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

Percentage Accurate: 91.2% → 96.4%

Time: 8.5s

Alternatives: 11

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% 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: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+187}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+187)))
     (- (/ (* y 0.5) (/ a x)) (* t (* (/ z a) 4.5)))
     (/ (- (* x y) (* z (* 9.0 t))) (* 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+187)) {
		tmp = ((y * 0.5) / (a / x)) - (t * ((z / a) * 4.5));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+187)) {
		tmp = ((y * 0.5) / (a / x)) - (t * ((z / a) * 4.5));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (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):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+187):
		tmp = ((y * 0.5) / (a / x)) - (t * ((z / a) * 4.5))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (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)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+187))
		tmp = Float64(Float64(Float64(y * 0.5) / Float64(a / x)) - Float64(t * Float64(Float64(z / a) * 4.5)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / 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)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+187)))
		tmp = ((y * 0.5) / (a / x)) - (t * ((z / a) * 4.5));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+187]], $MachinePrecision]], N[(N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 1.99999999999999981e187 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 72.0%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. associate-*r* 72.0%

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

      2. *-commutative 72.0%

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

   5. Simplified 72.0%

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

      1. div-sub 66.9%

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

      2. times-frac 81.9%

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

      3. associate-*l* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-*r/ 92.3%

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

      6. times-frac 92.3%

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

      7. metadata-eval 92.3%

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

   7. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)} \]
   8. Step-by-step derivation

      1. div-inv 92.3%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\left(y \cdot \frac{1}{2}\right)} - t \cdot \left(\frac{z}{a} \cdot 4.5\right) \]

      2. metadata-eval 92.3%

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

      3. *-commutative 92.3%

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

      4. *-commutative 92.3%

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

      5. clear-num 92.3%

         \[\leadsto \left(0.5 \cdot y\right) \cdot \color{blue}{\frac{1}{\frac{a}{x}}} - t \cdot \left(\frac{z}{a} \cdot 4.5\right) \]

      6. un-div-inv 92.3%

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

      7. *-commutative 92.3%

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

   9. Applied egg-rr 92.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.99999999999999981e187

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 98.6%

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

      1. associate-*r* 98.6%

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

      2. *-commutative 98.6%

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

   5. Simplified 98.6%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+187}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+241)))
     (- (* (/ x a) (/ y 2.0)) (* t (* (/ z a) 4.5)))
     (/ (- (* x y) (* z (* 9.0 t))) (* 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+241)) {
		tmp = ((x / a) * (y / 2.0)) - (t * ((z / a) * 4.5));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+241)) {
		tmp = ((x / a) * (y / 2.0)) - (t * ((z / a) * 4.5));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (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):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+241):
		tmp = ((x / a) * (y / 2.0)) - (t * ((z / a) * 4.5))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (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)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+241))
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(t * Float64(Float64(z / a) * 4.5)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / 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)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+241)))
		tmp = ((x / a) * (y / 2.0)) - (t * ((z / a) * 4.5));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+241]], $MachinePrecision]], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 2.0000000000000001e241 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 66.6%

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

   3. Taylor expanded in z around 0 66.6%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

   5. Simplified 66.6%

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

      1. div-sub 60.6%

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

      2. times-frac 79.9%

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

      3. associate-*l* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r/ 92.4%

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

      6. times-frac 92.4%

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

      7. metadata-eval 92.4%

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

   7. Applied egg-rr 92.4%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.0000000000000001e241

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 98.7%

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

      1. associate-*r* 98.7%

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

      2. *-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -1e+259)
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 1e+287)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (* (* y 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) <= -1e+259) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 1e+287) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (y * 0.5) * (x / 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 * y) <= (-1d+259)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((x * y) <= 1d+287) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = (y * 0.5d0) * (x / 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 * y) <= -1e+259) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 1e+287) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (y * 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) <= -1e+259:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= 1e+287:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = (y * 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) <= -1e+259)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 1e+287)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * 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) <= -1e+259)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= 1e+287)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = (y * 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], -1e+259], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+287], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.999999999999999e258

