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

Percentage Accurate: 91.0% → 96.3%

Time: 11.6s

Alternatives: 10

Speedup: 0.5×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+214} \lor \neg \left(t_1 \leq 5 \cdot 10^{+274}\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - t \cdot \frac{z}{\frac{a}{4.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 -4e+214) (not (<= t_1 5e+274)))
     (- (/ (* x (/ y a)) 2.0) (* t (/ z (/ a 4.5))))
     (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -4e+214) || !(t_1 <= 5e+274)) {
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)));
	} else {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if ((t_1 <= (-4d+214)) .or. (.not. (t_1 <= 5d+274))) then
        tmp = ((x * (y / a)) / 2.0d0) - (t * (z / (a / 4.5d0)))
    else
        tmp = ((x * y) - (9.0d0 * (z * t))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -4e+214) || !(t_1 <= 5e+274)) {
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)));
	} else {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -4e+214) or not (t_1 <= 5e+274):
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)))
	else:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -4e+214) || !(t_1 <= 5e+274))
		tmp = Float64(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(t * Float64(z / Float64(a / 4.5))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -4e+214) || ~((t_1 <= 5e+274)))
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)));
	else
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+214], N[Not[LessEqual[t$95$1, 5e+274]], $MachinePrecision]], N[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(t * N[(z / N[(a / 4.5), $MachinePrecision]), $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 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -3.9999999999999998e214 or 4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 74.0%

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

      1. *-commutative 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*l* 74.0%

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

   3. Simplified 74.0%

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

      1. div-sub 69.4%

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

      2. sub-neg 69.4%

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

      3. *-commutative 69.4%

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

      4. times-frac 77.1%

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

      5. div-inv 77.1%

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

      6. associate-*r* 77.2%

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

      7. *-commutative 77.2%

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

      8. associate-*l* 77.1%

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

      9. *-commutative 77.1%

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

      10. associate-/r* 77.1%

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

      11. metadata-eval 77.1%

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

   5. Applied egg-rr 77.1%

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

      1. sub-neg 77.1%

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

      2. associate-*l/ 77.1%

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

      3. associate-*r/ 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-*l* 77.1%

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

      6. *-commutative 77.1%

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

      7. metadata-eval 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in t around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*l/ 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-*r* 77.1%

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

      6. associate-*r/ 92.0%

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

      7. associate-/l* 92.0%

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

   10. Simplified 92.0%

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

   if -3.9999999999999998e214 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.9999999999999998e274

   1. Initial program 99.1%

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

      1. fma-neg 99.1%

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

      2. associate-*l* 99.1%

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

      3. distribute-rgt-neg-in 99.1%

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

      4. *-commutative 99.1%

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

      5. distribute-rgt-neg-in 99.1%

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

      6. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. *-commutative 99.1%

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

      2. metadata-eval 99.1%

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

      3. distribute-lft-neg-in 99.1%

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

      4. distribute-rgt-neg-in 99.1%

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

      5. fma-neg 99.0%

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

      6. associate-*r* 99.1%

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

      7. *-commutative 99.1%

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

      8. associate-*l* 99.2%

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

   5. Applied egg-rr 99.2%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -4 \cdot 10^{+214} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+274}\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - t \cdot \frac{z}{\frac{a}{4.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+281}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{elif}\;t_1 \leq 10^{+291}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{t \cdot -4.5}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -1e+281)
     (/ (* t -4.5) (/ a z))
     (if (<= t_1 1e+291)
       (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
       (/ z (/ a (* t -4.5)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e+281) {
		tmp = (t * -4.5) / (a / z);
	} else if (t_1 <= 1e+291) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = z / (a / (t * -4.5));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 = (z * 9.0d0) * t
    if (t_1 <= (-1d+281)) then
        tmp = (t * (-4.5d0)) / (a / z)
    else if (t_1 <= 1d+291) then
        tmp = ((x * y) - (9.0d0 * (z * t))) / (a * 2.0d0)
    else
        tmp = z / (a / (t * (-4.5d0)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e+281) {
		tmp = (t * -4.5) / (a / z);
	} else if (t_1 <= 1e+291) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = z / (a / (t * -4.5));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -1e+281:
		tmp = (t * -4.5) / (a / z)
	elif t_1 <= 1e+291:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = z / (a / (t * -4.5))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -1e+281)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	elseif (t_1 <= 1e+291)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(z / Float64(a / Float64(t * -4.5)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -1e+281)
		tmp = (t * -4.5) / (a / z);
	elseif (t_1 <= 1e+291)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = z / (a / (t * -4.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+281], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+291], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z / N[(a / N[(t * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z 9) t) < -1e281

