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

Percentage Accurate: 91.2% → 94.5%

Time: 9.4s

Alternatives: 11

Speedup: 0.5×

• 27.9% 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: 91.2% 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: 94.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+206}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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 (<= (* x y) (- INFINITY))
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 4e+206)
     (/ (fma x y (* z (* t -9.0))) (* a 2.0))
     (* y (+ (* -4.5 (/ (* z t) (* y a))) (* 0.5 (/ x 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 ((x * y) <= -((double) INFINITY)) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 4e+206) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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(x * y) <= Float64(-Inf))
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 4e+206)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(Float64(-4.5 * Float64(Float64(z * t) / Float64(y * a))) + Float64(0.5 * Float64(x / 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[(x * y), $MachinePrecision], (-Infinity)], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+206], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 63.0%

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

   3. Taylor expanded in x around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. times-frac 99.8%

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

      5. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 99.6%

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

   9. Simplified 99.6%

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

   if -inf.0 < (*.f64 x y) < 4.0000000000000002e206

   1. Initial program 95.3%

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

      1. div-sub 94.3%

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

      2. *-commutative 94.3%

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

      3. div-sub 95.3%

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

      4. cancel-sign-sub-inv 95.3%

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

      5. *-commutative 95.3%

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

      6. fma-define 95.3%

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

      7. distribute-rgt-neg-in 95.3%

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

      8. associate-*r* 95.3%

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

      9. distribute-lft-neg-in 95.3%

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

      10. *-commutative 95.3%

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

      11. distribute-rgt-neg-in 95.3%

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

      12. metadata-eval 95.3%

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

   3. Simplified 95.3%

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

   if 4.0000000000000002e206 < (*.f64 x y)

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 99.8%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+206}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* y (/ (* x 0.5) a))))
   (if (<= (* x y) -5e-59)
     t_1
     (if (<= (* x y) 2e-88)
       (/ (* t (* z -4.5)) a)
       (if (<= (* x y) 1e-15)
         (/ (* x y) (* a 2.0))
         (if (<= (* x y) 1e+47) (* -4.5 (/ z (/ a t))) 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 = y * ((x * 0.5) / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_1;
	} else if ((x * y) <= 2e-88) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 1e+47) {
		tmp = -4.5 * (z / (a / t));
	} 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 = y * ((x * 0.5d0) / a)
    if ((x * y) <= (-5d-59)) then
        tmp = t_1
    else if ((x * y) <= 2d-88) then
        tmp = (t * (z * (-4.5d0))) / a
    else if ((x * y) <= 1d-15) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 1d+47) then
        tmp = (-4.5d0) * (z / (a / t))
    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 = y * ((x * 0.5) / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_1;
	} else if ((x * y) <= 2e-88) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 1e+47) {
		tmp = -4.5 * (z / (a / t));
	} 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 = y * ((x * 0.5) / a)
	tmp = 0
	if (x * y) <= -5e-59:
		tmp = t_1
	elif (x * y) <= 2e-88:
		tmp = (t * (z * -4.5)) / a
	elif (x * y) <= 1e-15:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 1e+47:
		tmp = -4.5 * (z / (a / t))
	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(y * Float64(Float64(x * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -5e-59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-88)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif (Float64(x * y) <= 1e-15)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 1e+47)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	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 = y * ((x * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -5e-59)
		tmp = t_1;
	elseif ((x * y) <= 2e-88)
		tmp = (t * (z * -4.5)) / a;
	elseif ((x * y) <= 1e-15)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 1e+47)
		tmp = -4.5 * (z / (a / t));
	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[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-88], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-15], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+47], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.0000000000000001e-59 or 1e47 < (*.f64 x y)

