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

Percentage Accurate: 91.1% → 93.0%

Time: 8.4s

Alternatives: 9

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: 91.1% 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: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+288}:\\ \;\;\;\;t \cdot \frac{z}{\frac{a}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) -5e+288)
   (* t (/ z (/ a -4.5)))
   (/ (fma x y (* -9.0 (* z t))) (* a 2.0))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= -5e+288) {
		tmp = t * (z / (a / -4.5));
	} else {
		tmp = fma(x, y, (-9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= -5e+288)
		tmp = Float64(t * Float64(z / Float64(a / -4.5)));
	else
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(z * t))) / Float64(a * 2.0));
	end
	return 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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], -5e+288], N[(t * N[(z / N[(a / -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z 9) t) < -5.0000000000000003e288

   1. Initial program 76.3%

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

      1. associate-*l* 76.4%

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

   3. Simplified 76.4%

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

      1. div-sub 72.2%

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

      2. associate-*r* 72.1%

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

      3. div-sub 76.3%

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

      4. associate-*r* 76.4%

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

      5. *-commutative 76.4%

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

      6. cancel-sign-sub-inv 76.4%

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

      7. distribute-lft-neg-in 76.4%

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

      8. metadata-eval 76.4%

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

      9. associate-*r* 76.2%

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

      10. *-commutative 76.2%

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

      11. fma-udef 76.2%

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

      12. *-un-lft-identity 76.2%

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

      13. associate-/l* 76.2%

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

      14. inv-pow 76.2%

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

   5. Applied egg-rr 76.4%

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

   6. Taylor expanded in x around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. *-commutative 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-*r* 76.3%

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

      6. associate-*r/ 99.8%

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

      7. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   if -5.0000000000000003e288 < (*.f64 (*.f64 z 9) t)

   1. Initial program 94.9%

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

      1. fma-neg 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*l* 95.3%

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

      4. distribute-lft-neg-in 95.3%

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

      5. metadata-eval 95.3%

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

   3. Simplified 95.3%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+288}:\\ \;\;\;\;t \cdot \frac{z}{\frac{a}{-4.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+134}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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) -2e+29)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 2e+44)
     (* -4.5 (/ (* z t) a))
     (if (<= (* x y) 5e+117)
       (* 0.5 (/ (* x y) a))
       (if (<= (* x y) 5e+134)
         (* -4.5 (* t (/ z a)))
         (* 0.5 (/ x (/ a y))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+29) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+44) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+117) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5e+134) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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) <= (-2d+29)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= 2d+44) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d+117) then
        tmp = 0.5d0 * ((x * y) / a)
    else if ((x * y) <= 5d+134) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = 0.5d0 * (x / (a / y))
    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) <= -2e+29) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+44) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+117) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5e+134) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+29:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 2e+44:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e+117:
		tmp = 0.5 * ((x * y) / a)
	elif (x * y) <= 5e+134:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+29)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 2e+44)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e+117)
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	elseif (Float64(x * y) <= 5e+134)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	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) <= -2e+29)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 2e+44)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e+117)
		tmp = 0.5 * ((x * y) / a);
	elseif ((x * y) <= 5e+134)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = 0.5 * (x / (a / y));
	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], -2e+29], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+44], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+117], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+134], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999983e29

   1. Initial program 89.2%

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

      1. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

      1. div-sub 84.9%

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

      2. associate-*r* 84.9%

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

      3. div-sub 89.2%

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

      4. associate-*r* 89.2%

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

      5. *-commutative 89.2%

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

      6. cancel-sign-sub-inv 89.2%

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

      7. distribute-lft-neg-in 89.2%

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

      8. metadata-eval 89.2%

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

      9. associate-*r* 89.2%

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

      10. *-commutative 89.2%

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

      11. fma-udef 89.2%

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

      12. *-un-lft-identity 89.2%

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

      13. associate-/l* 89.0%

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

      14. inv-pow 89.0%

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

   5. Applied egg-rr 89.0%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. associate-*r/ 79.3%

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

   8. Simplified 79.3%

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

   if -1.99999999999999983e29 < (*.f64 x y) < 2.0000000000000002e44

   1. Initial program 93.5%

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

      1. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around 0 75.0%

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

   if 2.0000000000000002e44 < (*.f64 x y) < 4.99999999999999983e117

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 4.99999999999999983e117 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 99.2%