   1. Initial program 77.6%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. associate-*r* 77.6%

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

      2. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in x around inf 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-/l* 99.9%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

   8. Simplified 99.9%

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

   if -9.999999999999999e258 < (*.f64 x y) < 1.0000000000000001e287

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 94.5%

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

      1. associate-*r* 94.5%

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

      2. *-commutative 94.5%

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

   5. Simplified 94.5%

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

   if 1.0000000000000001e287 < (*.f64 x y)

   1. Initial program 58.5%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. associate-*r/ 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-*r* 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

      1. *-commutative 58.5%

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

      2. metadata-eval 58.5%

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

      3. div-inv 58.5%

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

      4. associate-*l/ 99.8%

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

      5. div-inv 99.8%

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

      6. metadata-eval 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+287}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -2.9e-26)
   (/ (* y 0.5) (/ a x))
   (if (<= x -2e-238)
     (* t (* z (/ -4.5 a)))
     (if (<= x 4e-94) (* z (* t (/ -4.5 a))) (* (* y 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 <= -2.9e-26) {
		tmp = (y * 0.5) / (a / x);
	} else if (x <= -2e-238) {
		tmp = t * (z * (-4.5 / a));
	} else if (x <= 4e-94) {
		tmp = z * (t * (-4.5 / a));
	} else {
		tmp = (y * 0.5) * (x / 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 <= (-2.9d-26)) then
        tmp = (y * 0.5d0) / (a / x)
    else if (x <= (-2d-238)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (x <= 4d-94) then
        tmp = z * (t * ((-4.5d0) / a))
    else
        tmp = (y * 0.5d0) * (x / 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 <= -2.9e-26) {
		tmp = (y * 0.5) / (a / x);
	} else if (x <= -2e-238) {
		tmp = t * (z * (-4.5 / a));
	} else if (x <= 4e-94) {
		tmp = z * (t * (-4.5 / a));
	} else {
		tmp = (y * 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 <= -2.9e-26:
		tmp = (y * 0.5) / (a / x)
	elif x <= -2e-238:
		tmp = t * (z * (-4.5 / a))
	elif x <= 4e-94:
		tmp = z * (t * (-4.5 / a))
	else:
		tmp = (y * 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 (x <= -2.9e-26)
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	elseif (x <= -2e-238)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (x <= 4e-94)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	else
		tmp = Float64(Float64(y * 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 <= -2.9e-26)
		tmp = (y * 0.5) / (a / x);
	elseif (x <= -2e-238)
		tmp = t * (z * (-4.5 / a));
	elseif (x <= 4e-94)
		tmp = z * (t * (-4.5 / a));
	else
		tmp = (y * 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[x, -2.9e-26], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e-238], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-94], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8999999999999998e-26

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. associate-*r/ 74.1%

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

      2. *-commutative 74.1%

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

      3. associate-*r* 74.1%

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

      4. *-commutative 74.1%

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

   5. Simplified 74.1%

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

      1. *-commutative 74.1%

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

      2. metadata-eval 74.1%

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

      3. div-inv 74.1%

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

      4. associate-*l/ 72.7%

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

      5. div-inv 72.7%

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

      6. metadata-eval 72.7%

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

   7. Applied egg-rr 72.7%

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

      1. *-commutative 72.7%

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

      2. clear-num 72.7%

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

      3. div-inv 74.7%

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

   9. Applied egg-rr 74.7%

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

   if -2.8999999999999998e-26 < x < -2e-238

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 95.6%

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

      1. associate-*r* 95.7%

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

      2. *-commutative 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 71.7%

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

      3. associate-*r/ 71.6%

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

      4. associate-*l* 70.9%

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

   8. Simplified 70.9%

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

   if -2e-238 < x < 3.9999999999999998e-94

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0 72.5%

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

      1. associate-*r/ 72.4%

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

   5. Simplified 72.4%

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

      1. pow1 72.4%

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

      2. *-commutative 72.4%

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

   7. Applied egg-rr 72.4%

      \[\leadsto \frac{\color{blue}{{\left(\left(t \cdot z\right) \cdot -4.5\right)}^{1}}}{a} \]
   8. Step-by-step derivation