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 84.8%

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

   4. Taylor expanded in t around 0 79.6%

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

      1. associate-*r/ 79.6%

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

   6. Simplified 79.6%

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

   if -5.0000000000000001e-59 < (*.f64 x y) < 1.99999999999999987e-88

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 91.8%

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

      1. associate-/l* 85.9%

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

   5. Simplified 85.9%

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

      1. associate-*r* 85.9%

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

      2. div-inv 85.9%

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

      3. associate-*r* 91.9%

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

      4. associate-*r* 91.8%

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

      5. *-commutative 91.8%

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

      6. associate-*r* 91.8%

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

      7. associate-*r* 83.9%

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

      8. div-inv 83.9%

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

      9. *-commutative 83.9%

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

      10. associate-*l/ 91.9%

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

      11. *-commutative 91.9%

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

   7. Applied egg-rr 91.9%

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

   if 1.99999999999999987e-88 < (*.f64 x y) < 1.0000000000000001e-15

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf 72.6%

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

   if 1.0000000000000001e-15 < (*.f64 x y) < 1e47

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 67.9%

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

      1. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

      1. associate-*r* 67.9%

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

      2. div-inv 67.8%

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

      3. associate-*r* 67.9%

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

      4. associate-*r* 67.7%

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

      5. *-commutative 67.7%

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

      6. associate-*r* 67.7%

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

      7. associate-*r* 76.1%

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

      8. div-inv 76.1%

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

      9. clear-num 76.2%

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

      10. un-div-inv 76.2%

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

      11. *-commutative 76.2%

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

   7. Applied egg-rr 76.2%

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

      1. *-commutative 76.2%

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

      2. *-un-lft-identity 76.2%

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

      3. times-frac 76.2%

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

      4. metadata-eval 76.2%

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

   9. Applied egg-rr 76.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* y (/ (* x 0.5) a))))
   (if (<= (* x y) -5e-59)
     t_1
     (if (<= (* x y) 2e-88)
       (/ (* z (* t -4.5)) a)
       (if (<= (* x y) 1e-15)
         (/ (* x y) (* a 2.0))
         (if (<= (* x y) 1e+47) (* -4.5 (/ z (/ a t))) 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 = y * ((x * 0.5) / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_1;
	} else if ((x * y) <= 2e-88) {
		tmp = (z * (t * -4.5)) / a;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 1e+47) {
		tmp = -4.5 * (z / (a / t));
	} 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 = y * ((x * 0.5d0) / a)
    if ((x * y) <= (-5d-59)) then
        tmp = t_1
    else if ((x * y) <= 2d-88) then
        tmp = (z * (t * (-4.5d0))) / a
    else if ((x * y) <= 1d-15) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 1d+47) then
        tmp = (-4.5d0) * (z / (a / t))
    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 = y * ((x * 0.5) / a);
	double tmp;
	if ((x * y) <= -5e-59) {
		tmp = t_1;
	} else if ((x * y) <= 2e-88) {
		tmp = (z * (t * -4.5)) / a;
	} else if ((x * y) <= 1e-15) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 1e+47) {
		tmp = -4.5 * (z / (a / t));
	} 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 = y * ((x * 0.5) / a)
	tmp = 0
	if (x * y) <= -5e-59:
		tmp = t_1
	elif (x * y) <= 2e-88:
		tmp = (z * (t * -4.5)) / a
	elif (x * y) <= 1e-15:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 1e+47:
		tmp = -4.5 * (z / (a / t))
	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(y * Float64(Float64(x * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -5e-59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-88)
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	elseif (Float64(x * y) <= 1e-15)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 1e+47)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	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 = y * ((x * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -5e-59)
		tmp = t_1;
	elseif ((x * y) <= 2e-88)
		tmp = (z * (t * -4.5)) / a;
	elseif ((x * y) <= 1e-15)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 1e+47)
		tmp = -4.5 * (z / (a / t));
	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[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-88], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-15], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+47], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.0000000000000001e-59 or 1e47 < (*.f64 x y)

