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

Percentage Accurate: 90.8% → 97.0%

Time: 12.6s

Alternatives: 14

Speedup: 0.6×

• 28.4% 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: 90.8% 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: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+301}\right):\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} + -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+301)))
     (+ (* y (/ x (* a 2.0))) (* -4.5 (* z (/ t a))))
     (/ t_1 (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+301)) {
		tmp = (y * (x / (a * 2.0))) + (-4.5 * (z * (t / a)));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+301)) {
		tmp = (y * (x / (a * 2.0))) + (-4.5 * (z * (t / a)));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+301):
		tmp = (y * (x / (a * 2.0))) + (-4.5 * (z * (t / a)))
	else:
		tmp = t_1 / (a * 2.0)
	return tmp

Julia

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(t * Float64(z * 9.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+301))
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) + Float64(-4.5 * Float64(z * Float64(t / a))));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (t * (z * 9.0));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+301)))
		tmp = (y * (x / (a * 2.0))) + (-4.5 * (z * (t / a)));
	else
		tmp = t_1 / (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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+301]], $MachinePrecision]], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 4.00000000000000021e301 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 67.7%

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

      1. div-sub 66.1%

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

      2. *-commutative 66.1%

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

      3. div-sub 67.7%

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

      4. *-commutative 67.7%

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

      5. cancel-sign-sub-inv 67.7%

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

      6. fma-def 69.3%

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

      7. distribute-lft-neg-in 69.3%

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

      8. associate-*l* 69.3%

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

      9. distribute-rgt-neg-in 69.3%

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

      10. *-commutative 69.3%

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

      11. distribute-rgt-neg-in 69.3%

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

      12. metadata-eval 69.3%

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

   3. Simplified 69.3%

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

      1. *-commutative 69.3%

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

      2. metadata-eval 69.3%

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

      3. distribute-lft-neg-in 69.3%

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

      4. distribute-rgt-neg-in 69.3%

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

      5. fma-neg 67.7%

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

      6. associate-*r* 67.7%

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

      7. *-commutative 67.7%

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

      8. associate-*l* 67.7%

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

   6. Applied egg-rr 67.7%

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

      1. div-sub 66.1%

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

      2. sub-neg 66.1%

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

      3. associate-/l* 76.6%

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

      4. frac-2neg 76.6%

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

      5. distribute-frac-neg 76.6%

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

      6. *-commutative 76.6%

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

      7. distribute-rgt-neg-in 76.6%

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

      8. *-commutative 76.6%

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

      9. metadata-eval 76.6%

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

      10. associate-*r* 76.6%

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

      11. frac-2neg 76.6%

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

      12. associate-*r* 76.6%

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

      13. *-commutative 76.6%

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

      14. times-frac 76.6%

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

      15. metadata-eval 76.6%

          \[\leadsto \frac{x}{\frac{a \cdot 2}{y}} + \frac{z \cdot t}{a} \cdot \color{blue}{-4.5} \]

      16. associate-*r/ 93.3%

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

      17. associate-*l* 93.3%

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

   8. Applied egg-rr 93.3%

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

      1. associate-/r/ 91.6%

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

      2. associate-*r* 91.6%

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

      3. *-commutative 91.6%

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

   10. Simplified 91.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.00000000000000021e301

   1. Initial program 98.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -\infty \lor \neg \left(x \cdot y - t \cdot \left(z \cdot 9\right) \leq 4 \cdot 10^{+301}\right):\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} + -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 2e-64)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (fma -4.5 (/ t (/ a z)) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e-64) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = fma(-4.5, (t / (a / z)), (0.5 * (x / (a / y))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 2e-64)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(t / Float64(a / z)), Float64(0.5 * Float64(x / Float64(a / y))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 2e-64], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 1.99999999999999993e-64

   1. Initial program 92.6%

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

      1. div-sub 89.9%

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

      2. *-commutative 89.9%

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

      3. div-sub 92.6%

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

      4. *-commutative 92.6%

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

      5. cancel-sign-sub-inv 92.6%

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

      6. fma-def 93.2%

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

      7. distribute-lft-neg-in 93.2%

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

      8. associate-*l* 93.2%

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

      9. distribute-rgt-neg-in 93.2%

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

      10. *-commutative 93.2%

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

      11. distribute-rgt-neg-in 93.2%

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

      12. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   if 1.99999999999999993e-64 < (*.f64 a 2)