      1. unpow1 72.4%

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

      2. associate-*l* 72.5%

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

   9. Simplified 72.5%

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

       1. associate-/l* 71.0%

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

       2. associate-*r/ 71.0%

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

       3. *-commutative 71.0%

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

       4. associate-*r* 72.6%

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

   11. Applied egg-rr 72.6%

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

   if 3.9999999999999998e-94 < x

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf 53.2%

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

      1. associate-*r/ 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-*r* 53.2%

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

      4. *-commutative 53.2%

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

   5. Simplified 53.2%

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

      1. *-commutative 53.2%

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

      2. metadata-eval 53.2%

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

      3. div-inv 53.2%

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

      4. associate-*l/ 57.6%

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

      5. div-inv 57.6%

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

      6. metadata-eval 57.6%

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

   7. Applied egg-rr 57.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(y \cdot 0.5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{if}\;x \leq -1.26 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-238}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 0.5) (/ x a))))
   (if (<= x -1.26e-14)
     t_1
     (if (<= x -1.85e-238)
       (* -4.5 (* t (/ z a)))
       (if (<= x 4.2e-94) (* z (* t (/ -4.5 a))) 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 * 0.5) * (x / a);
	double tmp;
	if (x <= -1.26e-14) {
		tmp = t_1;
	} else if (x <= -1.85e-238) {
		tmp = -4.5 * (t * (z / a));
	} else if (x <= 4.2e-94) {
		tmp = z * (t * (-4.5 / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * 0.5d0) * (x / a)
    if (x <= (-1.26d-14)) then
        tmp = t_1
    else if (x <= (-1.85d-238)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if (x <= 4.2d-94) then
        tmp = z * (t * ((-4.5d0) / a))
    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 * 0.5) * (x / a);
	double tmp;
	if (x <= -1.26e-14) {
		tmp = t_1;
	} else if (x <= -1.85e-238) {
		tmp = -4.5 * (t * (z / a));
	} else if (x <= 4.2e-94) {
		tmp = z * (t * (-4.5 / a));
	} 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 * 0.5) * (x / a)
	tmp = 0
	if x <= -1.26e-14:
		tmp = t_1
	elif x <= -1.85e-238:
		tmp = -4.5 * (t * (z / a))
	elif x <= 4.2e-94:
		tmp = z * (t * (-4.5 / a))
	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(Float64(y * 0.5) * Float64(x / a))
	tmp = 0.0
	if (x <= -1.26e-14)
		tmp = t_1;
	elseif (x <= -1.85e-238)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (x <= 4.2e-94)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	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 * 0.5) * (x / a);
	tmp = 0.0;
	if (x <= -1.26e-14)
		tmp = t_1;
	elseif (x <= -1.85e-238)
		tmp = -4.5 * (t * (z / a));
	elseif (x <= 4.2e-94)
		tmp = z * (t * (-4.5 / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.26e-14], t$95$1, If[LessEqual[x, -1.85e-238], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-94], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25999999999999996e-14 or 4.2000000000000002e-94 < x

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 62.1%

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

      1. associate-*r/ 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-*r* 62.1%

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

      4. *-commutative 62.1%

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

   5. Simplified 62.1%

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

      1. *-commutative 62.1%

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

      2. metadata-eval 62.1%

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

      3. div-inv 62.1%

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

      4. associate-*l/ 63.9%

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

      5. div-inv 63.9%

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

      6. metadata-eval 63.9%

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

   7. Applied egg-rr 63.9%

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

   if -1.25999999999999996e-14 < x < -1.85000000000000012e-238

   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 z around 0 95.8%

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

      1. associate-*r* 95.9%

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

      2. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in x around 0 70.6%

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

      1. associate-*r/ 69.9%

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

   8. Simplified 69.9%

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

   if -1.85000000000000012e-238 < x < 4.2000000000000002e-94

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0 72.5%

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

      1. associate-*r/ 72.4%

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

   5. Simplified 72.4%

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

      1. pow1 72.4%

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

      2. *-commutative 72.4%

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

   7. Applied egg-rr 72.4%

      \[\leadsto \frac{\color{blue}{{\left(\left(t \cdot z\right) \cdot -4.5\right)}^{1}}}{a} \]
   8. Step-by-step derivation

