15. associate-*l* 96.0%

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

   6. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]
   7. Step-by-step derivation

      1. fma-udef 95.6%

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

   8. Applied egg-rr 95.6%

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

   if 1e262 < (*.f64 x y)

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*l* 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in x around inf 74.3%

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

      1. associate-*r/ 99.8%

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

   6. Simplified 99.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+262}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + t \cdot \left(z \cdot -9\right)}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 3: 93.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 1e+262)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* 0.5 (* x (/ y a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+262) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= 1d+262) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+262) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 1e+262:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 1e+262)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 1e+262)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 1e+262], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 1e262

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   if 1e262 < (*.f64 x y)

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*l* 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in x around inf 74.3%

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

      1. associate-*r/ 99.8%

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

   6. Simplified 99.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2000000000.0)
   (/ 0.5 (/ a (* x y)))
   (if (<= (* x y) 2e+90) (* -4.5 (/ (* z t) a)) (* 0.5 (* x (/ y a))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 2e+90) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x and y 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) <= (-2000000000.0d0)) then
        tmp = 0.5d0 / (a / (x * y))
    else if ((x * y) <= 2d+90) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 2e+90) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = 0.5 / (a / (x * y))
	elif (x * y) <= 2e+90:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	elseif (Float64(x * y) <= 2e+90)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = 0.5 / (a / (x * y));
	elseif ((x * y) <= 2e+90)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+90], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e9

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around 0 93.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 93.9%

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

      2. cancel-sign-sub-inv 93.9%

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

      3. metadata-eval 93.9%

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

      4. +-commutative 93.9%

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

      5. associate-/l* 93.7%

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

      6. +-commutative 93.7%

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

      7. metadata-eval 93.7%

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

      8. cancel-sign-sub-inv 93.7%

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

      9. fma-neg 95.3%

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

      10. *-commutative 95.3%

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

      11. distribute-lft-neg-in 95.3%

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

      12. metadata-eval 95.3%

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

      13. *-commutative 95.3%

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

      14. *-commutative 95.3%

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

      15. associate-*l* 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in x around inf 78.8%

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

   if -2e9 < (*.f64 x y) < 1.99999999999999993e90

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around 0 75.3%

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

   if 1.99999999999999993e90 < (*.f64 x y)

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around inf 80.1%

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

      1. associate-*r/ 90.6%

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

   6. Simplified 90.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 5: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2000000000.0)
   (/ 0.5 (/ a (* x y)))
   (if (<= (* x y) 2e+90) (* -4.5 (/ (* z t) a)) (/ 0.5 (/ (/ a y) x)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 2e+90) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 / ((a / y) / x);
	}
	return tmp;
}

Fortran

NOTE: x and y 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) <= (-2000000000.0d0)) then
        tmp = 0.5d0 / (a / (x * y))
    else if ((x * y) <= 2d+90) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 / ((a / y) / x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 2e+90) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 / ((a / y) / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = 0.5 / (a / (x * y))
	elif (x * y) <= 2e+90:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 / ((a / y) / x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	elseif (Float64(x * y) <= 2e+90)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 / Float64(Float64(a / y) / x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = 0.5 / (a / (x * y));
	elseif ((x * y) <= 2e+90)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 / ((a / y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+90], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(N[(a / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e9

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around 0 93.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 93.9%

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

      2. cancel-sign-sub-inv 93.9%

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

      3. metadata-eval 93.9%

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

      4. +-commutative 93.9%

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

      5. associate-/l* 93.7%

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

      6. +-commutative 93.7%

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

      7. metadata-eval 93.7%

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

      8. cancel-sign-sub-inv 93.7%

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

      9. fma-neg 95.3%

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

      10. *-commutative 95.3%

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

      11. distribute-lft-neg-in 95.3%

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

      12. metadata-eval 95.3%

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

      13. *-commutative 95.3%

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

      14. *-commutative 95.3%

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

      15. associate-*l* 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in x around inf 78.8%

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

   if -2e9 < (*.f64 x y) < 1.99999999999999993e90

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around 0 75.3%

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

   if 1.99999999999999993e90 < (*.f64 x y)

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 84.9%

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

      2. cancel-sign-sub-inv 84.9%

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

      3. metadata-eval 84.9%

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

      4. +-commutative 84.9%

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

      5. associate-/l* 84.9%

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

      6. +-commutative 84.9%

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

      7. metadata-eval 84.9%

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

      8. cancel-sign-sub-inv 84.9%

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

      9. fma-neg 84.9%

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

      10. *-commutative 84.9%

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

      11. distribute-lft-neg-in 84.9%

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

      12. metadata-eval 84.9%

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

      13. *-commutative 84.9%

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

      14. *-commutative 84.9%

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

      15. associate-*l* 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in x around inf 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/r* 90.8%

