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

Percentage Accurate: 91.3% → 93.3%

Time: 9.0s

Alternatives: 14

Speedup: 0.8×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.3% 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: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq 10^{+308}:\\ \;\;\;\;\frac{x \cdot y - t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

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+308) (/ (- (* x y) t_1) (* a 2.0)) (* z (/ (* t -4.5) a)))))

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+308) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= 1d+308) then
        tmp = ((x * y) - t_1) / (a * 2.0d0)
    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 t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= 1e+308) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	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+308:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = z * ((t * -4.5) / a)
	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+308)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	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+308)
		tmp = ((x * y) - t_1) / (a * 2.0);
	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_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+308], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z 9) t) < 1e308

   1. Initial program 96.6%

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

   if 1e308 < (*.f64 (*.f64 z 9) t)

   1. Initial program 54.4%

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

      1. *-commutative 54.4%

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

      2. *-commutative 54.4%

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

      3. associate-*l* 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in x around 0 54.4%

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

      1. associate-*r/ 54.4%

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

      2. associate-*r* 54.4%

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

   6. Simplified 54.4%

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

      1. associate-*l* 54.4%

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

      2. *-un-lft-identity 54.4%

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

      3. times-frac 54.4%

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

      4. metadata-eval 54.4%

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

      5. associate-*l/ 99.7%

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

      6. associate-*r* 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. expm1-log1p-u 47.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-4.5 \cdot \frac{t}{a}\right)\right)} \cdot z \]

      2. expm1-udef 34.0%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(-4.5 \cdot \frac{t}{a}\right)} - 1\right)} \cdot z \]

      3. associate-*r/ 34.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{-4.5 \cdot t}{a}}\right)} - 1\right) \cdot z \]

      4. *-commutative 34.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{t \cdot -4.5}}{a}\right)} - 1\right) \cdot z \]

      5. associate-/l* 34.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{a}{-4.5}}}\right)} - 1\right) \cdot z \]

   10. Applied egg-rr 34.0%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{\frac{a}{-4.5}}\right)} - 1\right)} \cdot z \]
   11. Step-by-step derivation

       1. expm1-def 48.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{\frac{a}{-4.5}}\right)\right)} \cdot z \]

       2. expm1-log1p 99.8%

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

       3. associate-/l* 99.8%

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

       4. *-commutative 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 10^{+308}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \]

Alternative 2: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) -400000000.0)
     t_1
     (if (<= (* x y) -1e-33)
       (* z (* -4.5 (/ t a)))
       (if (<= (* x y) -4e-84)
         t_1
         (if (<= (* x y) 1e+26)
           (/ (* -9.0 (* z t)) (* a 2.0))
           (* x (* y (/ 0.5 a)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else {
		tmp = x * (y * (0.5 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / (a * 2.0d0)
    if ((x * y) <= (-400000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-1d-33)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if ((x * y) <= (-4d-84)) then
        tmp = t_1
    else if ((x * y) <= 1d+26) then
        tmp = ((-9.0d0) * (z * t)) / (a * 2.0d0)
    else
        tmp = x * (y * (0.5d0 / 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 t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -400000000.0:
		tmp = t_1
	elif (x * y) <= -1e-33:
		tmp = z * (-4.5 * (t / a))
	elif (x * y) <= -4e-84:
		tmp = t_1
	elif (x * y) <= 1e+26:
		tmp = (-9.0 * (z * t)) / (a * 2.0)
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -400000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-33)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+26)
		tmp = Float64(Float64(-9.0 * Float64(z * t)) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -400000000.0)
		tmp = t_1;
	elseif ((x * y) <= -1e-33)
		tmp = z * (-4.5 * (t / a));
	elseif ((x * y) <= -4e-84)
		tmp = t_1;
	elseif ((x * y) <= 1e+26)
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	else
		tmp = x * (y * (0.5 / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -400000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-33], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+26], N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e8 or -1.0000000000000001e-33 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -4e8 < (*.f64 x y) < -1.0000000000000001e-33

   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* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around 0 73.7%

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

      1. associate-*r/ 74.2%

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

      2. associate-*r* 74.2%

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

   6. Simplified 74.2%

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

      1. associate-*l* 74.2%

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

      2. *-un-lft-identity 74.2%

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

      3. times-frac 73.7%

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

      4. metadata-eval 73.7%

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

      5. associate-*l/ 86.6%

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

      6. associate-*r* 87.0%

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

   8. Applied egg-rr 87.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 1.00000000000000005e26

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around 0 84.1%

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

   if 1.00000000000000005e26 < (*.f64 x y)