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 84.8%

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

   4. Taylor expanded in t around 0 79.6%

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

      1. associate-*r/ 79.6%

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

   6. Simplified 79.6%

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

   if -5.0000000000000001e-59 < (*.f64 x y) < 1.99999999999999987e-88

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 91.8%

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

      1. associate-*r/ 91.9%

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

      2. associate-*r* 91.9%

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

      3. associate-*l/ 83.9%

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

      4. associate-*r/ 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-*r/ 83.9%

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

   5. Simplified 83.9%

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

      1. associate-*r/ 91.9%

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

      2. *-commutative 91.9%

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

   7. Applied egg-rr 91.9%

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

   if 1.99999999999999987e-88 < (*.f64 x y) < 1.0000000000000001e-15

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf 72.6%

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

   if 1.0000000000000001e-15 < (*.f64 x y) < 1e47

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 67.9%

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

      1. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

      1. associate-*r* 67.9%

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

      2. div-inv 67.8%

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

      3. associate-*r* 67.9%

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

      4. associate-*r* 67.7%

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

      5. *-commutative 67.7%

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

      6. associate-*r* 67.7%

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

      7. associate-*r* 76.1%

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

      8. div-inv 76.1%

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

      9. clear-num 76.2%

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

      10. un-div-inv 76.2%

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

      11. *-commutative 76.2%

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

   7. Applied egg-rr 76.2%

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

      1. *-commutative 76.2%

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

      2. *-un-lft-identity 76.2%

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

      3. times-frac 76.2%

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

      4. metadata-eval 76.2%

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

   9. Applied egg-rr 76.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+206}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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 (<= (* x y) (- INFINITY))
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 4e+206)
     (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
     (* y (+ (* -4.5 (/ (* z t) (* y a))) (* 0.5 (/ x 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 ((x * y) <= -((double) INFINITY)) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 4e+206) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	}
	return tmp;
}

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) <= -Double.POSITIVE_INFINITY) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 4e+206) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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 (x * y) <= -math.inf:
		tmp = x / (a * (2.0 / y))
	elif (x * y) <= 4e+206:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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(x * y) <= Float64(-Inf))
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 4e+206)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(Float64(-4.5 * Float64(Float64(z * t) / Float64(y * a))) + Float64(0.5 * Float64(x / 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 ((x * y) <= -Inf)
		tmp = x / (a * (2.0 / y));
	elseif ((x * y) <= 4e+206)
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], (-Infinity)], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+206], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 63.0%

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

   3. Taylor expanded in x around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. times-frac 99.8%

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

      5. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 99.6%

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

   9. Simplified 99.6%

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

   if -inf.0 < (*.f64 x y) < 4.0000000000000002e206

   1. Initial program 95.3%

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

   if 4.0000000000000002e206 < (*.f64 x y)

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 99.8%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+206}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) (- INFINITY))
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 2e+220)
     (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
     (* y (/ (* x 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 ((x * y) <= -((double) INFINITY)) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 2e+220) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = y * ((x * 0.5) / a);
	}
	return tmp;
}

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) <= -Double.POSITIVE_INFINITY) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 2e+220) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = y * ((x * 0.5) / 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 (x * y) <= -math.inf:
		tmp = x / (a * (2.0 / y))
	elif (x * y) <= 2e+220:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = y * ((x * 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(x * y) <= Float64(-Inf))
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 2e+220)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(Float64(x * 0.5) / 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 ((x * y) <= -Inf)
		tmp = x / (a * (2.0 / y));
	elseif ((x * y) <= 2e+220)
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = y * ((x * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], (-Infinity)], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+220], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 63.0%

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

   3. Taylor expanded in x around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. times-frac 99.8%

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

      5. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 99.6%

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

   9. Simplified 99.6%

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

   if -inf.0 < (*.f64 x y) < 2e220

   1. Initial program 95.4%

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

   if 2e220 < (*.f64 x y)