   1. Initial program 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-*l* 56.9%

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

   3. Simplified 56.9%

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

   4. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 93.5%

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

      3. associate-*l/ 93.7%

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

   6. Simplified 93.7%

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

   if -1e281 < (*.f64 (*.f64 z 9) t) < 9.9999999999999996e290

   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. fma-neg 95.7%

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

      2. associate-*l* 95.7%

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

      3. distribute-rgt-neg-in 95.7%

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

      4. *-commutative 95.7%

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

      5. distribute-rgt-neg-in 95.7%

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

      6. metadata-eval 95.7%

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

   3. Simplified 95.7%

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

      1. *-commutative 95.7%

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

      2. metadata-eval 95.7%

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

      3. distribute-lft-neg-in 95.7%

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

      4. distribute-rgt-neg-in 95.7%

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

      5. fma-neg 95.7%

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

      6. associate-*r* 95.7%

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

      7. *-commutative 95.7%

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

      8. associate-*l* 95.8%

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

   5. Applied egg-rr 95.8%

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

   if 9.9999999999999996e290 < (*.f64 (*.f64 z 9) t)

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*l* 65.4%

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

   3. Simplified 65.4%

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

      1. div-sub 60.2%

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

      2. sub-neg 60.2%

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

      3. *-commutative 60.2%

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

      4. times-frac 60.2%

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

      5. div-inv 60.2%

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

      6. associate-*r* 60.2%

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

      7. *-commutative 60.2%

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

      8. associate-*l* 60.2%

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

      9. *-commutative 60.2%

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

      10. associate-/r* 60.2%

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

      11. metadata-eval 60.2%

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

   5. Applied egg-rr 60.2%

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

      1. sub-neg 60.2%

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

      2. associate-*l/ 60.2%

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

      3. associate-*r/ 60.2%

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

      4. *-commutative 60.2%

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

      5. associate-*l* 60.2%

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

      6. *-commutative 60.2%

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

      7. metadata-eval 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in t around 0 60.2%

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

      1. *-commutative 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-*l/ 60.2%

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

      4. *-commutative 60.2%

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

      5. associate-*r* 60.2%

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

      6. associate-*r/ 94.3%

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

      7. associate-/l* 94.4%

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

   10. Simplified 94.4%

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

   11. Taylor expanded in x around 0 65.4%

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

       1. associate-*r/ 65.4%

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

       2. associate-*r* 65.4%

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

       3. *-commutative 65.4%

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

       4. *-commutative 65.4%

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

       5. associate-/l* 95.0%

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

   13. Simplified 95.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+281}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+291}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{t \cdot -4.5}}\\ \end{array} \]