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

      1. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in t around 0 84.1%

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

      1. associate-*r/ 99.5%

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

   9. Simplified 99.5%

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

   if 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 97.2%

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

      1. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around inf 90.3%

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

      1. associate-/l* 92.8%

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

   6. Simplified 92.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+134}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+134}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \end{array} \]

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) -2e+29)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 2e+44)
     (* -4.5 (/ (* z t) a))
     (if (<= (* x y) 5e+117)
       (* 0.5 (/ (* x y) a))
       (if (<= (* x y) 5e+134)
         (* -4.5 (* t (/ z a)))
         (* y (/ (* x 0.5) a)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+29) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+44) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+117) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5e+134) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = y * ((x * 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) <= (-2d+29)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= 2d+44) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d+117) then
        tmp = 0.5d0 * ((x * y) / a)
    else if ((x * y) <= 5d+134) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = y * ((x * 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) <= -2e+29) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+44) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+117) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5e+134) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = y * ((x * 0.5) / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+29:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 2e+44:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e+117:
		tmp = 0.5 * ((x * y) / a)
	elif (x * y) <= 5e+134:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = y * ((x * 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) <= -2e+29)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 2e+44)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e+117)
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	elseif (Float64(x * y) <= 5e+134)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(x * 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) <= -2e+29)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 2e+44)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e+117)
		tmp = 0.5 * ((x * y) / a);
	elseif ((x * y) <= 5e+134)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = y * ((x * 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], -2e+29], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+44], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+117], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+134], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999983e29

   1. Initial program 89.2%

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

      1. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

      1. div-sub 84.9%

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

      2. associate-*r* 84.9%

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

      3. div-sub 89.2%

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

      4. associate-*r* 89.2%

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

      5. *-commutative 89.2%

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

      6. cancel-sign-sub-inv 89.2%

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

      7. distribute-lft-neg-in 89.2%

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

      8. metadata-eval 89.2%

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

      9. associate-*r* 89.2%

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

      10. *-commutative 89.2%

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

      11. fma-udef 89.2%

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

      12. *-un-lft-identity 89.2%

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

      13. associate-/l* 89.0%

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

      14. inv-pow 89.0%

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

   5. Applied egg-rr 89.0%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. associate-*r/ 79.3%

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

   8. Simplified 79.3%

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

   if -1.99999999999999983e29 < (*.f64 x y) < 2.0000000000000002e44

   1. Initial program 93.5%

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

      1. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around 0 75.0%

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

   if 2.0000000000000002e44 < (*.f64 x y) < 4.99999999999999983e117

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 4.99999999999999983e117 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 99.2%

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

      1. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in t around 0 84.1%

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

      1. associate-*r/ 99.5%

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

   9. Simplified 99.5%

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

   if 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 97.2%

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

      1. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

      1. div-sub 97.2%

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

      2. associate-*r* 97.2%

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

      3. div-sub 97.2%

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

      4. associate-*r* 97.2%

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

      5. *-commutative 97.2%

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

      6. cancel-sign-sub-inv 97.2%

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

      7. distribute-lft-neg-in 97.2%

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

      8. metadata-eval 97.2%

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

      9. associate-*r* 97.1%

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

      10. *-commutative 97.1%

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

      11. fma-udef 97.1%

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

      12. *-un-lft-identity 97.1%

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

      13. associate-/l* 97.0%

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

      14. inv-pow 97.0%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in x around inf 90.3%

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

      1. associate-/l* 92.8%

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

      2. associate-*r/ 92.8%

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

      3. associate-/r/ 92.8%

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

      4. *-commutative 92.8%

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

   8. Simplified 92.8%

      \[\leadsto \color{blue}{\frac{x \cdot 0.5}{a} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+134}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+134}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \end{array} \]