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 71.2%

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

      1. associate-*r/ 71.2%

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

      2. associate-*l/ 71.2%

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

      3. *-commutative 71.2%

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

      4. associate-*l* 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) -400000000.0)
     t_1
     (if (<= (* x y) -1e-33)
       (* z (* -4.5 (/ t a)))
       (if (<= (* x y) -4e-84)
         t_1
         (if (<= (* x y) 1e+26)
           (/ (* t (* z -9.0)) (* a 2.0))
           (* x (* y (/ 0.5 a)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = (t * (z * -9.0)) / (a * 2.0);
	} else {
		tmp = x * (y * (0.5 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / (a * 2.0d0)
    if ((x * y) <= (-400000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-1d-33)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if ((x * y) <= (-4d-84)) then
        tmp = t_1
    else if ((x * y) <= 1d+26) then
        tmp = (t * (z * (-9.0d0))) / (a * 2.0d0)
    else
        tmp = x * (y * (0.5d0 / 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 t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = (t * (z * -9.0)) / (a * 2.0);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -400000000.0:
		tmp = t_1
	elif (x * y) <= -1e-33:
		tmp = z * (-4.5 * (t / a))
	elif (x * y) <= -4e-84:
		tmp = t_1
	elif (x * y) <= 1e+26:
		tmp = (t * (z * -9.0)) / (a * 2.0)
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -400000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-33)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+26)
		tmp = Float64(Float64(t * Float64(z * -9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -400000000.0)
		tmp = t_1;
	elseif ((x * y) <= -1e-33)
		tmp = z * (-4.5 * (t / a));
	elseif ((x * y) <= -4e-84)
		tmp = t_1;
	elseif ((x * y) <= 1e+26)
		tmp = (t * (z * -9.0)) / (a * 2.0);
	else
		tmp = x * (y * (0.5 / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -400000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-33], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+26], N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e8 or -1.0000000000000001e-33 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -4e8 < (*.f64 x y) < -1.0000000000000001e-33

   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* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around 0 73.7%

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

      1. associate-*r/ 74.2%

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

      2. associate-*r* 74.2%

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

   6. Simplified 74.2%

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

      1. associate-*l* 74.2%

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

      2. *-un-lft-identity 74.2%

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

      3. times-frac 73.7%

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

      4. metadata-eval 73.7%

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

      5. associate-*l/ 86.6%

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

      6. associate-*r* 87.0%

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

   8. Applied egg-rr 87.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 1.00000000000000005e26

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-*r* 84.1%

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

   6. Simplified 84.1%

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

   if 1.00000000000000005e26 < (*.f64 x y)

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 71.2%

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

      1. associate-*r/ 71.2%

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

      2. associate-*l/ 71.2%

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

      3. *-commutative 71.2%

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

      4. associate-*l* 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]

Alternative 4: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{-4.5}{\frac{a}{z \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) -400000000.0)
     t_1
     (if (<= (* x y) -1e-33)
       (* z (* -4.5 (/ t a)))
       (if (<= (* x y) -4e-84)
         t_1
         (if (<= (* x y) 1e+26)
           (/ -4.5 (/ a (* z t)))
           (* x (* y (/ 0.5 a)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = -4.5 / (a / (z * t));
	} else {
		tmp = x * (y * (0.5 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / (a * 2.0d0)
    if ((x * y) <= (-400000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-1d-33)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if ((x * y) <= (-4d-84)) then
        tmp = t_1
    else if ((x * y) <= 1d+26) then
        tmp = (-4.5d0) / (a / (z * t))
    else
        tmp = x * (y * (0.5d0 / 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 t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = -4.5 / (a / (z * t));
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -400000000.0:
		tmp = t_1
	elif (x * y) <= -1e-33:
		tmp = z * (-4.5 * (t / a))
	elif (x * y) <= -4e-84:
		tmp = t_1
	elif (x * y) <= 1e+26:
		tmp = -4.5 / (a / (z * t))
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -400000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-33)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+26)
		tmp = Float64(-4.5 / Float64(a / Float64(z * t)));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -400000000.0)
		tmp = t_1;
	elseif ((x * y) <= -1e-33)
		tmp = z * (-4.5 * (t / a));
	elseif ((x * y) <= -4e-84)
		tmp = t_1;
	elseif ((x * y) <= 1e+26)
		tmp = -4.5 / (a / (z * t));
	else
		tmp = x * (y * (0.5 / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -400000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-33], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+26], N[(-4.5 / N[(a / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e8 or -1.0000000000000001e-33 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -4e8 < (*.f64 x y) < -1.0000000000000001e-33

   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* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around 0 73.7%