Alternative 3: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.55 \cdot 10^{-88}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+122} \lor \neg \left(t \leq 1.45 \cdot 10^{+140}\right) \land t \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.55e-88)
   (* -4.5 (/ t (/ a z)))
   (if (or (<= t 4.1e+122) (and (not (<= t 1.45e+140)) (<= t 5.5e+148)))
     (* (* x (/ y a)) 0.5)
     (* -4.5 (* z (/ t a))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.55e-88) {
		tmp = -4.5 * (t / (a / z));
	} else if ((t <= 4.1e+122) || (!(t <= 1.45e+140) && (t <= 5.5e+148))) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-3.55d-88)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((t <= 4.1d+122) .or. (.not. (t <= 1.45d+140)) .and. (t <= 5.5d+148)) then
        tmp = (x * (y / a)) * 0.5d0
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.55e-88) {
		tmp = -4.5 * (t / (a / z));
	} else if ((t <= 4.1e+122) || (!(t <= 1.45e+140) && (t <= 5.5e+148))) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.55e-88:
		tmp = -4.5 * (t / (a / z))
	elif (t <= 4.1e+122) or (not (t <= 1.45e+140) and (t <= 5.5e+148)):
		tmp = (x * (y / a)) * 0.5
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.55e-88)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif ((t <= 4.1e+122) || (!(t <= 1.45e+140) && (t <= 5.5e+148)))
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.55e-88)
		tmp = -4.5 * (t / (a / z));
	elseif ((t <= 4.1e+122) || (~((t <= 1.45e+140)) && (t <= 5.5e+148)))
		tmp = (x * (y / a)) * 0.5;
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.55e-88], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.1e+122], And[N[Not[LessEqual[t, 1.45e+140]], $MachinePrecision], LessEqual[t, 5.5e+148]]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.55e-88

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around 0 51.0%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

   if -3.55e-88 < t < 4.1000000000000002e122 or 1.4499999999999999e140 < t < 5.5e148

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around inf 69.3%

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

      1. associate-*r/ 66.3%

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

   6. Simplified 66.3%

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

   if 4.1000000000000002e122 < t < 1.4499999999999999e140 or 5.5e148 < t

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in x around 0 74.8%

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

      1. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

      1. associate-/r/ 79.2%

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

   8. Applied egg-rr 79.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.55 \cdot 10^{-88}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+122} \lor \neg \left(t \leq 1.45 \cdot 10^{+140}\right) \land t \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 4: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-85}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+140} \lor \neg \left(t \leq 5.2 \cdot 10^{+148}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-85)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 7.8e+121)
     (* 0.5 (/ x (/ a y)))
     (if (or (<= t 1.35e+140) (not (<= t 5.2e+148)))
       (* -4.5 (* z (/ t a)))
       (* (* x (/ y a)) 0.5)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-85) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 7.8e+121) {
		tmp = 0.5 * (x / (a / y));
	} else if ((t <= 1.35e+140) || !(t <= 5.2e+148)) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = (x * (y / a)) * 0.5;
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-1.2d-85)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 7.8d+121) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((t <= 1.35d+140) .or. (.not. (t <= 5.2d+148))) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = (x * (y / a)) * 0.5d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-85) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 7.8e+121) {
		tmp = 0.5 * (x / (a / y));
	} else if ((t <= 1.35e+140) || !(t <= 5.2e+148)) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = (x * (y / a)) * 0.5;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-85:
		tmp = -4.5 * (t / (a / z))
	elif t <= 7.8e+121:
		tmp = 0.5 * (x / (a / y))
	elif (t <= 1.35e+140) or not (t <= 5.2e+148):
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = (x * (y / a)) * 0.5
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-85)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 7.8e+121)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif ((t <= 1.35e+140) || !(t <= 5.2e+148))
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-85)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 7.8e+121)
		tmp = 0.5 * (x / (a / y));
	elseif ((t <= 1.35e+140) || ~((t <= 5.2e+148)))
		tmp = -4.5 * (z * (t / a));
	else
		tmp = (x * (y / a)) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-85], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+121], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.35e+140], N[Not[LessEqual[t, 5.2e+148]], $MachinePrecision]], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2e-85