   1. Initial program 87.2%

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

      1. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around 0 87.0%

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

      1. fma-def 87.0%

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

      2. associate-/l* 93.0%

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

      3. associate-/l* 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x (/ a y)))))
   (if (<= (* x y) -2e+17)
     t_1
     (if (<= (* x y) 5e-113)
       (/ (* t (* z -4.5)) a)
       (if (<= (* x y) 2e+15)
         (/ (* x (* y 0.5)) a)
         (if (<= (* x y) 7e+99) (* t (* -4.5 (/ z a))) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 2e+15) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (x / (a / y))
    if ((x * y) <= (-2d+17)) then
        tmp = t_1
    else if ((x * y) <= 5d-113) then
        tmp = (t * (z * (-4.5d0))) / a
    else if ((x * y) <= 2d+15) then
        tmp = (x * (y * 0.5d0)) / a
    else if ((x * y) <= 7d+99) then
        tmp = t * ((-4.5d0) * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 2e+15) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if (x * y) <= -2e+17:
		tmp = t_1
	elif (x * y) <= 5e-113:
		tmp = (t * (z * -4.5)) / a
	elif (x * y) <= 2e+15:
		tmp = (x * (y * 0.5)) / a
	elif (x * y) <= 7e+99:
		tmp = t * (-4.5 * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+17)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-113)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif (Float64(x * y) <= 2e+15)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (Float64(x * y) <= 7e+99)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if ((x * y) <= -2e+17)
		tmp = t_1;
	elseif ((x * y) <= 5e-113)
		tmp = (t * (z * -4.5)) / a;
	elseif ((x * y) <= 2e+15)
		tmp = (x * (y * 0.5)) / a;
	elseif ((x * y) <= 7e+99)
		tmp = t * (-4.5 * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-113], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+15], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7e+99], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e17 or 6.9999999999999995e99 < (*.f64 x y)

   1. Initial program 86.1%

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

      1. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in x around inf 74.0%

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

      1. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

   if -2e17 < (*.f64 x y) < 4.9999999999999997e-113

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. associate-/l* 73.4%

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

   7. Simplified 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-/r/ 75.7%

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

      3. associate-*r* 75.6%

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

      4. associate-*l/ 77.2%

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

   9. Applied egg-rr 77.2%

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

   if 4.9999999999999997e-113 < (*.f64 x y) < 2e15

   1. Initial program 99.5%

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

      1. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 70.9%

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

   7. Simplified 70.9%

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

   if 2e15 < (*.f64 x y) < 6.9999999999999995e99

   1. Initial program 93.1%

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

      1. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

      1. div-sub 86.1%

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

      2. sub-neg 86.1%

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

      3. *-commutative 86.1%

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

      4. times-frac 86.2%

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

      5. div-inv 86.1%

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

      6. associate-*r* 85.9%

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

      7. *-commutative 85.9%

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

      8. associate-*l* 86.2%

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

      9. *-commutative 86.2%

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

      10. associate-/r* 86.2%

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

      11. metadata-eval 86.2%

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

   6. Applied egg-rr 86.2%

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

      1. sub-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*l/ 86.2%

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

      4. associate-*l/ 86.1%

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

      5. *-commutative 86.1%

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

      6. *-commutative 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

      9. metadata-eval 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in x around 0 66.4%