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

      1. associate-*r/ 74.2%

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

      2. associate-*r* 74.2%

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

   6. Simplified 74.2%

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

      1. associate-*l* 74.2%

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

      2. *-un-lft-identity 74.2%

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

      3. times-frac 73.7%

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

      4. metadata-eval 73.7%

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

      5. associate-*l/ 86.6%

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

      6. associate-*r* 87.0%

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

   8. Applied egg-rr 87.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 1.00000000000000005e26

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around 0 84.0%

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

      1. associate-*r/ 84.1%

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

      2. associate-*r* 84.1%

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

   6. Simplified 84.1%

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

      1. associate-*l* 84.1%

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

      2. *-un-lft-identity 84.1%

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

      3. times-frac 84.0%

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

      4. metadata-eval 84.0%

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

      5. associate-*l/ 74.6%

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

      6. associate-*r* 74.6%

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

   8. Applied egg-rr 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate-/r/ 77.9%

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

      3. clear-num 77.8%

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

      4. un-div-inv 77.9%

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

      5. associate-/l/ 84.1%

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

   10. Applied egg-rr 84.1%

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

   if 1.00000000000000005e26 < (*.f64 x y)

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 71.2%

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

      1. associate-*r/ 71.2%

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

      2. associate-*l/ 71.2%

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

      3. *-commutative 71.2%

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

      4. associate-*l* 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{-4.5}{\frac{a}{z \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]

Alternative 5: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) -400000000.0)
     t_1
     (if (<= (* x y) -1e-33)
       (* z (* -4.5 (/ t a)))
       (if (<= (* x y) -4e-84)
         t_1
         (if (<= (* x y) 1e+26)
           (/ (* z (* t -4.5)) a)
           (* x (* y (/ 0.5 a)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = x * (y * (0.5 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / (a * 2.0d0)
    if ((x * y) <= (-400000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-1d-33)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if ((x * y) <= (-4d-84)) then
        tmp = t_1
    else if ((x * y) <= 1d+26) then
        tmp = (z * (t * (-4.5d0))) / a
    else
        tmp = x * (y * (0.5d0 / 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 t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -400000000.0) {
		tmp = t_1;
	} else if ((x * y) <= -1e-33) {
		tmp = z * (-4.5 * (t / a));
	} else if ((x * y) <= -4e-84) {
		tmp = t_1;
	} else if ((x * y) <= 1e+26) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -400000000.0:
		tmp = t_1
	elif (x * y) <= -1e-33:
		tmp = z * (-4.5 * (t / a))
	elif (x * y) <= -4e-84:
		tmp = t_1
	elif (x * y) <= 1e+26:
		tmp = (z * (t * -4.5)) / a
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -400000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-33)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+26)
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -400000000.0)
		tmp = t_1;
	elseif ((x * y) <= -1e-33)
		tmp = z * (-4.5 * (t / a));
	elseif ((x * y) <= -4e-84)
		tmp = t_1;
	elseif ((x * y) <= 1e+26)
		tmp = (z * (t * -4.5)) / a;
	else
		tmp = x * (y * (0.5 / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -400000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-33], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+26], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e8 or -1.0000000000000001e-33 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -4e8 < (*.f64 x y) < -1.0000000000000001e-33

   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* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around 0 73.7%

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

      1. associate-*r/ 74.2%

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

      2. associate-*r* 74.2%

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

   6. Simplified 74.2%

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

      1. associate-*l* 74.2%

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

      2. *-un-lft-identity 74.2%

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

      3. times-frac 73.7%

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

      4. metadata-eval 73.7%

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

      5. associate-*l/ 86.6%

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

      6. associate-*r* 87.0%

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

   8. Applied egg-rr 87.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 1.00000000000000005e26

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around 0 84.0%

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

      1. associate-*r/ 84.1%

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

      2. associate-*r* 84.1%

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

   6. Simplified 84.1%

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

   if 1.00000000000000005e26 < (*.f64 x y)

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 71.2%

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

      1. associate-*r/ 71.2%

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

      2. associate-*l/ 71.2%

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

      3. *-commutative 71.2%

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

      4. associate-*l* 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -400000000:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]

Alternative 6: 93.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 5e+303)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* x (/ (* y 0.5) a))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 5e+303) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= 5d+303) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= 5e+303) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 5e+303:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 5e+303)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / 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 ((x * y) <= 5e+303)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = x * ((y * 0.5) / 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[N[(x * y), $MachinePrecision], 5e+303], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 4.9999999999999997e303

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   if 4.9999999999999997e303 < (*.f64 x y)

   1. Initial program 69.0%

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

      1. *-commutative 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*l* 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in x around inf 69.0%

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

      1. associate-*r/ 69.0%

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

      2. associate-*l/ 69.0%

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

      3. *-commutative 69.0%

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

      4. associate-*l* 99.8%

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

   6. Simplified 99.8%

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

      1. associate-*r/ 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]