      1. unpow1 72.4%

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

      2. associate-*l* 72.5%

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

   9. Simplified 72.5%

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

       1. associate-/l* 71.0%

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

       2. associate-*r/ 71.0%

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

       3. *-commutative 71.0%

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

       4. associate-*r* 72.6%

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

   11. Applied egg-rr 72.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-14}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-238}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \leq -1 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= x -1e-23)
     t_1
     (if (<= x -1.85e-238)
       (* t (* z (/ -4.5 a)))
       (if (<= x 1.65e-93) (* z (* t (/ -4.5 a))) 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 = x * ((y * 0.5) / a);
	double tmp;
	if (x <= -1e-23) {
		tmp = t_1;
	} else if (x <= -1.85e-238) {
		tmp = t * (z * (-4.5 / a));
	} else if (x <= 1.65e-93) {
		tmp = z * (t * (-4.5 / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    if (x <= (-1d-23)) then
        tmp = t_1
    else if (x <= (-1.85d-238)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (x <= 1.65d-93) then
        tmp = z * (t * ((-4.5d0) / a))
    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 = x * ((y * 0.5) / a);
	double tmp;
	if (x <= -1e-23) {
		tmp = t_1;
	} else if (x <= -1.85e-238) {
		tmp = t * (z * (-4.5 / a));
	} else if (x <= 1.65e-93) {
		tmp = z * (t * (-4.5 / a));
	} 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 = x * ((y * 0.5) / a)
	tmp = 0
	if x <= -1e-23:
		tmp = t_1
	elif x <= -1.85e-238:
		tmp = t * (z * (-4.5 / a))
	elif x <= 1.65e-93:
		tmp = z * (t * (-4.5 / a))
	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(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (x <= -1e-23)
		tmp = t_1;
	elseif (x <= -1.85e-238)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (x <= 1.65e-93)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	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 = x * ((y * 0.5) / a);
	tmp = 0.0;
	if (x <= -1e-23)
		tmp = t_1;
	elseif (x <= -1.85e-238)
		tmp = t * (z * (-4.5 / a));
	elseif (x <= 1.65e-93)
		tmp = z * (t * (-4.5 / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-23], t$95$1, If[LessEqual[x, -1.85e-238], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-93], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999996e-24 or 1.6500000000000001e-93 < x

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 87.2%

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

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-/l* 66.5%

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

      3. associate-*r* 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-*r/ 66.5%

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

   8. Simplified 66.5%

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

   if -9.9999999999999996e-24 < x < -1.85000000000000012e-238

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 95.6%

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

      1. associate-*r* 95.7%

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

      2. *-commutative 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 71.7%

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

      3. associate-*r/ 71.6%

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

      4. associate-*l* 70.9%

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

   8. Simplified 70.9%

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

   if -1.85000000000000012e-238 < x < 1.6500000000000001e-93

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0 72.5%

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

      1. associate-*r/ 72.4%

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

   5. Simplified 72.4%

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

      1. pow1 72.4%

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

      2. *-commutative 72.4%

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

   7. Applied egg-rr 72.4%

      \[\leadsto \frac{\color{blue}{{\left(\left(t \cdot z\right) \cdot -4.5\right)}^{1}}}{a} \]
   8. Step-by-step derivation

      1. unpow1 72.4%

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

      2. associate-*l* 72.5%

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

   9. Simplified 72.5%

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

       1. associate-/l* 71.0%

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

       2. associate-*r/ 71.0%

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

       3. *-commutative 71.0%

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

       4. associate-*r* 72.6%

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

   11. Applied egg-rr 72.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-26} \lor \neg \left(x \leq 1.65 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= x -1.22e-26) (not (<= x 1.65e-93)))
   (* 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 ((x <= -1.22e-26) || !(x <= 1.65e-93)) {
		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 ((x <= (-1.22d-26)) .or. (.not. (x <= 1.65d-93))) 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 ((x <= -1.22e-26) || !(x <= 1.65e-93)) {
		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 (x <= -1.22e-26) or not (x <= 1.65e-93):
		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 ((x <= -1.22e-26) || !(x <= 1.65e-93))
		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 ((x <= -1.22e-26) || ~((x <= 1.65e-93)))
		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[x, -1.22e-26], N[Not[LessEqual[x, 1.65e-93]], $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 x < -1.22e-26 or 1.6500000000000001e-93 < x