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

       1. associate-*r/ 72.8%

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

       2. *-commutative 72.8%

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

       3. associate-*r* 73.0%

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

       4. *-commutative 73.0%

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

   11. Simplified 73.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x (/ a y)))))
   (if (<= (* x y) -2e+17)
     t_1
     (if (<= (* x y) 5e-113)
       (/ (* t (* z -9.0)) (* a 2.0))
       (if (<= (* x y) 2e+15)
         (/ (* x (* y 0.5)) a)
         (if (<= (* x y) 7e+99) (* t (* -4.5 (/ z a))) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = (t * (z * -9.0)) / (a * 2.0);
	} else if ((x * y) <= 2e+15) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (x / (a / y))
    if ((x * y) <= (-2d+17)) then
        tmp = t_1
    else if ((x * y) <= 5d-113) then
        tmp = (t * (z * (-9.0d0))) / (a * 2.0d0)
    else if ((x * y) <= 2d+15) then
        tmp = (x * (y * 0.5d0)) / a
    else if ((x * y) <= 7d+99) then
        tmp = t * ((-4.5d0) * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = t_1;
	} else if ((x * y) <= 5e-113) {
		tmp = (t * (z * -9.0)) / (a * 2.0);
	} else if ((x * y) <= 2e+15) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 7e+99) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if (x * y) <= -2e+17:
		tmp = t_1
	elif (x * y) <= 5e-113:
		tmp = (t * (z * -9.0)) / (a * 2.0)
	elif (x * y) <= 2e+15:
		tmp = (x * (y * 0.5)) / a
	elif (x * y) <= 7e+99:
		tmp = t * (-4.5 * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+17)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-113)
		tmp = Float64(Float64(t * Float64(z * -9.0)) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 2e+15)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (Float64(x * y) <= 7e+99)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if ((x * y) <= -2e+17)
		tmp = t_1;
	elseif ((x * y) <= 5e-113)
		tmp = (t * (z * -9.0)) / (a * 2.0);
	elseif ((x * y) <= 2e+15)
		tmp = (x * (y * 0.5)) / a;
	elseif ((x * y) <= 7e+99)
		tmp = t * (-4.5 * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-113], N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+15], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7e+99], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e17 or 6.9999999999999995e99 < (*.f64 x y)

   1. Initial program 86.1%

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

      1. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in x around inf 74.0%

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

      1. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

   if -2e17 < (*.f64 x y) < 4.9999999999999997e-113

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r* 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

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

   7. Simplified 77.2%

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

   if 4.9999999999999997e-113 < (*.f64 x y) < 2e15

   1. Initial program 99.5%

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

      1. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 70.9%

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

   7. Simplified 70.9%

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

   if 2e15 < (*.f64 x y) < 6.9999999999999995e99

   1. Initial program 93.1%

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

      1. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

      1. div-sub 86.1%

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

      2. sub-neg 86.1%

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

      3. *-commutative 86.1%

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

      4. times-frac 86.2%

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

      5. div-inv 86.1%

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

      6. associate-*r* 85.9%

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

      7. *-commutative 85.9%

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

      8. associate-*l* 86.2%

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

      9. *-commutative 86.2%

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

      10. associate-/r* 86.2%

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

      11. metadata-eval 86.2%

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

   6. Applied egg-rr 86.2%

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

      1. sub-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*l/ 86.2%

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

      4. associate-*l/ 86.1%

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

      5. *-commutative 86.1%

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

      6. *-commutative 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

      9. metadata-eval 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in x around 0 66.4%

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

       1. associate-*r/ 72.8%

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

       2. *-commutative 72.8%

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

       3. associate-*r* 73.0%

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

       4. *-commutative 73.0%

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

   11. Simplified 73.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+240}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* z 9.0))))
   (if (<= t_1 (- INFINITY))
     (* t (* -4.5 (/ z a)))
     (if (<= t_1 5e+240)
       (/ (- (* x y) t_1) (* a 2.0))
       (* -4.5 (/ t (/ a z)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t * (-4.5 * (z / a));
	} else if (t_1 <= 5e+240) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t * (-4.5 * (z / a));
	} else if (t_1 <= 5e+240) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (z * 9.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t * (-4.5 * (z / a))
	elif t_1 <= 5e+240:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z * 9.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	elseif (t_1 <= 5e+240)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z * 9.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t * (-4.5 * (z / a));
	elseif (t_1 <= 5e+240)
		tmp = ((x * y) - t_1) / (a * 2.0);
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+240], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z 9) t) < -inf.0

   1. Initial program 53.2%

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

      1. associate-*l* 53.2%

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

   3. Simplified 53.2%

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

      1. div-sub 53.2%

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

      2. sub-neg 53.2%

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

      3. *-commutative 53.2%

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

      4. times-frac 46.1%

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

      5. div-inv 46.1%

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

      6. associate-*r* 46.1%

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

      7. *-commutative 46.1%

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

      8. associate-*l* 46.1%

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

      9. *-commutative 46.1%

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

      10. associate-/r* 46.1%

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

      11. metadata-eval 46.1%

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

   6. Applied egg-rr 46.1%

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

      1. sub-neg 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*l/ 46.1%

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

      4. associate-*l/ 46.1%

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

      5. *-commutative 46.1%

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

      6. *-commutative 46.1%

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

      7. associate-*l* 46.1%

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

      8. *-commutative 46.1%

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

      9. metadata-eval 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in x around 0 53.2%

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

       1. associate-*r/ 92.3%

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

       2. *-commutative 92.3%

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

       3. associate-*r* 92.6%

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

       4. *-commutative 92.6%

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

   11. Simplified 92.6%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < 5.0000000000000003e240

   1. Initial program 95.2%

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

   if 5.0000000000000003e240 < (*.f64 (*.f64 z 9) t)

