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

Percentage Accurate: 98.2% → 98.4%

Time: 30.0s

Alternatives: 10

Speedup: 0.1×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 4.4615969743612705e-208
  2. y = 9.639480171657537e+39
  3. z = 1.3895418240950962e-170
  4. t = 5.693610098935886e-286
  5. a = 1.5675405107948216e+153

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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a} \end{array} \]

FPCore

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

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	return fma(x, y, (z * (t * -9.0))) * (0.5 / a);
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	return Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a))
end

Wolfram

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

Derivation

1. Initial program 97.5%

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

   1. sub-neg 97.5%

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

   2. +-commutative 97.5%

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

   3. neg-sub0 97.5%

      \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

   4. associate-+l- 97.5%

      \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

   5. sub0-neg 97.5%

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

   6. neg-mul-1 97.5%

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

   7. associate-/l* 97.3%

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

   8. associate-/r/ 97.4%

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

   9. *-commutative 97.4%

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

   10. sub-neg 97.4%

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

   11. +-commutative 97.4%

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

   12. neg-sub0 97.4%

       \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

   13. associate-+l- 97.4%

       \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

   14. sub0-neg 97.4%

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

   15. distribute-lft-neg-out 97.4%

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

   16. distribute-rgt-neg-in 97.4%

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

3. Simplified 98.2%

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

4. Final simplification 98.2%

   \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a} \]

Alternative 2: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-102} \lor \neg \left(y \leq 1.52 \cdot 10^{+44}\right) \land \left(y \leq 3.9 \cdot 10^{+86} \lor \neg \left(y \leq 1.02 \cdot 10^{+101}\right)\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 -5e-102)
         (and (not (<= y 1.52e+44))
              (or (<= y 3.9e+86) (not (<= y 1.02e+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 <= -5e-102) || (!(y <= 1.52e+44) && ((y <= 3.9e+86) || !(y <= 1.02e+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 <= (-5d-102)) .or. (.not. (y <= 1.52d+44)) .and. (y <= 3.9d+86) .or. (.not. (y <= 1.02d+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 <= -5e-102) || (!(y <= 1.52e+44) && ((y <= 3.9e+86) || !(y <= 1.02e+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 <= -5e-102) or (not (y <= 1.52e+44) and ((y <= 3.9e+86) or not (y <= 1.02e+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 <= -5e-102) || (!(y <= 1.52e+44) && ((y <= 3.9e+86) || !(y <= 1.02e+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 <= -5e-102) || (~((y <= 1.52e+44)) && ((y <= 3.9e+86) || ~((y <= 1.02e+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, -5e-102], And[N[Not[LessEqual[y, 1.52e+44]], $MachinePrecision], Or[LessEqual[y, 3.9e+86], N[Not[LessEqual[y, 1.02e+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 < -5.00000000000000026e-102 or 1.52000000000000003e44 < y < 3.9000000000000002e86 or 1.02000000000000002e101 < y

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. +-commutative 97.8%

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

      3. neg-sub0 97.8%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.8%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.8%

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

      6. neg-mul-1 97.8%

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

      7. associate-/l* 97.7%

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

      8. associate-/r/ 97.7%

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

      9. *-commutative 97.7%

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

      10. sub-neg 97.7%

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

      11. +-commutative 97.7%

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

      12. neg-sub0 97.7%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.7%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.7%

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

      15. distribute-lft-neg-out 97.7%

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

      16. distribute-rgt-neg-in 97.7%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.2%

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

      2. clear-num 99.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 99.1%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 76.7%

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

      1. associate-*r/ 76.0%

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

   8. Simplified 76.0%

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

   if -5.00000000000000026e-102 < y < 1.52000000000000003e44 or 3.9000000000000002e86 < y < 1.02000000000000002e101