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

   9. Simplified 90.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \]

Alternative 6: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2000000000.0)
   (/ (* x (* y 0.5)) a)
   (if (<= (* x y) 2e+90) (* -4.5 (/ (* z t) a)) (/ 0.5 (/ (/ a y) x)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 2e+90) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 / ((a / y) / x);
	}
	return tmp;
}

Fortran

NOTE: x and y 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) <= (-2000000000.0d0)) then
        tmp = (x * (y * 0.5d0)) / a
    else if ((x * y) <= 2d+90) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 / ((a / y) / x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 2e+90) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 / ((a / y) / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = (x * (y * 0.5)) / a
	elif (x * y) <= 2e+90:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 / ((a / y) / x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (Float64(x * y) <= 2e+90)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 / Float64(Float64(a / y) / x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = (x * (y * 0.5)) / a;
	elseif ((x * y) <= 2e+90)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 / ((a / y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+90], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(N[(a / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e9

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around 0 93.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 93.9%

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

      2. cancel-sign-sub-inv 93.9%

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

      3. metadata-eval 93.9%

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

      4. +-commutative 93.9%

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

      5. associate-/l* 93.7%

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

      6. +-commutative 93.7%

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

      7. metadata-eval 93.7%

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

      8. cancel-sign-sub-inv 93.7%

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

      9. fma-neg 95.3%

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

      10. *-commutative 95.3%

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

      11. distribute-lft-neg-in 95.3%

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

      12. metadata-eval 95.3%

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

      13. *-commutative 95.3%

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

      14. *-commutative 95.3%

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

      15. associate-*l* 95.3%

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

   6. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]
   7. Step-by-step derivation

      1. fma-udef 93.7%

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

   8. Applied egg-rr 93.7%

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

   9. Taylor expanded in x around inf 78.9%

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

       1. *-commutative 78.9%

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

       2. associate-*l/ 78.9%

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

       3. associate-*l* 78.9%

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

   11. Simplified 78.9%

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

   if -2e9 < (*.f64 x y) < 1.99999999999999993e90

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around 0 75.3%

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

   if 1.99999999999999993e90 < (*.f64 x y)

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 84.9%

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

      2. cancel-sign-sub-inv 84.9%

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

      3. metadata-eval 84.9%

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

      4. +-commutative 84.9%

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

      5. associate-/l* 84.9%

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

      6. +-commutative 84.9%

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

      7. metadata-eval 84.9%

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

      8. cancel-sign-sub-inv 84.9%

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

      9. fma-neg 84.9%

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

      10. *-commutative 84.9%

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

      11. distribute-lft-neg-in 84.9%

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

      12. metadata-eval 84.9%

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

      13. *-commutative 84.9%

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

      14. *-commutative 84.9%

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

      15. associate-*l* 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in x around inf 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/r* 90.8%

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

   9. Simplified 90.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \]

Alternative 7: 65.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-33}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+81)
   (* -4.5 (/ z (/ a t)))
   (if (<= z 2.95e-33) (* 0.5 (* x (/ y a))) (* -4.5 (/ t (/ a z))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+81) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 2.95e-33) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.8d+81)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if (z <= 2.95d-33) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+81) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 2.95e-33) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+81:
		tmp = -4.5 * (z / (a / t))
	elif z <= 2.95e-33:
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+81)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (z <= 2.95e-33)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+81)
		tmp = -4.5 * (z / (a / t));
	elseif (z <= 2.95e-33)
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+81], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e-33], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999995e81

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

      1. associate-/r/ 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. clear-num 83.0%

         \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right) \]

      3. un-div-inv 83.0%

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

   10. Applied egg-rr 83.0%

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

   if -2.79999999999999995e81 < z < 2.94999999999999993e-33

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 63.8%

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

      1. associate-*r/ 63.0%

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

   6. Simplified 63.0%

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

   if 2.94999999999999993e-33 < z

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 55.2%

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

   6. Simplified 55.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-33}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 65.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-32}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+80)
   (* -4.5 (/ z (/ a t)))
   (if (<= z 1.12e-32) (* 0.5 (/ x (/ a y))) (* -4.5 (/ t (/ a z))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+80) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 1.12e-32) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+80)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if (z <= 1.12d-32) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+80) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 1.12e-32) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+80:
		tmp = -4.5 * (z / (a / t))
	elif z <= 1.12e-32:
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+80)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (z <= 1.12e-32)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+80)
		tmp = -4.5 * (z / (a / t));
	elseif (z <= 1.12e-32)
		tmp = 0.5 * (x / (a / y));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+80], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-32], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000004e80

