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

Percentage Accurate: 91.1% → 94.6%

Time: 10.6s

Alternatives: 12

Speedup: 0.5×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 91.1% 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: 94.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{elif}\;t_1 \leq 200000:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - \frac{\left(z \cdot t\right) \cdot 4.5}{a}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* t (* z 9.0))))
   (if (<= t_1 -2e+296)
     (* (/ t a) (* z -4.5))
     (if (<= t_1 2e-239)
       (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
       (if (<= t_1 200000.0)
         (- (/ (* x (/ y a)) 2.0) (/ (* (* z t) 4.5) a))
         (if (<= t_1 2e+294)
           (/ (- (* x y) t_1) (* a 2.0))
           (* (/ z a) (* t -4.5))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -2e+296) {
		tmp = (t / a) * (z * -4.5);
	} else if (t_1 <= 2e-239) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else if (t_1 <= 200000.0) {
		tmp = ((x * (y / a)) / 2.0) - (((z * t) * 4.5) / a);
	} else if (t_1 <= 2e+294) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = t * (z * 9.0d0)
    if (t_1 <= (-2d+296)) then
        tmp = (t / a) * (z * (-4.5d0))
    else if (t_1 <= 2d-239) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else if (t_1 <= 200000.0d0) then
        tmp = ((x * (y / a)) / 2.0d0) - (((z * t) * 4.5d0) / a)
    else if (t_1 <= 2d+294) then
        tmp = ((x * y) - t_1) / (a * 2.0d0)
    else
        tmp = (z / a) * (t * (-4.5d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -2e+296) {
		tmp = (t / a) * (z * -4.5);
	} else if (t_1 <= 2e-239) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else if (t_1 <= 200000.0) {
		tmp = ((x * (y / a)) / 2.0) - (((z * t) * 4.5) / a);
	} else if (t_1 <= 2e+294) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (z * 9.0)
	tmp = 0
	if t_1 <= -2e+296:
		tmp = (t / a) * (z * -4.5)
	elif t_1 <= 2e-239:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	elif t_1 <= 200000.0:
		tmp = ((x * (y / a)) / 2.0) - (((z * t) * 4.5) / a)
	elif t_1 <= 2e+294:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = (z / a) * (t * -4.5)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+296)
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	elseif (t_1 <= 2e-239)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	elseif (t_1 <= 200000.0)
		tmp = Float64(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(Float64(Float64(z * t) * 4.5) / a));
	elseif (t_1 <= 2e+294)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z * 9.0);
	tmp = 0.0;
	if (t_1 <= -2e+296)
		tmp = (t / a) * (z * -4.5);
	elseif (t_1 <= 2e-239)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	elseif (t_1 <= 200000.0)
		tmp = ((x * (y / a)) / 2.0) - (((z * t) * 4.5) / a);
	elseif (t_1 <= 2e+294)
		tmp = ((x * y) - t_1) / (a * 2.0);
	else
		tmp = (z / a) * (t * -4.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+296], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-239], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200000.0], N[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(N[(N[(z * t), $MachinePrecision] * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+294], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 z 9) t) < -1.99999999999999996e296

   1. Initial program 68.0%

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

      1. associate-*l* 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in x around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/l* 99.8%

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

      3. associate-*l/ 99.9%

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

   6. Simplified 99.9%

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

      1. associate-*l/ 99.8%

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

      2. associate-/r/ 99.8%

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

      3. associate-*l* 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -1.99999999999999996e296 < (*.f64 (*.f64 z 9) t) < 2.0000000000000002e-239

   1. Initial program 96.5%

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

      1. 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%

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

   if 2.0000000000000002e-239 < (*.f64 (*.f64 z 9) t) < 2e5

   1. Initial program 87.5%

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

      1. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

      1. div-sub 87.5%

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

      2. sub-neg 87.5%

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

      3. *-commutative 87.5%

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

      4. times-frac 93.0%

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

      5. div-inv 92.9%

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

      6. associate-*r* 92.9%

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

      7. *-commutative 92.9%

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

      8. associate-*l* 93.0%

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

      9. *-commutative 93.0%

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

      10. associate-/r* 93.0%

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

      11. metadata-eval 93.0%

          \[\leadsto \frac{x}{2} \cdot \frac{y}{a} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   5. Applied egg-rr 93.0%