   1. Initial program 78.2%

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

      1. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in x around 0 81.9%

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

      1. associate-/l* 96.5%

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

   7. Simplified 96.5%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+240}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	return tmp

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y / (a / x));
	else
		tmp = ((x * y) - (9.0 * (z * 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 62.6%

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

      1. associate-*l* 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in x around inf 69.2%

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

      1. associate-*r/ 97.1%

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

   7. Simplified 97.1%

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

      1. associate-*r/ 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-/l* 97.2%

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

   9. Applied egg-rr 97.2%

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

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

   1. Initial program 92.9%

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

      1. div-sub 90.9%

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

      2. *-commutative 90.9%

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

      3. div-sub 92.9%

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

      4. *-commutative 92.9%

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

      5. cancel-sign-sub-inv 92.9%

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

      6. fma-def 93.4%

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

      7. distribute-lft-neg-in 93.4%

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

      8. associate-*l* 93.4%

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

      9. distribute-rgt-neg-in 93.4%

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

      10. *-commutative 93.4%

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

      11. distribute-rgt-neg-in 93.4%

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

      12. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

      1. *-commutative 93.4%

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

      2. metadata-eval 93.4%

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

      3. distribute-lft-neg-in 93.4%

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

      4. distribute-rgt-neg-in 93.4%

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

      5. fma-neg 93.0%

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

      6. associate-*r* 92.9%

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

      7. *-commutative 92.9%

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

      8. associate-*l* 93.0%

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

   6. Applied egg-rr 93.0%

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

4. Final simplification 93.2%

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

Alternative 7: 92.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 62.6%

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

      1. associate-*l* 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in x around inf 69.2%

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

      1. associate-*r/ 97.1%

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

   7. Simplified 97.1%

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

      1. associate-*r/ 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-/l* 97.2%

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

   9. Applied egg-rr 97.2%

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

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

   1. Initial program 92.9%

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

      1. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

4. Final simplification 93.2%

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

Alternative 8: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-65} \lor \neg \left(x \leq 1.04 \cdot 10^{-29}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.5e-65) (not (<= x 1.04e-29)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.5e-65) || !(x <= 1.04e-29)) {
		tmp = 0.5 * (x * (y / 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.
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 <= (-3.5d-65)) .or. (.not. (x <= 1.04d-29))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.5e-65) || !(x <= 1.04e-29)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.5e-65) or not (x <= 1.04e-29):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.5e-65) || !(x <= 1.04e-29))
		tmp = Float64(0.5 * Float64(x * Float64(y / 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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.5e-65) || ~((x <= 1.04e-29)))
		tmp = 0.5 * (x * (y / 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.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.5e-65], N[Not[LessEqual[x, 1.04e-29]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / 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 < -3.50000000000000005e-65 or 1.03999999999999995e-29 < x

   1. Initial program 88.3%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf 62.8%

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

      1. associate-*r/ 63.6%

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

   7. Simplified 63.6%

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

   if -3.50000000000000005e-65 < x < 1.03999999999999995e-29

   1. Initial program 95.7%

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

      1. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around 0 70.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-65} \lor \neg \left(x \leq 1.04 \cdot 10^{-29}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-80}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-29}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.95e-80)
   (* 0.5 (* x (/ y a)))
   (if (<= x 2.85e-29) (* -4.5 (/ (* z t) a)) (* 0.5 (* y (/ x a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.95e-80) {
		tmp = 0.5 * (x * (y / a));
	} else if (x <= 2.85e-29) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.95d-80)) then
        tmp = 0.5d0 * (x * (y / a))
    else if (x <= 2.85d-29) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.95e-80) {
		tmp = 0.5 * (x * (y / a));
	} else if (x <= 2.85e-29) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.95e-80:
		tmp = 0.5 * (x * (y / a))
	elif x <= 2.85e-29:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.95e-80)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (x <= 2.85e-29)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.95e-80)
		tmp = 0.5 * (x * (y / a));
	elseif (x <= 2.85e-29)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.95e-80], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e-29], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.95e-80

   1. Initial program 87.4%

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

      1. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 65.2%

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

      1. associate-*r/ 64.6%

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

   7. Simplified 64.6%

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

   if -2.95e-80 < x < 2.85e-29

   1. Initial program 96.6%

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

      1. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around 0 71.0%

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

   if 2.85e-29 < x

   1. Initial program 88.3%

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

      1. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 59.2%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/r/ 63.0%