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

      1. associate-/r/ 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. clear-num 83.0%

         \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right) \]

      3. un-div-inv 83.0%

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

   10. Applied egg-rr 83.0%

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

   if -2.30000000000000004e80 < z < 1.12e-32

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   if 1.12e-32 < z

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 55.2%

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

   6. Simplified 55.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-32}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-34}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+80)
   (* -4.5 (/ z (/ a t)))
   (if (<= z 8e-34) (* 0.5 (/ x (/ a y))) (* z (* -4.5 (/ t a))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+80) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 8e-34) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = z * (-4.5 * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+80)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if (z <= 8d-34) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = z * ((-4.5d0) * (t / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+80) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 8e-34) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = z * (-4.5 * (t / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+80:
		tmp = -4.5 * (z / (a / t))
	elif z <= 8e-34:
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = z * (-4.5 * (t / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+80)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (z <= 8e-34)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+80)
		tmp = -4.5 * (z / (a / t));
	elseif (z <= 8e-34)
		tmp = 0.5 * (x / (a / y));
	else
		tmp = z * (-4.5 * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+80], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-34], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000004e80

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

      1. associate-/r/ 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. clear-num 83.0%

         \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right) \]

      3. un-div-inv 83.0%

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

   10. Applied egg-rr 83.0%

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

   if -2.30000000000000004e80 < z < 7.99999999999999942e-34

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   if 7.99999999999999942e-34 < z

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 55.2%

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

   6. Simplified 55.2%

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

      1. associate-*r/ 55.1%

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

      2. associate-/l* 55.1%

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

      3. associate-/l/ 53.6%

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

   8. Applied egg-rr 53.6%

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

      1. associate-/r* 58.0%

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

      2. associate-/r/ 58.0%

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

      3. un-div-inv 58.0%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{1}{\frac{a}{t}}\right)} \cdot z \]

      4. clear-num 58.1%

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

      5. *-commutative 58.1%

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

   10. Applied egg-rr 58.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-34}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 10: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-32}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t}{\frac{a}{-4.5}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+81)
   (* -4.5 (/ z (/ a t)))
   (if (<= z 3.1e-32) (* 0.5 (/ x (/ a y))) (* z (/ t (/ a -4.5))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+81) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 3.1e-32) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = z * (t / (a / -4.5));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.8d+81)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if (z <= 3.1d-32) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = z * (t / (a / (-4.5d0)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+81) {
		tmp = -4.5 * (z / (a / t));
	} else if (z <= 3.1e-32) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = z * (t / (a / -4.5));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+81:
		tmp = -4.5 * (z / (a / t))
	elif z <= 3.1e-32:
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = z * (t / (a / -4.5))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+81)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (z <= 3.1e-32)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(z * Float64(t / Float64(a / -4.5)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+81)
		tmp = -4.5 * (z / (a / t));
	elseif (z <= 3.1e-32)
		tmp = 0.5 * (x / (a / y));
	else
		tmp = z * (t / (a / -4.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+81], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-32], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t / N[(a / -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999995e81

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

      1. associate-/r/ 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. clear-num 83.0%

         \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right) \]

      3. un-div-inv 83.0%

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

   10. Applied egg-rr 83.0%

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

   if -2.79999999999999995e81 < z < 3.10000000000000011e-32

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   if 3.10000000000000011e-32 < z

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 55.2%

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

      2. associate-*r/ 55.1%

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

   6. Simplified 55.1%

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

      1. associate-/r/ 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-/l* 58.1%

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

   8. Applied egg-rr 58.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-32}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t}{\frac{a}{-4.5}}\\ \end{array} \]

Alternative 11: 51.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x and y 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) * (z * (t / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. *-commutative 93.8%

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

   2. *-commutative 93.8%

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

   3. associate-*l* 93.8%

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

3. Simplified 93.8%

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

4. Taylor expanded in x around 0 52.2%

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

   1. associate-/l* 50.3%

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

6. Simplified 50.3%

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

   1. associate-/r/ 53.6%

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

8. Applied egg-rr 53.6%

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

9. Final simplification 53.6%

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

Developer target: 93.2% accurate, 0.7× 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 2023320 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (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)))