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around 0 51.0%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

   if -1.2e-85 < t < 7.79999999999999967e121

   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. *-commutative 95.7%

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

      2. *-commutative 95.7%

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

      3. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around inf 69.6%

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

      1. associate-/l* 67.0%

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

   6. Simplified 67.0%

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

   if 7.79999999999999967e121 < t < 1.35000000000000009e140 or 5.2e148 < t

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in x around 0 74.8%

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

      1. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

      1. associate-/r/ 79.2%

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

   8. Applied egg-rr 79.2%

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

   if 1.35000000000000009e140 < t < 5.2e148

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-85}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+140} \lor \neg \left(t \leq 5.2 \cdot 10^{+148}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \end{array} \]

Alternative 5: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-107}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+122}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e-107)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 5e+122)
     (* 0.5 (/ x (/ a y)))
     (if (<= t 1.5e+140)
       (* -4.5 (* z (/ t a)))
       (if (<= t 5.2e+148) (* (* x (/ y a)) 0.5) (* z (* t (/ -4.5 a))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e-107) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 5e+122) {
		tmp = 0.5 * (x / (a / y));
	} else if (t <= 1.5e+140) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 5.2e+148) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-2.3d-107)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 5d+122) then
        tmp = 0.5d0 * (x / (a / y))
    else if (t <= 1.5d+140) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 5.2d+148) then
        tmp = (x * (y / a)) * 0.5d0
    else
        tmp = z * (t * ((-4.5d0) / a))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e-107) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 5e+122) {
		tmp = 0.5 * (x / (a / y));
	} else if (t <= 1.5e+140) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 5.2e+148) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e-107:
		tmp = -4.5 * (t / (a / z))
	elif t <= 5e+122:
		tmp = 0.5 * (x / (a / y))
	elif t <= 1.5e+140:
		tmp = -4.5 * (z * (t / a))
	elif t <= 5.2e+148:
		tmp = (x * (y / a)) * 0.5
	else:
		tmp = z * (t * (-4.5 / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e-107)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 5e+122)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (t <= 1.5e+140)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 5.2e+148)
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e-107)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 5e+122)
		tmp = 0.5 * (x / (a / y));
	elseif (t <= 1.5e+140)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 5.2e+148)
		tmp = (x * (y / a)) * 0.5;
	else
		tmp = z * (t * (-4.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e-107], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+122], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+140], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+148], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.30000000000000003e-107

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around 0 50.3%

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

      1. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   if -2.30000000000000003e-107 < t < 4.99999999999999989e122

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 69.7%

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

      1. associate-/l* 67.7%

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

   6. Simplified 67.7%

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

   if 4.99999999999999989e122 < t < 1.49999999999999998e140

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

      1. associate-/r/ 75.9%

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

   8. Applied egg-rr 75.9%

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

   if 1.49999999999999998e140 < t < 5.2e148

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   if 5.2e148 < t

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-/l* 79.7%

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

      3. associate-*l/ 79.6%

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

   6. Simplified 79.6%

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

      1. associate-/r/ 79.6%

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

   8. Applied egg-rr 79.6%

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

   9. Taylor expanded in t around 0 79.6%

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

       1. associate-*r/ 79.6%

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

       2. *-commutative 79.6%

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

       3. *-rgt-identity 79.6%

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

       4. associate-*r/ 79.6%

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

       5. associate-*l* 79.6%

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

       6. associate-*r/ 79.6%

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

       7. metadata-eval 79.6%

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

   11. Simplified 79.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-107}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+122}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \]