Alternative 7: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ t_2 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-149}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* 0.5 (/ x (/ a y)))) (t_2 (* -4.5 (* z (/ t a)))))
   (if (<= t -2.3e-131)
     t_2
     (if (<= t 8.4e-170)
       t_1
       (if (<= t 5.7e-149)
         (* -4.5 (/ (* z t) a))
         (if (<= t 1.06e+120) t_1 t_2))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double t_2 = -4.5 * (z * (t / a));
	double tmp;
	if (t <= -2.3e-131) {
		tmp = t_2;
	} else if (t <= 8.4e-170) {
		tmp = t_1;
	} else if (t <= 5.7e-149) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1.06e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 0.5d0 * (x / (a / y))
    t_2 = (-4.5d0) * (z * (t / a))
    if (t <= (-2.3d-131)) then
        tmp = t_2
    else if (t <= 8.4d-170) then
        tmp = t_1
    else if (t <= 5.7d-149) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 1.06d+120) then
        tmp = t_1
    else
        tmp = t_2
    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 = 0.5 * (x / (a / y));
	double t_2 = -4.5 * (z * (t / a));
	double tmp;
	if (t <= -2.3e-131) {
		tmp = t_2;
	} else if (t <= 8.4e-170) {
		tmp = t_1;
	} else if (t <= 5.7e-149) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1.06e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	t_2 = -4.5 * (z * (t / a))
	tmp = 0
	if t <= -2.3e-131:
		tmp = t_2
	elif t <= 8.4e-170:
		tmp = t_1
	elif t <= 5.7e-149:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 1.06e+120:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	t_2 = Float64(-4.5 * Float64(z * Float64(t / a)))
	tmp = 0.0
	if (t <= -2.3e-131)
		tmp = t_2;
	elseif (t <= 8.4e-170)
		tmp = t_1;
	elseif (t <= 5.7e-149)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 1.06e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	t_2 = -4.5 * (z * (t / a));
	tmp = 0.0;
	if (t <= -2.3e-131)
		tmp = t_2;
	elseif (t <= 8.4e-170)
		tmp = t_1;
	elseif (t <= 5.7e-149)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 1.06e+120)
		tmp = t_1;
	else
		tmp = t_2;
	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[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-131], t$95$2, If[LessEqual[t, 8.4e-170], t$95$1, If[LessEqual[t, 5.7e-149], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+120], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.30000000000000022e-131 or 1.05999999999999994e120 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 69.4%

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

      2. associate-/r/ 71.7%

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

   6. Simplified 71.7%

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

   if -2.30000000000000022e-131 < t < 8.4000000000000002e-170 or 5.6999999999999999e-149 < t < 1.05999999999999994e120

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 65.4%

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

      1. associate-/l* 62.6%

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

   6. Simplified 62.6%

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

   if 8.4000000000000002e-170 < t < 5.6999999999999999e-149

   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. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 71.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-131}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-170}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-149}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+120}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 8: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ t_2 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-149}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ 0.5 a)))) (t_2 (* -4.5 (* z (/ t a)))))
   (if (<= t -3.4e-131)
     t_2
     (if (<= t 9e-170)
       t_1
       (if (<= t 5.2e-149)
         (* -4.5 (/ (* z t) a))
         (if (<= t 8.6e+119) t_1 t_2))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y * (0.5 / a));
	double t_2 = -4.5 * (z * (t / a));
	double tmp;
	if (t <= -3.4e-131) {
		tmp = t_2;
	} else if (t <= 9e-170) {
		tmp = t_1;
	} else if (t <= 5.2e-149) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 8.6e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * (y * (0.5d0 / a))
    t_2 = (-4.5d0) * (z * (t / a))
    if (t <= (-3.4d-131)) then
        tmp = t_2
    else if (t <= 9d-170) then
        tmp = t_1
    else if (t <= 5.2d-149) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 8.6d+119) then
        tmp = t_1
    else
        tmp = t_2
    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 * (0.5 / a));
	double t_2 = -4.5 * (z * (t / a));
	double tmp;
	if (t <= -3.4e-131) {
		tmp = t_2;
	} else if (t <= 9e-170) {
		tmp = t_1;
	} else if (t <= 5.2e-149) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 8.6e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = x * (y * (0.5 / a))
	t_2 = -4.5 * (z * (t / a))
	tmp = 0
	if t <= -3.4e-131:
		tmp = t_2
	elif t <= 9e-170:
		tmp = t_1
	elif t <= 5.2e-149:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 8.6e+119:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y * Float64(0.5 / a)))
	t_2 = Float64(-4.5 * Float64(z * Float64(t / a)))
	tmp = 0.0
	if (t <= -3.4e-131)
		tmp = t_2;
	elseif (t <= 9e-170)
		tmp = t_1;
	elseif (t <= 5.2e-149)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 8.6e+119)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y * (0.5 / a));
	t_2 = -4.5 * (z * (t / a));
	tmp = 0.0;
	if (t <= -3.4e-131)
		tmp = t_2;
	elseif (t <= 9e-170)
		tmp = t_1;
	elseif (t <= 5.2e-149)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 8.6e+119)
		tmp = t_1;
	else
		tmp = t_2;
	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[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-131], t$95$2, If[LessEqual[t, 9e-170], t$95$1, If[LessEqual[t, 5.2e-149], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+119], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999995e-131 or 8.60000000000000063e119 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 69.4%