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 87.2%

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

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-/l* 66.5%

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

      3. associate-*r* 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-*r/ 66.5%

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

   8. Simplified 66.5%

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

   if -1.22e-26 < x < 1.6500000000000001e-93

   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 72.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-26} \lor \neg \left(x \leq 1.65 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-24} \lor \neg \left(x \leq 4.5 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 -5.6e-24) (not (<= x 4.5e-95)))
   (* 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 ((x <= -5.6e-24) || !(x <= 4.5e-95)) {
		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 ((x <= (-5.6d-24)) .or. (.not. (x <= 4.5d-95))) 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 ((x <= -5.6e-24) || !(x <= 4.5e-95)) {
		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 (x <= -5.6e-24) or not (x <= 4.5e-95):
		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 ((x <= -5.6e-24) || !(x <= 4.5e-95))
		tmp = Float64(x * Float64(y * Float64(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 <= -5.6e-24) || ~((x <= 4.5e-95)))
		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[x, -5.6e-24], N[Not[LessEqual[x, 4.5e-95]], $MachinePrecision]], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6000000000000003e-24 or 4.5e-95 < x

   1. Initial program 87.2%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. associate-*r/ 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*r* 62.6%

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

      4. associate-*r/ 66.5%

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

      5. associate-/l* 66.4%

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

   5. Simplified 66.4%

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

   if -5.6000000000000003e-24 < x < 4.5e-95

   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 72.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-24} \lor \neg \left(x \leq 4.5 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= z -8e+95) (* t (* z (/ -4.5 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 (z <= -8e+95) {
		tmp = t * (z * (-4.5 / 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 (z <= (-8d+95)) then
        tmp = t * (z * ((-4.5d0) / 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 (z <= -8e+95) {
		tmp = t * (z * (-4.5 / 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 z <= -8e+95:
		tmp = t * (z * (-4.5 / 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 (z <= -8e+95)
		tmp = Float64(t * Float64(z * Float64(-4.5 / 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 (z <= -8e+95)
		tmp = t * (z * (-4.5 / 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[LessEqual[z, -8e+95], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000016e95

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-*r* 86.5%

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

      2. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in x around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l/ 57.0%

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

      3. associate-*r/ 59.7%

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

      4. associate-*l* 67.5%

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

   8. Simplified 67.5%

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

   if -8.00000000000000016e95 < z

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 47.5%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+103}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= z -2.4e+103) (* -4.5 (* t (/ z 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 (z <= -2.4e+103) {
		tmp = -4.5 * (t * (z / 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 (z <= (-2.4d+103)) then
        tmp = (-4.5d0) * (t * (z / 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 (z <= -2.4e+103) {
		tmp = -4.5 * (t * (z / 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 z <= -2.4e+103:
		tmp = -4.5 * (t * (z / 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 (z <= -2.4e+103)
		tmp = Float64(-4.5 * Float64(t * Float64(z / 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 (z <= -2.4e+103)
		tmp = -4.5 * (t * (z / 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[LessEqual[z, -2.4e+103], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999998e103

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-*r* 86.5%

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

      2. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in x around 0 59.7%

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

      1. associate-*r/ 67.5%

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

   8. Simplified 67.5%

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

   if -2.3999999999999998e103 < z

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 47.5%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+103}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% 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 90.3%

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

3. Taylor expanded in z around 0 90.3%

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

   1. associate-*r* 90.3%

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

   2. *-commutative 90.3%

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

5. Simplified 90.3%

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

6. Taylor expanded in x around 0 49.2%

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

   1. associate-*r/ 49.5%

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

8. Simplified 49.5%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
9. 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 2024106 
(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)))