Alternative 6: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-104}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-104)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 2.8e+122)
     (* 0.5 (/ x (/ a y)))
     (if (<= t 1.5e+140)
       (* -4.5 (* z (/ t a)))
       (if (<= t 5.2e+148) (* (* x (/ y a)) 0.5) (* -4.5 (/ z (/ a t))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-104) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 2.8e+122) {
		tmp = 0.5 * (x / (a / y));
	} else if (t <= 1.5e+140) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 5.2e+148) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-1.6d-104)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 2.8d+122) then
        tmp = 0.5d0 * (x / (a / y))
    else if (t <= 1.5d+140) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 5.2d+148) then
        tmp = (x * (y / a)) * 0.5d0
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-104) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 2.8e+122) {
		tmp = 0.5 * (x / (a / y));
	} else if (t <= 1.5e+140) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 5.2e+148) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e-104:
		tmp = -4.5 * (t / (a / z))
	elif t <= 2.8e+122:
		tmp = 0.5 * (x / (a / y))
	elif t <= 1.5e+140:
		tmp = -4.5 * (z * (t / a))
	elif t <= 5.2e+148:
		tmp = (x * (y / a)) * 0.5
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-104)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 2.8e+122)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (t <= 1.5e+140)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 5.2e+148)
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e-104)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 2.8e+122)
		tmp = 0.5 * (x / (a / y));
	elseif (t <= 1.5e+140)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 5.2e+148)
		tmp = (x * (y / a)) * 0.5;
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-104], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+122], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+140], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+148], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.59999999999999994e-104

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around 0 50.3%

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

      1. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   if -1.59999999999999994e-104 < t < 2.8e122

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 69.7%

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

      1. associate-/l* 67.7%

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

   6. Simplified 67.7%

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

   if 2.8e122 < t < 1.49999999999999998e140

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

      1. associate-/r/ 75.9%

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

   8. Applied egg-rr 75.9%

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

   if 1.49999999999999998e140 < t < 5.2e148

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   if 5.2e148 < t

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

      1. div-sub 76.6%

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

      2. sub-neg 76.6%

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

      3. *-commutative 76.6%

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

      4. times-frac 79.1%

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

      5. div-inv 79.1%

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

      6. associate-*r* 79.2%

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

      7. *-commutative 79.2%

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

      8. associate-*l* 79.1%

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

      9. *-commutative 79.1%

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

      10. associate-/r* 79.1%

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

      11. metadata-eval 79.1%

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

   5. Applied egg-rr 79.1%

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

      1. sub-neg 79.1%

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

      2. associate-*l/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*l* 79.1%

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

      6. *-commutative 79.1%

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

      7. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in t around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*l/ 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*r* 79.1%

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

      6. associate-*r/ 83.9%

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

      7. associate-/l* 83.9%

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

   10. Simplified 83.9%

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

   11. Taylor expanded in x around 0 77.2%

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

       1. associate-*r/ 77.1%

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

       2. associate-*r* 77.1%

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

       3. *-commutative 77.1%

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

       4. *-commutative 77.1%

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

       5. associate-/l* 80.9%

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

   13. Simplified 80.9%

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

       1. associate-/r* 81.0%

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

       2. associate-/r/ 81.1%

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

   15. Applied egg-rr 81.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-104}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 7: 67.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-104}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+140}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e-104)
   (/ t (/ (/ a z) -4.5))
   (if (<= t 2.7e+122)
     (* 0.5 (/ x (/ a y)))
     (if (<= t 1.15e+140)
       (* -4.5 (* z (/ t a)))
       (if (<= t 5.2e+148) (* (* x (/ y a)) 0.5) (* -4.5 (/ z (/ a t))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e-104) {
		tmp = t / ((a / z) / -4.5);
	} else if (t <= 2.7e+122) {
		tmp = 0.5 * (x / (a / y));
	} else if (t <= 1.15e+140) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 5.2e+148) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-1.8d-104)) then
        tmp = t / ((a / z) / (-4.5d0))
    else if (t <= 2.7d+122) then
        tmp = 0.5d0 * (x / (a / y))
    else if (t <= 1.15d+140) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 5.2d+148) then
        tmp = (x * (y / a)) * 0.5d0
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e-104) {
		tmp = t / ((a / z) / -4.5);
	} else if (t <= 2.7e+122) {
		tmp = 0.5 * (x / (a / y));
	} else if (t <= 1.15e+140) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 5.2e+148) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e-104:
		tmp = t / ((a / z) / -4.5)
	elif t <= 2.7e+122:
		tmp = 0.5 * (x / (a / y))
	elif t <= 1.15e+140:
		tmp = -4.5 * (z * (t / a))
	elif t <= 5.2e+148:
		tmp = (x * (y / a)) * 0.5
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e-104)
		tmp = Float64(t / Float64(Float64(a / z) / -4.5));
	elseif (t <= 2.7e+122)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (t <= 1.15e+140)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 5.2e+148)
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e-104)
		tmp = t / ((a / z) / -4.5);
	elseif (t <= 2.7e+122)
		tmp = 0.5 * (x / (a / y));
	elseif (t <= 1.15e+140)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 5.2e+148)
		tmp = (x * (y / a)) * 0.5;
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e-104], N[(t / N[(N[(a / z), $MachinePrecision] / -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+122], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+140], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+148], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7999999999999999e-104