      \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 93.0%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-*l/ 93.0%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 93.0%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 93.0%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. associate-*l* 93.0%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(z \cdot t\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      6. *-commutative 93.0%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right)} \cdot \left(9 \cdot 0.5\right)}{a} \]

      7. metadata-eval 93.0%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\left(t \cdot z\right) \cdot \color{blue}{4.5}}{a} \]

   7. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{a}}{2} - \frac{\left(t \cdot z\right) \cdot 4.5}{a}} \]

   if 2e5 < (*.f64 (*.f64 z 9) t) < 2.00000000000000013e294

   1. Initial program 99.6%

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

   if 2.00000000000000013e294 < (*.f64 (*.f64 z 9) t)

   1. Initial program 52.6%

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

      1. associate-*l* 57.7%

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

   3. Simplified 57.7%

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

   4. Taylor expanded in x around 0 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/l* 89.1%

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

      3. associate-*l/ 89.0%

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

   6. Simplified 89.0%

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

      1. clear-num 89.0%

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

      2. associate-/r/ 89.1%

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

      3. clear-num 89.3%

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

   8. Applied egg-rr 89.3%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(t \cdot -4.5\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 200000:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - \frac{\left(z \cdot t\right) \cdot 4.5}{a}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \]

Alternative 2: 92.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, \frac{x \cdot \left(y \cdot 0.5\right)}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= (* a 2.0) 2e-59)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (fma -4.5 (* z (/ t a)) (/ (* x (* y 0.5)) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e-59) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = fma(-4.5, (z * (t / a)), ((x * (y * 0.5)) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 2e-59)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(Float64(x * Float64(y * 0.5)) / a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(a * 2.0), $MachinePrecision], 2e-59], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 2.0000000000000001e-59

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. *-commutative 92.0%

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

      3. cancel-sign-sub-inv 92.0%

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

      4. fma-def 93.1%

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

      5. distribute-rgt-neg-in 93.1%

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

      6. associate-*r* 93.6%

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

      7. distribute-lft-neg-in 93.6%

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

      8. *-commutative 93.6%

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

      9. distribute-rgt-neg-in 93.6%

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

      10. metadata-eval 93.6%

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

   3. Simplified 93.6%

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

   if 2.0000000000000001e-59 < (*.f64 a 2)

   1. Initial program 83.6%

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

      1. associate-*l* 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in x around 0 83.6%

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

      1. fma-def 83.6%

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

      2. associate-/l* 90.9%

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

      3. associate-/r/ 87.7%

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

      4. associate-*r/ 87.7%

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

      5. *-commutative 87.7%

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

      6. associate-*r* 87.7%

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

   6. Simplified 87.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, \frac{x \cdot \left(y \cdot 0.5\right)}{a}\right)\\ \end{array} \]

Alternative 3: 95.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* t (* z 9.0))))
   (if (<= t_1 -2e+296)
     (* (/ t a) (* z -4.5))
     (if (<= t_1 2e+294)
       (/ (- (* x y) t_1) (* a 2.0))
       (* (/ z a) (* t -4.5))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -2e+296) {
		tmp = (t / a) * (z * -4.5);
	} else if (t_1 <= 2e+294) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = t * (z * 9.0d0)
    if (t_1 <= (-2d+296)) then
        tmp = (t / a) * (z * (-4.5d0))
    else if (t_1 <= 2d+294) then
        tmp = ((x * y) - t_1) / (a * 2.0d0)
    else
        tmp = (z / a) * (t * (-4.5d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -2e+296) {
		tmp = (t / a) * (z * -4.5);
	} else if (t_1 <= 2e+294) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (z * 9.0)
	tmp = 0
	if t_1 <= -2e+296:
		tmp = (t / a) * (z * -4.5)
	elif t_1 <= 2e+294:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = (z / a) * (t * -4.5)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+296)
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	elseif (t_1 <= 2e+294)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z * 9.0);
	tmp = 0.0;
	if (t_1 <= -2e+296)
		tmp = (t / a) * (z * -4.5);
	elseif (t_1 <= 2e+294)
		tmp = ((x * y) - t_1) / (a * 2.0);
	else
		tmp = (z / a) * (t * -4.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+296], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+294], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z 9) t) < -1.99999999999999996e296