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) -2e+29)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 2e+44)
     (* -4.5 (/ (* z t) a))
     (if (<= (* x y) 5e+117)
       (* 0.5 (/ (* x y) a))
       (if (<= (* x y) 5e+134)
         (/ (* t -4.5) (/ a z))
         (* y (/ (* x 0.5) a)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+29) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+44) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+117) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5e+134) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = y * ((x * 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) <= (-2d+29)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= 2d+44) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d+117) then
        tmp = 0.5d0 * ((x * y) / a)
    else if ((x * y) <= 5d+134) then
        tmp = (t * (-4.5d0)) / (a / z)
    else
        tmp = y * ((x * 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) <= -2e+29) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+44) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+117) {
		tmp = 0.5 * ((x * y) / a);
	} else if ((x * y) <= 5e+134) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = y * ((x * 0.5) / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+29:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 2e+44:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e+117:
		tmp = 0.5 * ((x * y) / a)
	elif (x * y) <= 5e+134:
		tmp = (t * -4.5) / (a / z)
	else:
		tmp = y * ((x * 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) <= -2e+29)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 2e+44)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e+117)
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	elseif (Float64(x * y) <= 5e+134)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	else
		tmp = Float64(y * Float64(Float64(x * 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) <= -2e+29)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 2e+44)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e+117)
		tmp = 0.5 * ((x * y) / a);
	elseif ((x * y) <= 5e+134)
		tmp = (t * -4.5) / (a / z);
	else
		tmp = y * ((x * 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], -2e+29], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+44], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+117], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+134], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999983e29

   1. Initial program 89.2%

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

      1. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

      1. div-sub 84.9%

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

      2. associate-*r* 84.9%

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

      3. div-sub 89.2%

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

      4. associate-*r* 89.2%

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

      5. *-commutative 89.2%

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

      6. cancel-sign-sub-inv 89.2%

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

      7. distribute-lft-neg-in 89.2%

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

      8. metadata-eval 89.2%

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

      9. associate-*r* 89.2%

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

      10. *-commutative 89.2%

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

      11. fma-udef 89.2%

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

      12. *-un-lft-identity 89.2%

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

      13. associate-/l* 89.0%

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

      14. inv-pow 89.0%

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

   5. Applied egg-rr 89.0%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. associate-*r/ 79.3%

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

   8. Simplified 79.3%

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

   if -1.99999999999999983e29 < (*.f64 x y) < 2.0000000000000002e44

   1. Initial program 93.5%

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

      1. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around 0 75.0%

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

   if 2.0000000000000002e44 < (*.f64 x y) < 4.99999999999999983e117

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 4.99999999999999983e117 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 99.2%

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

      1. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in t around 0 84.1%

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

      1. associate-*r/ 99.5%

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

   9. Simplified 99.5%

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

       1. associate-*r* 100.0%

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

       2. clear-num 99.5%

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

       3. un-div-inv 99.7%

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

   11. Applied egg-rr 99.7%

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

   if 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 97.2%

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

      1. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

      1. div-sub 97.2%

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

      2. associate-*r* 97.2%

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

      3. div-sub 97.2%

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

      4. associate-*r* 97.2%

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

      5. *-commutative 97.2%

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

      6. cancel-sign-sub-inv 97.2%

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

      7. distribute-lft-neg-in 97.2%

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

      8. metadata-eval 97.2%

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

      9. associate-*r* 97.1%

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

      10. *-commutative 97.1%

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

      11. fma-udef 97.1%

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

      12. *-un-lft-identity 97.1%

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

      13. associate-/l* 97.0%

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

      14. inv-pow 97.0%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in x around inf 90.3%

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

      1. associate-/l* 92.8%

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

      2. associate-*r/ 92.8%

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

      3. associate-/r/ 92.8%

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

      4. *-commutative 92.8%

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

   8. Simplified 92.8%

      \[\leadsto \color{blue}{\frac{x \cdot 0.5}{a} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+134}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \end{array} \]

Alternative 5: 92.9% accurate, 0.7× speedup

Math

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

FPCore

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

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 <= -((double) INFINITY)) {
		tmp = t * (z / (a / -4.5));
	} else {
		tmp = ((x * y) - t_1) / (a * 2.0);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = t * (z / (a / -4.5));
	} else {
		tmp = ((x * y) - t_1) / (a * 2.0);
	}
	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 <= -math.inf:
		tmp = t * (z / (a / -4.5))
	else:
		tmp = ((x * y) - t_1) / (a * 2.0)
	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 <= Float64(-Inf))
		tmp = Float64(t * Float64(z / Float64(a / -4.5)));
	else
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 73.0%