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around 0 50.3%

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

      1. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

      1. associate-*r/ 58.7%

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

      2. *-commutative 58.7%

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

      3. associate-/l* 58.6%

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

   8. Applied egg-rr 58.6%

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

   if -1.7999999999999999e-104 < t < 2.6999999999999998e122

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 69.7%

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

      1. associate-/l* 67.7%

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

   6. Simplified 67.7%

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

   if 2.6999999999999998e122 < t < 1.14999999999999995e140

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

      1. associate-/r/ 75.9%

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

   8. Applied egg-rr 75.9%

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

   if 1.14999999999999995e140 < t < 5.2e148

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   if 5.2e148 < t

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

      1. div-sub 76.6%

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

      2. sub-neg 76.6%

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

      3. *-commutative 76.6%

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

      4. times-frac 79.1%

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

      5. div-inv 79.1%

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

      6. associate-*r* 79.2%

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

      7. *-commutative 79.2%

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

      8. associate-*l* 79.1%

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

      9. *-commutative 79.1%

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

      10. associate-/r* 79.1%

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

      11. metadata-eval 79.1%

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

   5. Applied egg-rr 79.1%

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

      1. sub-neg 79.1%

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

      2. associate-*l/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*l* 79.1%

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

      6. *-commutative 79.1%

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

      7. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in t around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*l/ 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*r* 79.1%

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

      6. associate-*r/ 83.9%

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

      7. associate-/l* 83.9%

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

   10. Simplified 83.9%

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

   11. Taylor expanded in x around 0 77.2%

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

       1. associate-*r/ 77.1%

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

       2. associate-*r* 77.1%

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

       3. *-commutative 77.1%

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

       4. *-commutative 77.1%

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

       5. associate-/l* 80.9%

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

   13. Simplified 80.9%

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

       1. associate-/r* 81.0%

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

       2. associate-/r/ 81.1%

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

   15. Applied egg-rr 81.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-104}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+122}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+140}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 8: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 10^{+149}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e-88)
   (/ t (/ (/ a z) -4.5))
   (if (<= t 1.7e+122)
     (/ (* x (* y 0.5)) a)
     (if (<= t 1.9e+139)
       (* -4.5 (* z (/ t a)))
       (if (<= t 1e+149) (* (* x (/ y a)) 0.5) (* -4.5 (/ z (/ a t))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-88) {
		tmp = t / ((a / z) / -4.5);
	} else if (t <= 1.7e+122) {
		tmp = (x * (y * 0.5)) / a;
	} else if (t <= 1.9e+139) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 1e+149) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-2.4d-88)) then
        tmp = t / ((a / z) / (-4.5d0))
    else if (t <= 1.7d+122) then
        tmp = (x * (y * 0.5d0)) / a
    else if (t <= 1.9d+139) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 1d+149) then
        tmp = (x * (y / a)) * 0.5d0
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-88) {
		tmp = t / ((a / z) / -4.5);
	} else if (t <= 1.7e+122) {
		tmp = (x * (y * 0.5)) / a;
	} else if (t <= 1.9e+139) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 1e+149) {
		tmp = (x * (y / a)) * 0.5;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e-88:
		tmp = t / ((a / z) / -4.5)
	elif t <= 1.7e+122:
		tmp = (x * (y * 0.5)) / a
	elif t <= 1.9e+139:
		tmp = -4.5 * (z * (t / a))
	elif t <= 1e+149:
		tmp = (x * (y / a)) * 0.5
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e-88)
		tmp = Float64(t / Float64(Float64(a / z) / -4.5));
	elseif (t <= 1.7e+122)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (t <= 1.9e+139)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 1e+149)
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e-88)
		tmp = t / ((a / z) / -4.5);
	elseif (t <= 1.7e+122)
		tmp = (x * (y * 0.5)) / a;
	elseif (t <= 1.9e+139)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 1e+149)
		tmp = (x * (y / a)) * 0.5;
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e-88], N[(t / N[(N[(a / z), $MachinePrecision] / -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+122], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1.9e+139], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+149], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.4e-88