   1. Initial program 68.0%

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

      1. associate-*l* 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in x around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/l* 99.8%

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

      3. associate-*l/ 99.9%

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

   6. Simplified 99.9%

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

      1. associate-*l/ 99.8%

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

      2. associate-/r/ 99.8%

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

      3. associate-*l* 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -1.99999999999999996e296 < (*.f64 (*.f64 z 9) t) < 2.00000000000000013e294

   1. Initial program 95.1%

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

   if 2.00000000000000013e294 < (*.f64 (*.f64 z 9) t)

   1. Initial program 52.6%

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

      1. associate-*l* 57.7%

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

   3. Simplified 57.7%

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

   4. Taylor expanded in x around 0 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/l* 89.1%

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

      3. associate-*l/ 89.0%

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

   6. Simplified 89.0%

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

      1. clear-num 89.0%

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

      2. associate-/r/ 89.1%

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

      3. clear-num 89.3%

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

   8. Applied egg-rr 89.3%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \]

Alternative 4: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+174} \lor \neg \left(z \leq -2.3 \cdot 10^{+151}\right) \land \left(z \leq -2.1 \cdot 10^{+66} \lor \neg \left(z \leq 6.2 \cdot 10^{-118}\right)\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.4e+174)
         (and (not (<= z -2.3e+151))
              (or (<= z -2.1e+66) (not (<= z 6.2e-118)))))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (* x (/ y a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+174) || (!(z <= -2.3e+151) && ((z <= -2.1e+66) || !(z <= 6.2e-118)))) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.4d+174)) .or. (.not. (z <= (-2.3d+151))) .and. (z <= (-2.1d+66)) .or. (.not. (z <= 6.2d-118))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+174) || (!(z <= -2.3e+151) && ((z <= -2.1e+66) || !(z <= 6.2e-118)))) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.4e+174) or (not (z <= -2.3e+151) and ((z <= -2.1e+66) or not (z <= 6.2e-118))):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.4e+174) || (!(z <= -2.3e+151) && ((z <= -2.1e+66) || !(z <= 6.2e-118))))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.4e+174) || (~((z <= -2.3e+151)) && ((z <= -2.1e+66) || ~((z <= 6.2e-118)))))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[z, -5.4e+174], And[N[Not[LessEqual[z, -2.3e+151]], $MachinePrecision], Or[LessEqual[z, -2.1e+66], N[Not[LessEqual[z, 6.2e-118]], $MachinePrecision]]]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3999999999999998e174 or -2.3000000000000001e151 < z < -2.10000000000000005e66 or 6.2000000000000002e-118 < z

   1. Initial program 85.9%

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

      1. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around 0 63.0%

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

      1. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   if -5.3999999999999998e174 < z < -2.3000000000000001e151 or -2.10000000000000005e66 < z < 6.2000000000000002e-118

   1. Initial program 94.6%

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

      1. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 77.6%

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

      1. associate-*r/ 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+174} \lor \neg \left(z \leq -2.3 \cdot 10^{+151}\right) \land \left(z \leq -2.1 \cdot 10^{+66} \lor \neg \left(z \leq 6.2 \cdot 10^{-118}\right)\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 5: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+174} \lor \neg \left(z \leq -3 \cdot 10^{+149} \lor \neg \left(z \leq -2.45 \cdot 10^{+69}\right) \land z \leq 6 \cdot 10^{-118}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.4e+174)
         (not (or (<= z -3e+149) (and (not (<= z -2.45e+69)) (<= z 6e-118)))))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (/ x (/ a y)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+174) || !((z <= -3e+149) || (!(z <= -2.45e+69) && (z <= 6e-118)))) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.4d+174)) .or. (.not. (z <= (-3d+149)) .or. (.not. (z <= (-2.45d+69))) .and. (z <= 6d-118))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+174) || !((z <= -3e+149) || (!(z <= -2.45e+69) && (z <= 6e-118)))) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.4e+174) or not ((z <= -3e+149) or (not (z <= -2.45e+69) and (z <= 6e-118))):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.4e+174) || !((z <= -3e+149) || (!(z <= -2.45e+69) && (z <= 6e-118))))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.4e+174) || ~(((z <= -3e+149) || (~((z <= -2.45e+69)) && (z <= 6e-118)))))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[z, -5.4e+174], N[Not[Or[LessEqual[z, -3e+149], And[N[Not[LessEqual[z, -2.45e+69]], $MachinePrecision], LessEqual[z, 6e-118]]]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3999999999999998e174 or -3.00000000000000003e149 < z < -2.45e69 or 6.00000000000000035e-118 < z