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. +-commutative 97.1%

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

      3. neg-sub0 97.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.1%

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

      6. neg-mul-1 97.1%

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

      7. associate-/l* 96.9%

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

      8. associate-/r/ 97.0%

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

      9. *-commutative 97.0%

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

      10. sub-neg 97.0%

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

      11. +-commutative 97.0%

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

      12. neg-sub0 97.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.0%

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

      15. distribute-lft-neg-out 97.0%

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

      16. distribute-rgt-neg-in 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 73.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-102} \lor \neg \left(y \leq 1.52 \cdot 10^{+44}\right) \land \left(y \leq 3.9 \cdot 10^{+86} \lor \neg \left(y \leq 1.02 \cdot 10^{+101}\right)\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 3: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+44} \lor \neg \left(y \leq 1.7 \cdot 10^{+87}\right) \land y \leq 1.02 \cdot 10^{+102}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.4e-101)
   (* 0.5 (* y (/ x a)))
   (if (or (<= y 1.32e+44) (and (not (<= y 1.7e+87)) (<= y 1.02e+102)))
     (* -4.5 (/ (* z t) a))
     (* 0.5 (/ (* x y) a)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4e-101) {
		tmp = 0.5 * (y * (x / a));
	} else if ((y <= 1.32e+44) || (!(y <= 1.7e+87) && (y <= 1.02e+102))) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * ((x * y) / 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 <= (-1.4d-101)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((y <= 1.32d+44) .or. (.not. (y <= 1.7d+87)) .and. (y <= 1.02d+102)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * ((x * y) / 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 <= -1.4e-101) {
		tmp = 0.5 * (y * (x / a));
	} else if ((y <= 1.32e+44) || (!(y <= 1.7e+87) && (y <= 1.02e+102))) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.4e-101:
		tmp = 0.5 * (y * (x / a))
	elif (y <= 1.32e+44) or (not (y <= 1.7e+87) and (y <= 1.02e+102)):
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * ((x * y) / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.4e-101)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif ((y <= 1.32e+44) || (!(y <= 1.7e+87) && (y <= 1.02e+102)))
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(Float64(x * y) / 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 <= -1.4e-101)
		tmp = 0.5 * (y * (x / a));
	elseif ((y <= 1.32e+44) || (~((y <= 1.7e+87)) && (y <= 1.02e+102)))
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * ((x * y) / 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[y, -1.4e-101], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.32e+44], And[N[Not[LessEqual[y, 1.7e+87]], $MachinePrecision], LessEqual[y, 1.02e+102]]], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999995e-101

   1. Initial program 97.6%

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

      1. sub-neg 97.6%

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

      2. +-commutative 97.6%

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

      3. neg-sub0 97.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.6%

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

      6. neg-mul-1 97.6%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.5%

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

      9. *-commutative 97.5%

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

      10. sub-neg 97.5%

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

      11. +-commutative 97.5%

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

      12. neg-sub0 97.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.5%

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

      15. distribute-lft-neg-out 97.5%

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

      16. distribute-rgt-neg-in 97.5%

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

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.7%

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

      2. clear-num 98.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 98.6%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 73.3%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

   if -1.39999999999999995e-101 < y < 1.3200000000000001e44 or 1.7000000000000001e87 < y < 1.01999999999999999e102

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. +-commutative 97.1%

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

      3. neg-sub0 97.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.1%

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

      6. neg-mul-1 97.1%

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

      7. associate-/l* 96.9%

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

      8. associate-/r/ 97.0%

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

      9. *-commutative 97.0%

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

      10. sub-neg 97.0%

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

      11. +-commutative 97.0%

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

      12. neg-sub0 97.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.0%

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

      15. distribute-lft-neg-out 97.0%

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

      16. distribute-rgt-neg-in 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 73.0%

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

   if 1.3200000000000001e44 < y < 1.7000000000000001e87 or 1.01999999999999999e102 < y

   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. sub-neg 98.1%

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

      2. +-commutative 98.1%

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

      3. neg-sub0 98.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 98.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-/l* 98.0%

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

      8. associate-/r/ 98.0%

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

      9. *-commutative 98.0%

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

      10. sub-neg 98.0%

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

      11. +-commutative 98.0%

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

      12. neg-sub0 98.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 98.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 98.0%

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

      15. distribute-lft-neg-out 98.0%

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

      16. distribute-rgt-neg-in 98.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+44} \lor \neg \left(y \leq 1.7 \cdot 10^{+87}\right) \land y \leq 1.02 \cdot 10^{+102}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]