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

      2. associate-/r/ 71.7%

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

   6. Simplified 71.7%

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

   if -3.39999999999999995e-131 < t < 9.00000000000000003e-170 or 5.19999999999999998e-149 < t < 8.60000000000000063e119

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 65.4%

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

      1. associate-*r/ 65.4%

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

      2. associate-*l/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-*l* 62.8%

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

   6. Simplified 62.8%

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

   if 9.00000000000000003e-170 < t < 5.19999999999999998e-149

   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. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 71.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-149}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 9: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-149}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.5 (* z (/ t a)))))
   (if (<= t -3.4e-131)
     t_1
     (if (<= t 7.6e-170)
       (* x (* y (/ 0.5 a)))
       (if (<= t 5.7e-149)
         (* -4.5 (/ (* z t) a))
         (if (<= t 9.2e+119) (* x (/ (* y 0.5) a)) t_1))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * (z * (t / a));
	double tmp;
	if (t <= -3.4e-131) {
		tmp = t_1;
	} else if (t <= 7.6e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 5.7e-149) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 9.2e+119) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = t_1;
	}
	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 = (-4.5d0) * (z * (t / a))
    if (t <= (-3.4d-131)) then
        tmp = t_1
    else if (t <= 7.6d-170) then
        tmp = x * (y * (0.5d0 / a))
    else if (t <= 5.7d-149) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 9.2d+119) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = t_1
    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 = -4.5 * (z * (t / a));
	double tmp;
	if (t <= -3.4e-131) {
		tmp = t_1;
	} else if (t <= 7.6e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 5.7e-149) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 9.2e+119) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = -4.5 * (z * (t / a))
	tmp = 0
	if t <= -3.4e-131:
		tmp = t_1
	elif t <= 7.6e-170:
		tmp = x * (y * (0.5 / a))
	elif t <= 5.7e-149:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 9.2e+119:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(z * Float64(t / a)))
	tmp = 0.0
	if (t <= -3.4e-131)
		tmp = t_1;
	elseif (t <= 7.6e-170)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (t <= 5.7e-149)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 9.2e+119)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * (z * (t / a));
	tmp = 0.0;
	if (t <= -3.4e-131)
		tmp = t_1;
	elseif (t <= 7.6e-170)
		tmp = x * (y * (0.5 / a));
	elseif (t <= 5.7e-149)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 9.2e+119)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = t_1;
	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[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-131], t$95$1, If[LessEqual[t, 7.6e-170], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.7e-149], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+119], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.39999999999999995e-131 or 9.2000000000000003e119 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 69.4%

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

      2. associate-/r/ 71.7%

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

   6. Simplified 71.7%

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

   if -3.39999999999999995e-131 < t < 7.5999999999999995e-170

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 71.4%

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

      1. associate-*r/ 71.4%

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

      2. associate-*l/ 71.4%

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

      3. *-commutative 71.4%

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

      4. associate-*l* 66.5%

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

   6. Simplified 66.5%

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

   if 7.5999999999999995e-170 < t < 5.6999999999999999e-149

   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. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 71.2%

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

   if 5.6999999999999999e-149 < t < 9.2000000000000003e119

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around inf 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l* 58.7%

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

   6. Simplified 58.7%

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

      1. associate-*r/ 58.8%

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

   8. Applied egg-rr 58.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-149}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 10: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-148}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 10^{+123}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.5 (/ t a)))))
   (if (<= t -3.4e-131)
     t_1
     (if (<= t 9e-170)
       (* x (* y (/ 0.5 a)))
       (if (<= t 1.95e-148)
         (* -4.5 (/ (* z t) a))
         (if (<= t 1e+123) (* x (/ (* y 0.5) a)) t_1))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-4.5 * (t / a));
	double tmp;
	if (t <= -3.4e-131) {
		tmp = t_1;
	} else if (t <= 9e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 1.95e-148) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1e+123) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = t_1;
	}
	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 * ((-4.5d0) * (t / a))
    if (t <= (-3.4d-131)) then
        tmp = t_1
    else if (t <= 9d-170) then
        tmp = x * (y * (0.5d0 / a))
    else if (t <= 1.95d-148) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 1d+123) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = t_1
    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 * (-4.5 * (t / a));
	double tmp;
	if (t <= -3.4e-131) {
		tmp = t_1;
	} else if (t <= 9e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 1.95e-148) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1e+123) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = z * (-4.5 * (t / a))
	tmp = 0
	if t <= -3.4e-131:
		tmp = t_1
	elif t <= 9e-170:
		tmp = x * (y * (0.5 / a))
	elif t <= 1.95e-148:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 1e+123:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(-4.5 * Float64(t / a)))
	tmp = 0.0
	if (t <= -3.4e-131)
		tmp = t_1;
	elseif (t <= 9e-170)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (t <= 1.95e-148)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 1e+123)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-4.5 * (t / a));
	tmp = 0.0;
	if (t <= -3.4e-131)
		tmp = t_1;
	elseif (t <= 9e-170)
		tmp = x * (y * (0.5 / a));
	elseif (t <= 1.95e-148)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 1e+123)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = t_1;
	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[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-131], t$95$1, If[LessEqual[t, 9e-170], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-148], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+123], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.39999999999999995e-131 or 9.99999999999999978e122 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 70.3%