   1. Initial program 85.9%

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

      1. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around 0 63.0%

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

      1. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   if -5.3999999999999998e174 < z < -3.00000000000000003e149 or -2.45e69 < z < 6.00000000000000035e-118

   1. Initial program 94.6%

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

      1. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 77.6%

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

      1. associate-/l* 72.6%

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

   6. Simplified 72.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+174} \lor \neg \left(z \leq -3 \cdot 10^{+149} \lor \neg \left(z \leq -2.45 \cdot 10^{+69}\right) \land z \leq 6 \cdot 10^{-118}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -3.45 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-92} \lor \neg \left(x \leq 8.5 \cdot 10^{-172}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* 0.5 (/ x (/ a y)))))
   (if (<= x -3.45e+115)
     t_1
     (if (<= x -3.8e-30)
       (* z (* -4.5 (/ t a)))
       (if (or (<= x -5.1e-92) (not (<= x 8.5e-172)))
         t_1
         (* -4.5 (/ t (/ a z))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -3.45e+115) {
		tmp = t_1;
	} else if (x <= -3.8e-30) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x <= -5.1e-92) || !(x <= 8.5e-172)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = 0.5d0 * (x / (a / y))
    if (x <= (-3.45d+115)) then
        tmp = t_1
    else if (x <= (-3.8d-30)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if ((x <= (-5.1d-92)) .or. (.not. (x <= 8.5d-172))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -3.45e+115) {
		tmp = t_1;
	} else if (x <= -3.8e-30) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x <= -5.1e-92) || !(x <= 8.5e-172)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if x <= -3.45e+115:
		tmp = t_1
	elif x <= -3.8e-30:
		tmp = z * (-4.5 * (t / a))
	elif (x <= -5.1e-92) or not (x <= 8.5e-172):
		tmp = t_1
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -3.45e+115)
		tmp = t_1;
	elseif (x <= -3.8e-30)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif ((x <= -5.1e-92) || !(x <= 8.5e-172))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if (x <= -3.45e+115)
		tmp = t_1;
	elseif (x <= -3.8e-30)
		tmp = z * (-4.5 * (t / a));
	elseif ((x <= -5.1e-92) || ~((x <= 8.5e-172)))
		tmp = t_1;
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.45e+115], t$95$1, If[LessEqual[x, -3.8e-30], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.1e-92], N[Not[LessEqual[x, 8.5e-172]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.44999999999999983e115 or -3.8000000000000003e-30 < x < -5.09999999999999972e-92 or 8.49999999999999963e-172 < x

   1. Initial program 92.4%

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

      1. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 65.6%

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

      1. associate-/l* 63.7%

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

   6. Simplified 63.7%

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

   if -3.44999999999999983e115 < x < -3.8000000000000003e-30

   1. Initial program 88.4%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around 0 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-/l* 58.5%