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

      1. associate-*l* 73.0%

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

   3. Simplified 73.0%

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

      1. div-sub 68.2%

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

      2. associate-*r* 68.2%

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

      3. div-sub 73.0%

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

      4. associate-*r* 73.0%

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

      5. *-commutative 73.0%

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

      6. cancel-sign-sub-inv 73.0%

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

      7. distribute-lft-neg-in 73.0%

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

      8. metadata-eval 73.0%

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

      9. associate-*r* 73.0%

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

      10. *-commutative 73.0%

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

      11. fma-udef 73.0%

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

      12. *-un-lft-identity 73.0%

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

      13. associate-/l* 73.0%

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

      14. inv-pow 73.0%

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

   5. Applied egg-rr 73.0%

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

   6. Taylor expanded in x around 0 73.0%

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

      1. associate-*r/ 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

      4. *-commutative 73.0%

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

      5. associate-*r* 73.0%

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

      6. associate-*r/ 99.9%

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

      7. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

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

   1. Initial program 95.0%

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

4. Final simplification 95.4%

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

Alternative 6: 92.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+205}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+205)
   (* 0.5 (/ x (/ a y)))
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+205) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d+205)) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+205) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+205:
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+205)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+205)
		tmp = 0.5 * (x / (a / y));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+205], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000002e205

   1. Initial program 82.9%

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

      1. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around inf 82.9%

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

      1. associate-/l* 97.1%

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

   6. Simplified 97.1%

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

   if -1.00000000000000002e205 < (*.f64 x y)

   1. Initial program 94.7%

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

      1. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+205}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 7: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-59}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.63 \cdot 10^{-14}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

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 (* 0.5 (* x (/ y a)))))
   (if (<= t -1.85e-59)
     (* -4.5 (/ t (/ a z)))
     (if (<= t 2.25e-48)
       t_1
       (if (<= t 1.63e-14)
         (* -4.5 (/ (* z t) a))
         (if (<= t 1.1e+61) t_1 (* -4.5 (* t (/ z a)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (t <= -1.85e-59) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 2.25e-48) {
		tmp = t_1;
	} else if (t <= 1.63e-14) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1.1e+61) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t * (z / 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 = 0.5d0 * (x * (y / a))
    if (t <= (-1.85d-59)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 2.25d-48) then
        tmp = t_1
    else if (t <= 1.63d-14) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 1.1d+61) then
        tmp = t_1
    else
        tmp = (-4.5d0) * (t * (z / 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 = 0.5 * (x * (y / a));
	double tmp;
	if (t <= -1.85e-59) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 2.25e-48) {
		tmp = t_1;
	} else if (t <= 1.63e-14) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1.1e+61) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x * (y / a))
	tmp = 0
	if t <= -1.85e-59:
		tmp = -4.5 * (t / (a / z))
	elif t <= 2.25e-48:
		tmp = t_1
	elif t <= 1.63e-14:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 1.1e+61:
		tmp = t_1
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.85e-59)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 2.25e-48)
		tmp = t_1;
	elseif (t <= 1.63e-14)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 1.1e+61)
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	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 * (y / a));
	tmp = 0.0;
	if (t <= -1.85e-59)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 2.25e-48)
		tmp = t_1;
	elseif (t <= 1.63e-14)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 1.1e+61)
		tmp = t_1;
	else
		tmp = -4.5 * (t * (z / 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[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e-59], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-48], t$95$1, If[LessEqual[t, 1.63e-14], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+61], t$95$1, N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.85e-59

   1. Initial program 90.8%

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

      1. 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. Step-by-step derivation

      1. div-sub 87.1%

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

      2. div-inv 87.2%

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

      3. *-commutative 87.2%

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

      4. associate-/r* 87.2%

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

      5. metadata-eval 87.2%

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

      6. times-frac 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 63.2%

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

      1. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   if -1.85e-59 < t < 2.24999999999999994e-48 or 1.63000000000000006e-14 < t < 1.1e61

   1. Initial program 94.8%

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

      1. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

      1. div-sub 95.6%

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

      2. associate-*r* 94.8%

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

      3. div-sub 94.8%

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

      4. associate-*r* 95.6%

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

      5. *-commutative 95.6%

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

      6. cancel-sign-sub-inv 95.6%

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

      7. distribute-lft-neg-in 95.6%

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

      8. metadata-eval 95.6%

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

      9. associate-*r* 95.6%

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

      10. *-commutative 95.6%

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

      11. fma-udef 95.6%

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

      12. *-un-lft-identity 95.6%

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

      13. associate-/l* 94.8%

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

      14. inv-pow 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in x around inf 76.0%