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-79} \lor \neg \left(y \leq 6.5 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= y -5.2e-79) (not (<= y 6.5e-33)))
   (* x (/ (* y 0.5) a))
   (* -4.5 (/ (* z t) 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 ((y <= -5.2e-79) || !(y <= 6.5e-33)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / 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 ((y <= (-5.2d-79)) .or. (.not. (y <= 6.5d-33))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * ((z * t) / 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 ((y <= -5.2e-79) || !(y <= 6.5e-33)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / 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 (y <= -5.2e-79) or not (y <= 6.5e-33):
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * ((z * t) / 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 ((y <= -5.2e-79) || !(y <= 6.5e-33))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / 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 ((y <= -5.2e-79) || ~((y <= 6.5e-33)))
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * ((z * t) / 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[y, -5.2e-79], N[Not[LessEqual[y, 6.5e-33]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999987e-79 or 6.4999999999999993e-33 < y

   1. Initial program 87.7%

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

   3. Taylor expanded in x around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-/l* 72.1%

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

      3. associate-*r* 72.0%

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

      4. *-commutative 72.0%

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

      5. associate-*r/ 72.0%

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

   5. Simplified 72.0%

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

   if -5.19999999999999987e-79 < y < 6.4999999999999993e-33

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 76.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-79} \lor \neg \left(y \leq 6.5 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -0.062 \lor \neg \left(x \leq 8.5 \cdot 10^{-119}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= x -0.062) (not (<= x 8.5e-119)))
   (* y (/ (* x 0.5) a))
   (* -4.5 (/ (* z t) 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 ((x <= -0.062) || !(x <= 8.5e-119)) {
		tmp = y * ((x * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / 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 ((x <= (-0.062d0)) .or. (.not. (x <= 8.5d-119))) then
        tmp = y * ((x * 0.5d0) / a)
    else
        tmp = (-4.5d0) * ((z * t) / 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 ((x <= -0.062) || !(x <= 8.5e-119)) {
		tmp = y * ((x * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / 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 (x <= -0.062) or not (x <= 8.5e-119):
		tmp = y * ((x * 0.5) / a)
	else:
		tmp = -4.5 * ((z * t) / 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 ((x <= -0.062) || !(x <= 8.5e-119))
		tmp = Float64(y * Float64(Float64(x * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / 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 ((x <= -0.062) || ~((x <= 8.5e-119)))
		tmp = y * ((x * 0.5) / a);
	else
		tmp = -4.5 * ((z * t) / 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[x, -0.062], N[Not[LessEqual[x, 8.5e-119]], $MachinePrecision]], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.062 or 8.49999999999999977e-119 < x

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 81.9%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. associate-*r/ 68.6%

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

   6. Simplified 68.6%

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

   if -0.062 < x < 8.49999999999999977e-119

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.062 \lor \neg \left(x \leq 8.5 \cdot 10^{-119}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -0.084 \lor \neg \left(x \leq 9 \cdot 10^{-119}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \end{array} \end{array} \]

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 (<= x -0.084) (not (<= x 9e-119)))
   (* y (/ (* x 0.5) a))
   (/ (* t (* z -4.5)) 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 ((x <= -0.084) || !(x <= 9e-119)) {
		tmp = y * ((x * 0.5) / a);
	} else {
		tmp = (t * (z * -4.5)) / 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 ((x <= (-0.084d0)) .or. (.not. (x <= 9d-119))) then
        tmp = y * ((x * 0.5d0) / a)
    else
        tmp = (t * (z * (-4.5d0))) / 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 ((x <= -0.084) || !(x <= 9e-119)) {
		tmp = y * ((x * 0.5) / a);
	} else {
		tmp = (t * (z * -4.5)) / 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 (x <= -0.084) or not (x <= 9e-119):
		tmp = y * ((x * 0.5) / a)
	else:
		tmp = (t * (z * -4.5)) / 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 ((x <= -0.084) || !(x <= 9e-119))
		tmp = Float64(y * Float64(Float64(x * 0.5) / a));
	else
		tmp = Float64(Float64(t * Float64(z * -4.5)) / 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 ((x <= -0.084) || ~((x <= 9e-119)))
		tmp = y * ((x * 0.5) / a);
	else
		tmp = (t * (z * -4.5)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[x, -0.084], N[Not[LessEqual[x, 9e-119]], $MachinePrecision]], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0840000000000000052 or 9.0000000000000005e-119 < x