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

      3. associate-*l/ 58.5%

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

   6. Simplified 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*r/ 58.5%

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

      3. associate-/r/ 55.8%

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

      4. associate-*r* 55.8%

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

   8. Applied egg-rr 55.8%

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

   if -5.09999999999999972e-92 < x < 8.49999999999999963e-172

   1. Initial program 86.1%

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

      1. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in x around 0 69.3%

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

      1. associate-/l* 78.9%

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

   6. Simplified 78.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.45 \cdot 10^{+115}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-92} \lor \neg \left(x \leq 8.5 \cdot 10^{-172}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-92}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-172}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* 0.5 (/ x (/ a y)))))
   (if (<= x -3.9e+117)
     t_1
     (if (<= x -1.05e-30)
       (* z (* -4.5 (/ t a)))
       (if (<= x -8e-92)
         (* (* y 0.5) (/ x a))
         (if (<= x 8.5e-172) (* -4.5 (/ t (/ a z))) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -3.9e+117) {
		tmp = t_1;
	} else if (x <= -1.05e-30) {
		tmp = z * (-4.5 * (t / a));
	} else if (x <= -8e-92) {
		tmp = (y * 0.5) * (x / a);
	} else if (x <= 8.5e-172) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = 0.5d0 * (x / (a / y))
    if (x <= (-3.9d+117)) then
        tmp = t_1
    else if (x <= (-1.05d-30)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if (x <= (-8d-92)) then
        tmp = (y * 0.5d0) * (x / a)
    else if (x <= 8.5d-172) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -3.9e+117) {
		tmp = t_1;
	} else if (x <= -1.05e-30) {
		tmp = z * (-4.5 * (t / a));
	} else if (x <= -8e-92) {
		tmp = (y * 0.5) * (x / a);
	} else if (x <= 8.5e-172) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if x <= -3.9e+117:
		tmp = t_1
	elif x <= -1.05e-30:
		tmp = z * (-4.5 * (t / a))
	elif x <= -8e-92:
		tmp = (y * 0.5) * (x / a)
	elif x <= 8.5e-172:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -3.9e+117)
		tmp = t_1;
	elseif (x <= -1.05e-30)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (x <= -8e-92)
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (x <= 8.5e-172)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if (x <= -3.9e+117)
		tmp = t_1;
	elseif (x <= -1.05e-30)
		tmp = z * (-4.5 * (t / a));
	elseif (x <= -8e-92)
		tmp = (y * 0.5) * (x / a);
	elseif (x <= 8.5e-172)
		tmp = -4.5 * (t / (a / z));
	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.
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[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+117], t$95$1, If[LessEqual[x, -1.05e-30], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-92], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-172], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.8999999999999999e117 or 8.49999999999999963e-172 < x

   1. Initial program 91.9%

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

      1. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 65.9%

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

      1. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   if -3.8999999999999999e117 < x < -1.0500000000000001e-30

   1. Initial program 88.4%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around 0 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-/l* 58.5%

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

      3. associate-*l/ 58.5%

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

   6. Simplified 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*r/ 58.5%

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

      3. associate-/r/ 55.8%

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

      4. associate-*r* 55.8%

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

   8. Applied egg-rr 55.8%

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

   if -1.0500000000000001e-30 < x < -7.9999999999999999e-92

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-/l* 99.2%

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

      6. +-commutative 99.2%

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

      7. metadata-eval 99.2%

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

      8. cancel-sign-sub-inv 99.2%

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

      9. fma-neg 99.2%

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

      10. *-commutative 99.2%

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

      11. distribute-lft-neg-in 99.2%

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

      12. metadata-eval 99.2%

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

      13. *-commutative 99.2%

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

      14. associate-*l* 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in x around inf 60.8%

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

      1. associate-/r* 61.0%

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

   9. Simplified 61.0%

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

       1. metadata-eval 61.0%

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

       2. associate-*l/ 61.0%

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

       3. div-inv 61.0%

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

       4. associate-*l/ 52.7%

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

       5. div-inv 52.7%

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

       6. clear-num 53.0%

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

       7. associate-/r/ 61.2%

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

       8. associate-*l* 61.2%

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

   11. Applied egg-rr 61.2%

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

   if -7.9999999999999999e-92 < x < 8.49999999999999963e-172

   1. Initial program 86.1%

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

      1. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in x around 0 69.3%

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

      1. associate-/l* 78.9%

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

   6. Simplified 78.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-92}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-172}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0008:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -0.0008)
   (/ 0.5 (/ a (* x y)))
   (if (<= (* x y) 5e+45) (* -4.5 (/ t (/ a z))) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -0.0008) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 5e+45) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-0.0008d0)) then
        tmp = 0.5d0 / (a / (x * y))
    else if ((x * y) <= 5d+45) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -0.0008) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 5e+45) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -0.0008:
		tmp = 0.5 / (a / (x * y))
	elif (x * y) <= 5e+45:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -0.0008)
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	elseif (Float64(x * y) <= 5e+45)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -0.0008)
		tmp = 0.5 / (a / (x * y));
	elseif ((x * y) <= 5e+45)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -0.0008], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+45], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.00000000000000038e-4