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

      1. associate-*r/ 77.7%

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

   8. Simplified 77.7%

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

   if 2.24999999999999994e-48 < t < 1.63000000000000006e-14

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 49.7%

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

   if 1.1e61 < t

   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. 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 72.4%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in t around 0 72.4%

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

      1. associate-*r/ 73.9%

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

   9. Simplified 73.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-59}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-48}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.63 \cdot 10^{-14}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+61}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]

Alternative 8: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-47}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.63 \cdot 10^{-14}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+62}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.75e-47)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 1.15e-48)
     (* 0.5 (* x (/ y a)))
     (if (<= t 1.63e-14)
       (* -4.5 (/ (* z t) a))
       (if (<= t 2.6e+62) (* 0.5 (/ x (/ a y))) (* -4.5 (* t (/ z a))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e-47) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.15e-48) {
		tmp = 0.5 * (x * (y / a));
	} else if (t <= 1.63e-14) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 2.6e+62) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (t * (z / 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 <= (-1.75d-47)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 1.15d-48) then
        tmp = 0.5d0 * (x * (y / a))
    else if (t <= 1.63d-14) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 2.6d+62) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = (-4.5d0) * (t * (z / 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 <= -1.75e-47) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.15e-48) {
		tmp = 0.5 * (x * (y / a));
	} else if (t <= 1.63e-14) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 2.6e+62) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.75e-47:
		tmp = -4.5 * (t / (a / z))
	elif t <= 1.15e-48:
		tmp = 0.5 * (x * (y / a))
	elif t <= 1.63e-14:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 2.6e+62:
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.75e-47)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 1.15e-48)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (t <= 1.63e-14)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 2.6e+62)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / 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 <= -1.75e-47)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 1.15e-48)
		tmp = 0.5 * (x * (y / a));
	elseif (t <= 1.63e-14)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 2.6e+62)
		tmp = 0.5 * (x / (a / y));
	else
		tmp = -4.5 * (t * (z / 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, -1.75e-47], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-48], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.63e-14], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+62], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7499999999999999e-47

   1. Initial program 90.7%

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

      1. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

      1. div-sub 87.0%

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

      2. div-inv 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-/r* 87.0%

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

      5. metadata-eval 87.0%

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

      6. times-frac 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in x around 0 62.8%

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

      1. associate-/l* 67.2%

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

   8. Simplified 67.2%

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

   if -1.7499999999999999e-47 < t < 1.15e-48

   1. Initial program 94.9%

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

      1. 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. Step-by-step derivation

      1. div-sub 95.9%

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

      2. associate-*r* 94.9%

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

      3. div-sub 94.9%

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

      4. associate-*r* 95.9%

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

      5. *-commutative 95.9%

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

      6. cancel-sign-sub-inv 95.9%

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

      7. distribute-lft-neg-in 95.9%

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

      8. metadata-eval 95.9%

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

      9. associate-*r* 95.9%

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

      10. *-commutative 95.9%

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

      11. fma-udef 95.9%

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

      12. *-un-lft-identity 95.9%

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

      13. associate-/l* 95.1%

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

      14. inv-pow 95.1%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in x around inf 81.1%

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

      1. associate-*r/ 81.1%

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

   8. Simplified 81.1%

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

   if 1.15e-48 < t < 1.63000000000000006e-14

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 49.7%

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

   if 1.63000000000000006e-14 < t < 2.59999999999999984e62

   1. Initial program 94.1%

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

      1. 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 inf 48.8%

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

      1. associate-/l* 60.0%

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

   6. Simplified 60.0%

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

   if 2.59999999999999984e62 < t

   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. 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 72.4%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in t around 0 72.4%

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

      1. associate-*r/ 73.9%

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

   9. Simplified 73.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-47}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.63 \cdot 10^{-14}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+62}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]

Alternative 9: 51.3% accurate, 1.9× speedup

Math

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

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 (* t (/ z a))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

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. associate-*l* 93.5%

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

3. Simplified 93.5%

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

4. Taylor expanded in x around 0 49.9%

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

   1. associate-/l* 51.0%

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

   2. associate-/r/ 48.9%

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

6. Simplified 48.9%

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

7. Taylor expanded in t around 0 49.9%

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

   1. associate-*r/ 50.6%

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

9. Simplified 50.6%

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

10. Final simplification 50.6%

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

Developer target: 93.0% 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 2023287 
(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)))