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

      1. associate-*r/ 70.4%

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

      2. associate-*r* 70.3%

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

   6. Simplified 70.3%

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

      1. associate-*l* 70.4%

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

      2. *-un-lft-identity 70.4%

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

      3. times-frac 70.3%

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

      4. metadata-eval 70.3%

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

      5. associate-*l/ 71.7%

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

      6. associate-*r* 71.8%

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

   8. Applied egg-rr 71.8%

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

   if -3.39999999999999995e-131 < t < 9.00000000000000003e-170

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 71.4%

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

      1. associate-*r/ 71.4%

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

      2. associate-*l/ 71.4%

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

      3. *-commutative 71.4%

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

      4. associate-*l* 66.5%

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

   6. Simplified 66.5%

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

   if 9.00000000000000003e-170 < t < 1.94999999999999997e-148

   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. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 71.2%

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

   if 1.94999999999999997e-148 < t < 9.99999999999999978e122

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around inf 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l* 58.7%

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

   6. Simplified 58.7%

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

      1. associate-*r/ 58.8%

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

   8. Applied egg-rr 58.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-148}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 10^{+123}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 11: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

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 -2e-132)
   (* z (* -4.5 (/ t a)))
   (if (<= t 6e-170)
     (* x (* y (/ 0.5 a)))
     (if (<= t 4.8e-146)
       (* -4.5 (/ (* z t) a))
       (if (<= t 8.6e+119) (* x (/ (* y 0.5) a)) (* 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 <= -2e-132) {
		tmp = z * (-4.5 * (t / a));
	} else if (t <= 6e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 4.8e-146) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 8.6e+119) {
		tmp = x * ((y * 0.5) / a);
	} 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 <= (-2d-132)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if (t <= 6d-170) then
        tmp = x * (y * (0.5d0 / a))
    else if (t <= 4.8d-146) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 8.6d+119) then
        tmp = x * ((y * 0.5d0) / a)
    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 <= -2e-132) {
		tmp = z * (-4.5 * (t / a));
	} else if (t <= 6e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 4.8e-146) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 8.6e+119) {
		tmp = x * ((y * 0.5) / a);
	} 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 <= -2e-132:
		tmp = z * (-4.5 * (t / a))
	elif t <= 6e-170:
		tmp = x * (y * (0.5 / a))
	elif t <= 4.8e-146:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 8.6e+119:
		tmp = x * ((y * 0.5) / a)
	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 <= -2e-132)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (t <= 6e-170)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (t <= 4.8e-146)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 8.6e+119)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(z * Float64(Float64(t * -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 <= -2e-132)
		tmp = z * (-4.5 * (t / a));
	elseif (t <= 6e-170)
		tmp = x * (y * (0.5 / a));
	elseif (t <= 4.8e-146)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 8.6e+119)
		tmp = x * ((y * 0.5) / a);
	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, -2e-132], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-170], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-146], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+119], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2e-132

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in x around 0 67.6%

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

      1. associate-*r/ 67.6%

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

      2. associate-*r* 67.6%

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

   6. Simplified 67.6%

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

      1. associate-*l* 67.6%

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

      2. *-un-lft-identity 67.6%

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

      3. times-frac 67.6%

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

      4. metadata-eval 67.6%

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

      5. associate-*l/ 66.5%

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

      6. associate-*r* 66.6%

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

   8. Applied egg-rr 66.6%

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

   if -2e-132 < t < 6.00000000000000027e-170

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 71.4%

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

      1. associate-*r/ 71.4%

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

      2. associate-*l/ 71.4%

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

      3. *-commutative 71.4%

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

      4. associate-*l* 66.5%

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

   6. Simplified 66.5%

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

   if 6.00000000000000027e-170 < t < 4.8000000000000003e-146

   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. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 71.2%

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

   if 4.8000000000000003e-146 < t < 8.60000000000000063e119

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around inf 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l* 58.7%