   1. Initial program 89.3%

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

      1. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in a around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. cancel-sign-sub-inv 89.3%

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

      3. metadata-eval 89.3%

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

      4. +-commutative 89.3%

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

      5. associate-/l* 89.2%

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

      6. +-commutative 89.2%

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

      7. metadata-eval 89.2%

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

      8. cancel-sign-sub-inv 89.2%

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

      9. fma-neg 92.4%

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

      10. *-commutative 92.4%

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

      11. distribute-lft-neg-in 92.4%

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

      12. metadata-eval 92.4%

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

      13. *-commutative 92.4%

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

      14. associate-*l* 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in x around inf 75.9%

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

   if -8.00000000000000038e-4 < (*.f64 x y) < 5e45

   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. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around 0 71.5%

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

      1. associate-/l* 72.7%

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

   6. Simplified 72.7%

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

   if 5e45 < (*.f64 x y)

   1. Initial program 88.7%

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

      1. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around inf 77.7%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0008:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0008:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -0.0008)
   (/ 0.5 (/ a (* x y)))
   (if (<= (* x y) 5e+45) (/ t (/ (/ a z) -4.5)) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -0.0008) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 5e+45) {
		tmp = t / ((a / z) / -4.5);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-0.0008d0)) then
        tmp = 0.5d0 / (a / (x * y))
    else if ((x * y) <= 5d+45) then
        tmp = t / ((a / z) / (-4.5d0))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -0.0008) {
		tmp = 0.5 / (a / (x * y));
	} else if ((x * y) <= 5e+45) {
		tmp = t / ((a / z) / -4.5);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -0.0008:
		tmp = 0.5 / (a / (x * y))
	elif (x * y) <= 5e+45:
		tmp = t / ((a / z) / -4.5)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -0.0008)
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	elseif (Float64(x * y) <= 5e+45)
		tmp = Float64(t / Float64(Float64(a / z) / -4.5));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -0.0008)
		tmp = 0.5 / (a / (x * y));
	elseif ((x * y) <= 5e+45)
		tmp = t / ((a / z) / -4.5);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -0.0008], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+45], N[(t / N[(N[(a / z), $MachinePrecision] / -4.5), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.00000000000000038e-4

   1. Initial program 89.3%

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

      1. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in a around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. cancel-sign-sub-inv 89.3%

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

      3. metadata-eval 89.3%

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

      4. +-commutative 89.3%

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

      5. associate-/l* 89.2%

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

      6. +-commutative 89.2%

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

      7. metadata-eval 89.2%

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

      8. cancel-sign-sub-inv 89.2%

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

      9. fma-neg 92.4%

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

      10. *-commutative 92.4%

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

      11. distribute-lft-neg-in 92.4%

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

      12. metadata-eval 92.4%

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

      13. *-commutative 92.4%

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

      14. associate-*l* 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in x around inf 75.9%

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

   if -8.00000000000000038e-4 < (*.f64 x y) < 5e45

   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. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

      1. div-sub 91.3%

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

      2. sub-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. times-frac 84.9%

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

      5. div-inv 84.8%

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

      6. associate-*r* 84.1%

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

      7. *-commutative 84.1%

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

      8. associate-*l* 84.9%

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

      9. *-commutative 84.9%

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

      10. associate-/r* 84.9%

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

      11. metadata-eval 84.9%

          \[\leadsto \frac{x}{2} \cdot \frac{y}{a} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   5. Applied egg-rr 84.9%

      \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 84.9%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-*l/ 84.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. associate-*l* 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(z \cdot t\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      6. *-commutative 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right)} \cdot \left(9 \cdot 0.5\right)}{a} \]

      7. metadata-eval 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\left(t \cdot z\right) \cdot \color{blue}{4.5}}{a} \]

   7. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{a}}{2} - \frac{\left(t \cdot z\right) \cdot 4.5}{a}} \]

   8. Taylor expanded in x around 0 71.5%

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

      1. associate-/l* 72.7%

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

      2. associate-*r/ 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-/l* 72.7%

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

   10. Simplified 72.7%

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

   if 5e45 < (*.f64 x y)