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

   9. Applied egg-rr 63.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-80}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-29}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-65}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{-19}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.2e-65)
   (* 0.5 (/ x (/ a y)))
   (if (<= x 1.72e-19) (* -4.5 (/ (* z t) a)) (* 0.5 (* y (/ x a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.2e-65) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 1.72e-19) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-9.2d-65)) then
        tmp = 0.5d0 * (x / (a / y))
    else if (x <= 1.72d-19) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.2e-65) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 1.72e-19) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -9.2e-65:
		tmp = 0.5 * (x / (a / y))
	elif x <= 1.72e-19:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9.2e-65)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (x <= 1.72e-19)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9.2e-65)
		tmp = 0.5 * (x / (a / y));
	elseif (x <= 1.72e-19)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9.2e-65], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.72e-19], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.1999999999999999e-65

   1. Initial program 88.3%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if -9.1999999999999999e-65 < x < 1.72000000000000004e-19

   1. Initial program 95.7%

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

      1. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around 0 69.8%

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

   if 1.72000000000000004e-19 < x

   1. Initial program 88.2%

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

      1. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in x around inf 58.6%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

      1. associate-/r/ 62.4%

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

   9. Applied egg-rr 62.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-65}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{-19}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-65}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-17}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.5e-65)
   (* 0.5 (/ x (/ a y)))
   (if (<= x 1.28e-17) (/ (* t (* z -4.5)) a) (* 0.5 (* y (/ x a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.5e-65) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 1.28e-17) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.5d-65)) then
        tmp = 0.5d0 * (x / (a / y))
    else if (x <= 1.28d-17) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.5e-65) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 1.28e-17) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.5e-65:
		tmp = 0.5 * (x / (a / y))
	elif x <= 1.28e-17:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.5e-65)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (x <= 1.28e-17)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.5e-65)
		tmp = 0.5 * (x / (a / y));
	elseif (x <= 1.28e-17)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.5e-65], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.28e-17], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5e-65

   1. Initial program 88.3%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if -6.5e-65 < x < 1.28e-17

   1. Initial program 95.7%

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

      1. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around 0 69.8%

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

      1. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-/r/ 71.0%

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

      3. associate-*r* 71.0%

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

      4. associate-*l/ 69.8%

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

   9. Applied egg-rr 69.8%

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

   if 1.28e-17 < x

   1. Initial program 88.2%

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

      1. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in x around inf 58.6%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

      1. associate-/r/ 62.4%

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

   9. Applied egg-rr 62.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-65}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-17}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-290}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.8e-290) (* -4.5 (/ t (/ a z))) (* -4.5 (* z (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.8e-290) {
		tmp = -4.5 * (t / (a / z));
	} 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.
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 <= (-5.8d-290)) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.8e-290) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.8e-290:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.8e-290)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.8e-290)
		tmp = -4.5 * (t / (a / z));
	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.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.8e-290], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999989e-290

   1. Initial program 88.9%

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

      1. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around 0 39.8%

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

      1. associate-/l* 42.5%

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

   7. Simplified 42.5%

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

   if -5.79999999999999989e-290 < x

   1. Initial program 93.3%

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

      1. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0 55.9%

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

      1. associate-/l* 54.5%

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

      2. associate-/r/ 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-290}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-76}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.4e-76) (* -4.5 (* z (/ t a))) (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e-76) {
		tmp = -4.5 * (z * (t / 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.
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 <= (-2.4d-76)) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e-76) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.4e-76:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.4e-76)
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.4e-76)
		tmp = -4.5 * (z * (t / 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.4e-76], N[(-4.5 * N[(z * N[(t / 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 < -2.40000000000000013e-76

   1. Initial program 88.3%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 32.3%

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

      1. associate-/l* 36.0%

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

      2. associate-/r/ 36.8%

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

   7. Simplified 36.8%

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

   if -2.40000000000000013e-76 < x

   1. Initial program 92.5%

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

      1. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around 0 55.6%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-76}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

   1. associate-*l* 91.2%

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

3. Simplified 91.2%

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

5. Taylor expanded in x around 0 48.1%

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

   1. associate-/l* 48.7%

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

   2. associate-/r/ 50.0%

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

7. Simplified 50.0%

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

8. Final simplification 50.0%

   \[\leadsto -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \]
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 2024027 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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