Alternative 4: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+86} \lor \neg \left(y \leq 1.3 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.35e-101)
   (* 0.5 (* y (/ x a)))
   (if (<= y 1.25e+44)
     (* (* z t) (/ -4.5 a))
     (if (or (<= y 8.2e+86) (not (<= y 1.3e+101)))
       (* 0.5 (/ (* x y) 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 <= -1.35e-101) {
		tmp = 0.5 * (y * (x / a));
	} else if (y <= 1.25e+44) {
		tmp = (z * t) * (-4.5 / a);
	} else if ((y <= 8.2e+86) || !(y <= 1.3e+101)) {
		tmp = 0.5 * ((x * y) / 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 <= (-1.35d-101)) then
        tmp = 0.5d0 * (y * (x / a))
    else if (y <= 1.25d+44) then
        tmp = (z * t) * ((-4.5d0) / a)
    else if ((y <= 8.2d+86) .or. (.not. (y <= 1.3d+101))) then
        tmp = 0.5d0 * ((x * y) / 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 <= -1.35e-101) {
		tmp = 0.5 * (y * (x / a));
	} else if (y <= 1.25e+44) {
		tmp = (z * t) * (-4.5 / a);
	} else if ((y <= 8.2e+86) || !(y <= 1.3e+101)) {
		tmp = 0.5 * ((x * y) / 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 <= -1.35e-101:
		tmp = 0.5 * (y * (x / a))
	elif y <= 1.25e+44:
		tmp = (z * t) * (-4.5 / a)
	elif (y <= 8.2e+86) or not (y <= 1.3e+101):
		tmp = 0.5 * ((x * y) / 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 <= -1.35e-101)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (y <= 1.25e+44)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a));
	elseif ((y <= 8.2e+86) || !(y <= 1.3e+101))
		tmp = Float64(0.5 * Float64(Float64(x * y) / 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 <= -1.35e-101)
		tmp = 0.5 * (y * (x / a));
	elseif (y <= 1.25e+44)
		tmp = (z * t) * (-4.5 / a);
	elseif ((y <= 8.2e+86) || ~((y <= 1.3e+101)))
		tmp = 0.5 * ((x * y) / 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[LessEqual[y, -1.35e-101], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+44], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.2e+86], N[Not[LessEqual[y, 1.3e+101]], $MachinePrecision]], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3500000000000001e-101

   1. Initial program 97.6%

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

      1. sub-neg 97.6%

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

      2. +-commutative 97.6%

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

      3. neg-sub0 97.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.6%

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

      6. neg-mul-1 97.6%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.5%

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

      9. *-commutative 97.5%

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

      10. sub-neg 97.5%

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

      11. +-commutative 97.5%

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

      12. neg-sub0 97.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.5%

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

      15. distribute-lft-neg-out 97.5%

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

      16. distribute-rgt-neg-in 97.5%

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

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.7%

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

      2. clear-num 98.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 98.6%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 73.3%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

   if -1.3500000000000001e-101 < y < 1.2499999999999999e44

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. +-commutative 97.0%

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

      3. neg-sub0 97.0%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.0%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.0%

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

      6. neg-mul-1 97.0%

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

      7. associate-/l* 96.7%

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

      8. associate-/r/ 96.9%

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

      9. *-commutative 96.9%

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

      10. sub-neg 96.9%

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

      11. +-commutative 96.9%

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

      12. neg-sub0 96.9%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 96.9%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 96.9%

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

      15. distribute-lft-neg-out 96.9%

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

      16. distribute-rgt-neg-in 96.9%

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

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 97.0%

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

      2. clear-num 96.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 96.8%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*l/ 72.9%

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

      4. metadata-eval 72.9%

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

      5. associate-*l* 72.9%

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

      6. *-commutative 72.9%

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

      7. associate-*r/ 72.9%

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

      8. *-commutative 72.9%

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

      9. associate-*r* 72.9%

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

      10. associate-*l/ 72.9%

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

      11. metadata-eval 72.9%

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

      12. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if 1.2499999999999999e44 < y < 8.1999999999999998e86 or 1.3e101 < y

   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. sub-neg 98.1%

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

      2. +-commutative 98.1%

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

      3. neg-sub0 98.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 98.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-/l* 98.0%

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

      8. associate-/r/ 98.0%

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

      9. *-commutative 98.0%

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

      10. sub-neg 98.0%

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

      11. +-commutative 98.0%

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

      12. neg-sub0 98.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 98.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 98.0%