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 81.9%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. associate-*r/ 68.6%

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

   6. Simplified 68.6%

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

   if -0.0840000000000000052 < x < 9.0000000000000005e-119

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

      1. associate-*r* 71.7%

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

      2. div-inv 71.8%

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

      3. associate-*r* 75.4%

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

      4. associate-*r* 75.3%

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

      5. *-commutative 75.3%

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

      6. associate-*r* 75.3%

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

      7. associate-*r* 73.3%

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

      8. div-inv 73.2%

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

      9. *-commutative 73.2%

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

      10. associate-*l/ 75.4%

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

      11. *-commutative 75.4%

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

   7. Applied egg-rr 75.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.084 \lor \neg \left(x \leq 9 \cdot 10^{-119}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -15.2:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-120}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -15.2)
   (* y (* x (/ 0.5 a)))
   (if (<= x 1.9e-120) (* -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 (x <= -15.2) {
		tmp = y * (x * (0.5 / a));
	} else if (x <= 1.9e-120) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-15.2d0)) then
        tmp = y * (x * (0.5d0 / a))
    else if (x <= 1.9d-120) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = x * ((y * 0.5d0) / 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 (x <= -15.2) {
		tmp = y * (x * (0.5 / a));
	} else if (x <= 1.9e-120) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = x * ((y * 0.5) / 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 x <= -15.2:
		tmp = y * (x * (0.5 / a))
	elif x <= 1.9e-120:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 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 (x <= -15.2)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (x <= 1.9e-120)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -15.2)
		tmp = y * (x * (0.5 / a));
	elseif (x <= 1.9e-120)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[x, -15.2], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-120], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -15.199999999999999

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf 84.2%

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

   4. Taylor expanded in t around 0 72.0%

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

      1. associate-*r/ 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-*r/ 71.9%

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

   6. Simplified 71.9%

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

   if -15.199999999999999 < x < 1.8999999999999999e-120

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 75.4%

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

   if 1.8999999999999999e-120 < x

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. associate-/l* 64.1%

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

      3. associate-*r* 64.1%

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

      4. *-commutative 64.1%

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

      5. associate-*r/ 64.1%

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

   5. Simplified 64.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -15.2:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-120}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in x around 0 49.7%

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

   1. associate-/l* 50.7%

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

5. Simplified 50.7%

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

6. Final simplification 50.7%

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

Alternative 11: 51.3% accurate, 1.9× speedup

Math

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

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 (/ z (/ a t))))

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 * (z / (a / t));
}

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) * (z / (a / t))
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 * (z / (a / t));
}

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 * (z / (a / t))

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(z / Float64(a / t)))
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 * (z / (a / t));
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[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in x around 0 49.7%

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

   1. associate-/l* 50.7%

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

5. Simplified 50.7%

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

   1. associate-*r* 50.7%

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

   2. div-inv 50.7%

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

   3. associate-*r* 49.7%

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

   4. associate-*r* 49.6%

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

   5. *-commutative 49.6%

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

   6. associate-*r* 49.6%

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

   7. associate-*r* 49.9%

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

   8. div-inv 49.9%

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

   9. clear-num 49.6%

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

   10. un-div-inv 49.3%

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

   11. *-commutative 49.3%

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

7. Applied egg-rr 49.3%

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

   1. *-commutative 49.3%

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

   2. *-un-lft-identity 49.3%

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

   3. times-frac 49.3%

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

   4. metadata-eval 49.3%

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

9. Applied egg-rr 49.3%

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

10. Final simplification 49.3%

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

Developer target: 93.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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