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

   6. Simplified 58.7%

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

      1. associate-*r/ 58.8%

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

   8. Applied egg-rr 58.8%

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

   if 8.60000000000000063e119 < t

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 78.5%

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

      1. associate-*r/ 78.6%

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

      2. associate-*r* 78.5%

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

   6. Simplified 78.5%

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

      1. associate-*l* 78.6%

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

      2. *-un-lft-identity 78.6%

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

      3. times-frac 78.5%

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

      4. metadata-eval 78.5%

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

      5. associate-*l/ 87.5%

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

      6. associate-*r* 87.5%

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

   8. Applied egg-rr 87.5%

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

      1. expm1-log1p-u 15.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-4.5 \cdot \frac{t}{a}\right)\right)} \cdot z \]

      2. expm1-udef 12.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(-4.5 \cdot \frac{t}{a}\right)} - 1\right)} \cdot z \]

      3. associate-*r/ 12.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{-4.5 \cdot t}{a}}\right)} - 1\right) \cdot z \]

      4. *-commutative 12.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{t \cdot -4.5}}{a}\right)} - 1\right) \cdot z \]

      5. associate-/l* 12.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{a}{-4.5}}}\right)} - 1\right) \cdot z \]

   10. Applied egg-rr 12.8%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{\frac{a}{-4.5}}\right)} - 1\right)} \cdot z \]
   11. Step-by-step derivation

       1. expm1-def 15.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{\frac{a}{-4.5}}\right)\right)} \cdot z \]

       2. expm1-log1p 87.5%

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

       3. associate-/l* 87.6%

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

       4. *-commutative 87.6%

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

   12. Simplified 87.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \]

Alternative 12: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-140}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;\frac{-4.5}{\frac{a}{z \cdot t}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

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 -1.5e-140)
   (* z (* -4.5 (/ t a)))
   (if (<= t 8.8e-170)
     (* x (* y (/ 0.5 a)))
     (if (<= t 5.1e-149)
       (/ -4.5 (/ a (* z t)))
       (if (<= t 1.25e+120) (* x (/ (* y 0.5) a)) (* 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 <= -1.5e-140) {
		tmp = z * (-4.5 * (t / a));
	} else if (t <= 8.8e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 5.1e-149) {
		tmp = -4.5 / (a / (z * t));
	} else if (t <= 1.25e+120) {
		tmp = x * ((y * 0.5) / a);
	} 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 <= (-1.5d-140)) then
        tmp = z * ((-4.5d0) * (t / a))
    else if (t <= 8.8d-170) then
        tmp = x * (y * (0.5d0 / a))
    else if (t <= 5.1d-149) then
        tmp = (-4.5d0) / (a / (z * t))
    else if (t <= 1.25d+120) then
        tmp = x * ((y * 0.5d0) / a)
    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 <= -1.5e-140) {
		tmp = z * (-4.5 * (t / a));
	} else if (t <= 8.8e-170) {
		tmp = x * (y * (0.5 / a));
	} else if (t <= 5.1e-149) {
		tmp = -4.5 / (a / (z * t));
	} else if (t <= 1.25e+120) {
		tmp = x * ((y * 0.5) / a);
	} 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 <= -1.5e-140:
		tmp = z * (-4.5 * (t / a))
	elif t <= 8.8e-170:
		tmp = x * (y * (0.5 / a))
	elif t <= 5.1e-149:
		tmp = -4.5 / (a / (z * t))
	elif t <= 1.25e+120:
		tmp = x * ((y * 0.5) / a)
	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 <= -1.5e-140)
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	elseif (t <= 8.8e-170)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (t <= 5.1e-149)
		tmp = Float64(-4.5 / Float64(a / Float64(z * t)));
	elseif (t <= 1.25e+120)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(z * Float64(Float64(t * -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 <= -1.5e-140)
		tmp = z * (-4.5 * (t / a));
	elseif (t <= 8.8e-170)
		tmp = x * (y * (0.5 / a));
	elseif (t <= 5.1e-149)
		tmp = -4.5 / (a / (z * t));
	elseif (t <= 1.25e+120)
		tmp = x * ((y * 0.5) / a);
	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, -1.5e-140], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-170], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-149], N[(-4.5 / N[(a / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+120], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.50000000000000009e-140

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. *-commutative 92.9%

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

      3. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 66.9%

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

      1. associate-*r/ 67.0%

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

      2. associate-*r* 67.0%

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

   6. Simplified 67.0%

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

      1. associate-*l* 67.0%

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

      2. *-un-lft-identity 67.0%

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

      3. times-frac 66.9%

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

      4. metadata-eval 66.9%

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

      5. associate-*l/ 65.9%

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

      6. associate-*r* 66.0%

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

   8. Applied egg-rr 66.0%

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

   if -1.50000000000000009e-140 < t < 8.80000000000000059e-170

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 71.0%

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

      1. associate-*r/ 71.0%

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

      2. associate-*l/ 71.0%

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

      3. *-commutative 71.0%

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

      4. associate-*l* 66.7%

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

   6. Simplified 66.7%

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

   if 8.80000000000000059e-170 < t < 5.09999999999999983e-149

   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. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around 0 71.2%