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

      15. distribute-lft-neg-out 98.0%

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

      16. distribute-rgt-neg-in 98.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.2%

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

   if 8.1999999999999998e86 < y < 1.3e101

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

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

      7. associate-/l* 100.0%

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

      8. associate-/r/ 99.6%

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

      9. *-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. +-commutative 99.6%

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

      12. neg-sub0 99.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 99.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 99.6%

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

      15. distribute-lft-neg-out 99.6%

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

      16. distribute-rgt-neg-in 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 75.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+86} \lor \neg \left(y \leq 1.3 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 5: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-79}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+87} \lor \neg \left(y \leq 1.02 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.9e-79)
   (* 0.5 (* y (/ x a)))
   (if (<= y 1.2e+44)
     (* (/ 0.5 a) (* z (* t -9.0)))
     (if (or (<= y 1.7e+87) (not (<= y 1.02e+101)))
       (* 0.5 (/ (* x y) 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 <= -1.9e-79) {
		tmp = 0.5 * (y * (x / a));
	} else if (y <= 1.2e+44) {
		tmp = (0.5 / a) * (z * (t * -9.0));
	} else if ((y <= 1.7e+87) || !(y <= 1.02e+101)) {
		tmp = 0.5 * ((x * y) / 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 <= (-1.9d-79)) then
        tmp = 0.5d0 * (y * (x / a))
    else if (y <= 1.2d+44) then
        tmp = (0.5d0 / a) * (z * (t * (-9.0d0)))
    else if ((y <= 1.7d+87) .or. (.not. (y <= 1.02d+101))) then
        tmp = 0.5d0 * ((x * y) / 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 <= -1.9e-79) {
		tmp = 0.5 * (y * (x / a));
	} else if (y <= 1.2e+44) {
		tmp = (0.5 / a) * (z * (t * -9.0));
	} else if ((y <= 1.7e+87) || !(y <= 1.02e+101)) {
		tmp = 0.5 * ((x * y) / 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 <= -1.9e-79:
		tmp = 0.5 * (y * (x / a))
	elif y <= 1.2e+44:
		tmp = (0.5 / a) * (z * (t * -9.0))
	elif (y <= 1.7e+87) or not (y <= 1.02e+101):
		tmp = 0.5 * ((x * y) / 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 <= -1.9e-79)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (y <= 1.2e+44)
		tmp = Float64(Float64(0.5 / a) * Float64(z * Float64(t * -9.0)));
	elseif ((y <= 1.7e+87) || !(y <= 1.02e+101))
		tmp = Float64(0.5 * Float64(Float64(x * y) / 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 <= -1.9e-79)
		tmp = 0.5 * (y * (x / a));
	elseif (y <= 1.2e+44)
		tmp = (0.5 / a) * (z * (t * -9.0));
	elseif ((y <= 1.7e+87) || ~((y <= 1.02e+101)))
		tmp = 0.5 * ((x * y) / 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[LessEqual[y, -1.9e-79], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+44], N[(N[(0.5 / a), $MachinePrecision] * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.7e+87], N[Not[LessEqual[y, 1.02e+101]], $MachinePrecision]], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9000000000000001e-79

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. +-commutative 97.5%

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

      3. neg-sub0 97.5%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.5%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.5%

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

      6. neg-mul-1 97.5%

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

      7. associate-/l* 97.4%

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

      8. associate-/r/ 97.4%

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

      9. *-commutative 97.4%

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

      10. sub-neg 97.4%

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

      11. +-commutative 97.4%

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

      12. neg-sub0 97.4%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.4%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.4%

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

      15. distribute-lft-neg-out 97.4%

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

      16. distribute-rgt-neg-in 97.4%

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

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.7%

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

      2. clear-num 98.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 98.6%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 74.3%

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

      1. associate-*r/ 73.1%

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

   8. Simplified 73.1%

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

   if -1.9000000000000001e-79 < y < 1.20000000000000007e44

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. +-commutative 97.1%

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

      3. neg-sub0 97.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.1%

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

      6. neg-mul-1 97.1%

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

      7. associate-/l* 96.9%

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

      8. associate-/r/ 97.0%

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

      9. *-commutative 97.0%

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

      10. sub-neg 97.0%

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

      11. +-commutative 97.0%

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

      12. neg-sub0 97.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.0%

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

      15. distribute-lft-neg-out 97.0%

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

      16. distribute-rgt-neg-in 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. associate-*l* 72.3%