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around 0 51.0%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

      1. associate-*r/ 59.8%

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

      2. *-commutative 59.8%

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

      3. associate-/l* 59.7%

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

   8. Applied egg-rr 59.7%

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

   if -2.4e-88 < t < 1.7e122

   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. *-commutative 95.7%

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

      2. *-commutative 95.7%

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

      3. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around inf 69.6%

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

      1. associate-*r/ 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*r* 69.6%

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

   6. Simplified 69.6%

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

   if 1.7e122 < t < 1.9e139

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

      1. associate-/r/ 75.9%

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

   8. Applied egg-rr 75.9%

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

   if 1.9e139 < t < 1.00000000000000005e149

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   if 1.00000000000000005e149 < t

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

      1. div-sub 76.6%

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

      2. sub-neg 76.6%

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

      3. *-commutative 76.6%

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

      4. times-frac 79.1%

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

      5. div-inv 79.1%

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

      6. associate-*r* 79.2%

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

      7. *-commutative 79.2%

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

      8. associate-*l* 79.1%

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

      9. *-commutative 79.1%

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

      10. associate-/r* 79.1%

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

      11. metadata-eval 79.1%

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

   5. Applied egg-rr 79.1%

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

      1. sub-neg 79.1%

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

      2. associate-*l/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*l* 79.1%

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

      6. *-commutative 79.1%

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

      7. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in t around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*l/ 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*r* 79.1%

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

      6. associate-*r/ 83.9%

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

      7. associate-/l* 83.9%

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

   10. Simplified 83.9%

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

   11. Taylor expanded in x around 0 77.2%

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

       1. associate-*r/ 77.1%

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

       2. associate-*r* 77.1%

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

       3. *-commutative 77.1%

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

       4. *-commutative 77.1%

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

       5. associate-/l* 80.9%

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

   13. Simplified 80.9%

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

       1. associate-/r* 81.0%

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

       2. associate-/r/ 81.1%

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

   15. Applied egg-rr 81.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{z}}{-4.5}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 10^{+149}:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 9: 51.2% accurate, 1.9× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 90.4%

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

   1. *-commutative 90.4%

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

   2. *-commutative 90.4%

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

   3. associate-*l* 90.4%

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

3. Simplified 90.4%

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

4. Taylor expanded in x around 0 46.0%

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

   1. associate-/l* 50.0%

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

6. Simplified 50.0%

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

   1. associate-/r/ 48.9%

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

8. Applied egg-rr 48.9%

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

9. Final simplification 48.9%

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

Alternative 10: 50.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

   1. *-commutative 90.4%

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

   2. *-commutative 90.4%

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

   3. associate-*l* 90.4%

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

3. Simplified 90.4%

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

4. Taylor expanded in x around 0 46.0%

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

   1. associate-/l* 50.0%

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

6. Simplified 50.0%

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

7. Final simplification 50.0%

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

Developer target: 93.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023305 
(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)))