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

      1. associate-*r/ 71.0%

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

      2. associate-*r* 71.0%

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

   6. Simplified 71.0%

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

      1. associate-*l* 71.0%

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

      2. *-un-lft-identity 71.0%

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

      3. times-frac 71.2%

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

      4. metadata-eval 71.2%

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

      5. associate-*l/ 51.9%

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

      6. associate-*r* 52.1%

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

   8. Applied egg-rr 52.1%

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

      1. associate-*l* 51.9%

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

      2. associate-/r/ 57.9%

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

      3. clear-num 57.7%

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

      4. un-div-inv 57.9%

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

      5. associate-/l/ 71.4%

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

   10. Applied egg-rr 71.4%

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

   if 5.09999999999999983e-149 < t < 1.25000000000000005e120

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around inf 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l* 58.7%

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

   6. Simplified 58.7%

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

      1. associate-*r/ 58.8%

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

   8. Applied egg-rr 58.8%

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

   if 1.25000000000000005e120 < t

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 78.5%

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

      1. associate-*r/ 78.6%

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

      2. associate-*r* 78.5%

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

   6. Simplified 78.5%

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

      1. associate-*l* 78.6%

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

      2. *-un-lft-identity 78.6%

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

      3. times-frac 78.5%

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

      4. metadata-eval 78.5%

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

      5. associate-*l/ 87.5%

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

      6. associate-*r* 87.5%

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

   8. Applied egg-rr 87.5%

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

      1. expm1-log1p-u 15.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-4.5 \cdot \frac{t}{a}\right)\right)} \cdot z \]

      2. expm1-udef 12.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(-4.5 \cdot \frac{t}{a}\right)} - 1\right)} \cdot z \]

      3. associate-*r/ 12.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{-4.5 \cdot t}{a}}\right)} - 1\right) \cdot z \]

      4. *-commutative 12.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{t \cdot -4.5}}{a}\right)} - 1\right) \cdot z \]

      5. associate-/l* 12.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{a}{-4.5}}}\right)} - 1\right) \cdot z \]

   10. Applied egg-rr 12.8%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{\frac{a}{-4.5}}\right)} - 1\right)} \cdot z \]
   11. Step-by-step derivation

       1. expm1-def 15.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{\frac{a}{-4.5}}\right)\right)} \cdot z \]

       2. expm1-log1p 87.5%

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

       3. associate-/l* 87.6%

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

       4. *-commutative 87.6%

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

   12. Simplified 87.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-140}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;\frac{-4.5}{\frac{a}{z \cdot t}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \]

Alternative 13: 65.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-68} \lor \neg \left(y \leq 1.4 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.2e-68) (not (<= y 1.4e+101)))
   (* 0.5 (* y (/ x a)))
   (* -4.5 (/ (* z t) a))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.2e-68) || !(y <= 1.4e+101)) {
		tmp = 0.5 * (y * (x / a));
	} 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 ((y <= (-7.2d-68)) .or. (.not. (y <= 1.4d+101))) then
        tmp = 0.5d0 * (y * (x / a))
    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 ((y <= -7.2e-68) || !(y <= 1.4e+101)) {
		tmp = 0.5 * (y * (x / a));
	} 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 (y <= -7.2e-68) or not (y <= 1.4e+101):
		tmp = 0.5 * (y * (x / a))
	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 ((y <= -7.2e-68) || !(y <= 1.4e+101))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * 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 ((y <= -7.2e-68) || ~((y <= 1.4e+101)))
		tmp = 0.5 * (y * (x / a));
	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[Or[LessEqual[y, -7.2e-68], N[Not[LessEqual[y, 1.4e+101]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000015e-68 or 1.39999999999999991e101 < y

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

      1. associate-/r/ 63.9%

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

   8. Applied egg-rr 63.9%

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

   if -7.20000000000000015e-68 < y < 1.39999999999999991e101

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. *-commutative 95.8%

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

      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 0 69.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-68} \lor \neg \left(y \leq 1.4 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 14: 51.6% 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 94.3%

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

   1. *-commutative 94.3%

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

   2. *-commutative 94.3%

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

   3. associate-*l* 94.2%

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

3. Simplified 94.2%

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

4. Taylor expanded in x around 0 53.3%

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

   1. associate-/l* 52.1%

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

   2. associate-/r/ 50.9%

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

6. Simplified 50.9%

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

7. Final simplification 50.9%

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

Developer target: 93.2% 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 2023308 
(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)))