   1. Initial program 88.7%

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

      1. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around inf 77.7%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0008:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0008:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -0.0008)
   (/ (* x (* y 0.5)) a)
   (if (<= (* x y) 5e+45) (/ t (/ (/ a z) -4.5)) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -0.0008) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 5e+45) {
		tmp = t / ((a / z) / -4.5);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-0.0008d0)) then
        tmp = (x * (y * 0.5d0)) / a
    else if ((x * y) <= 5d+45) then
        tmp = t / ((a / z) / (-4.5d0))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -0.0008) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 5e+45) {
		tmp = t / ((a / z) / -4.5);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -0.0008:
		tmp = (x * (y * 0.5)) / a
	elif (x * y) <= 5e+45:
		tmp = t / ((a / z) / -4.5)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -0.0008)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (Float64(x * y) <= 5e+45)
		tmp = Float64(t / Float64(Float64(a / z) / -4.5));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -0.0008)
		tmp = (x * (y * 0.5)) / a;
	elseif ((x * y) <= 5e+45)
		tmp = t / ((a / z) / -4.5);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -0.0008], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+45], N[(t / N[(N[(a / z), $MachinePrecision] / -4.5), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.00000000000000038e-4

   1. Initial program 89.3%

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

      1. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r* 76.0%

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

   6. Simplified 76.0%

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

   if -8.00000000000000038e-4 < (*.f64 x y) < 5e45

   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. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

      1. div-sub 91.3%

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

      2. sub-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. times-frac 84.9%

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

      5. div-inv 84.8%

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

      6. associate-*r* 84.1%

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

      7. *-commutative 84.1%

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

      8. associate-*l* 84.9%

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

      9. *-commutative 84.9%

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

      10. associate-/r* 84.9%

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

      11. metadata-eval 84.9%

          \[\leadsto \frac{x}{2} \cdot \frac{y}{a} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   5. Applied egg-rr 84.9%

      \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 84.9%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-*l/ 84.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. associate-*l* 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(z \cdot t\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      6. *-commutative 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right)} \cdot \left(9 \cdot 0.5\right)}{a} \]

      7. metadata-eval 84.9%

         \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \frac{\left(t \cdot z\right) \cdot \color{blue}{4.5}}{a} \]

   7. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{a}}{2} - \frac{\left(t \cdot z\right) \cdot 4.5}{a}} \]

   8. Taylor expanded in x around 0 71.5%

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

      1. associate-/l* 72.7%

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

      2. associate-*r/ 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-/l* 72.7%

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

   10. Simplified 72.7%

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

   if 5e45 < (*.f64 x y)

   1. Initial program 88.7%

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

      1. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around inf 77.7%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0008:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+221}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+221)
   (* (/ z a) (* t -4.5))
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+221) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+221)) then
        tmp = (z / a) * (t * (-4.5d0))
    else
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+221) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+221:
		tmp = (z / a) * (t * -4.5)
	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])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+221)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+221)
		tmp = (z / a) * (t * -4.5);
	else
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[z, -3.2e+221], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $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 z < -3.2e221

   1. Initial program 63.8%

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

      1. associate-*l* 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in x around 0 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-/l* 78.8%

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

      3. associate-*l/ 78.9%

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

   6. Simplified 78.9%

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

      1. clear-num 78.9%

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

      2. associate-/r/ 78.8%

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

      3. clear-num 78.9%

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

   8. Applied egg-rr 78.9%

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

   if -3.2e221 < z

   1. Initial program 92.6%

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

      1. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+221}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 12: 51.8% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (/ a z))))

C

assert(x < y && y < z && z < t && t < a);
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 / (a / z));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 / (a / z))
end function

Java

assert x < y && y < z && z < t && t < a;
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 / (a / z));
}

Python

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

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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(a / z)))
end

MATLAB

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.9%

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

   1. associate-*l* 90.3%

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

3. Simplified 90.3%

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

4. Taylor expanded in x around 0 48.2%

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

   1. associate-/l* 50.7%

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

6. Simplified 50.7%

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

7. Final simplification 50.7%

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

Developer target: 93.6% 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 2023332 
(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)))