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

   6. Simplified 72.3%

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

   7. Taylor expanded in t around 0 72.2%

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

      1. associate-*r* 72.2%

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

   9. Simplified 72.2%

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

   if 1.20000000000000007e44 < y < 1.7000000000000001e87 or 1.02000000000000002e101 < y

   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. sub-neg 98.1%

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

      2. +-commutative 98.1%

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

      3. neg-sub0 98.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 98.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-/l* 98.0%

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

      8. associate-/r/ 98.0%

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

      9. *-commutative 98.0%

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

      10. sub-neg 98.0%

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

      11. +-commutative 98.0%

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

      12. neg-sub0 98.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 98.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 98.0%

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

      15. distribute-lft-neg-out 98.0%

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

      16. distribute-rgt-neg-in 98.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.2%

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

   if 1.7000000000000001e87 < y < 1.02000000000000002e101

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

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

      7. associate-/l* 100.0%

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

      8. associate-/r/ 99.6%

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

      9. *-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. +-commutative 99.6%

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

      12. neg-sub0 99.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 99.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 99.6%

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

      15. distribute-lft-neg-out 99.6%

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

      16. distribute-rgt-neg-in 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 75.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-79}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+87} \lor \neg \left(y \leq 1.02 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 6: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-102}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{\frac{a}{0.5 \cdot \left(t \cdot \left(z \cdot -9\right)\right)}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+87} \lor \neg \left(y \leq 1.02 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5e-102)
   (* 0.5 (* y (/ x a)))
   (if (<= y 1.2e+44)
     (/ 1.0 (/ a (* 0.5 (* t (* z -9.0)))))
     (if (or (<= y 1.7e+87) (not (<= y 1.02e+101)))
       (* 0.5 (/ (* x y) 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 <= -5e-102) {
		tmp = 0.5 * (y * (x / a));
	} else if (y <= 1.2e+44) {
		tmp = 1.0 / (a / (0.5 * (t * (z * -9.0))));
	} else if ((y <= 1.7e+87) || !(y <= 1.02e+101)) {
		tmp = 0.5 * ((x * y) / 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 <= (-5d-102)) then
        tmp = 0.5d0 * (y * (x / a))
    else if (y <= 1.2d+44) then
        tmp = 1.0d0 / (a / (0.5d0 * (t * (z * (-9.0d0)))))
    else if ((y <= 1.7d+87) .or. (.not. (y <= 1.02d+101))) then
        tmp = 0.5d0 * ((x * y) / 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 <= -5e-102) {
		tmp = 0.5 * (y * (x / a));
	} else if (y <= 1.2e+44) {
		tmp = 1.0 / (a / (0.5 * (t * (z * -9.0))));
	} else if ((y <= 1.7e+87) || !(y <= 1.02e+101)) {
		tmp = 0.5 * ((x * y) / 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 <= -5e-102:
		tmp = 0.5 * (y * (x / a))
	elif y <= 1.2e+44:
		tmp = 1.0 / (a / (0.5 * (t * (z * -9.0))))
	elif (y <= 1.7e+87) or not (y <= 1.02e+101):
		tmp = 0.5 * ((x * y) / 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 <= -5e-102)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (y <= 1.2e+44)
		tmp = Float64(1.0 / Float64(a / Float64(0.5 * Float64(t * Float64(z * -9.0)))));
	elseif ((y <= 1.7e+87) || !(y <= 1.02e+101))
		tmp = Float64(0.5 * Float64(Float64(x * y) / 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 <= -5e-102)
		tmp = 0.5 * (y * (x / a));
	elseif (y <= 1.2e+44)
		tmp = 1.0 / (a / (0.5 * (t * (z * -9.0))));
	elseif ((y <= 1.7e+87) || ~((y <= 1.02e+101)))
		tmp = 0.5 * ((x * y) / 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[LessEqual[y, -5e-102], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+44], N[(1.0 / N[(a / N[(0.5 * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.7e+87], N[Not[LessEqual[y, 1.02e+101]], $MachinePrecision]], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.00000000000000026e-102

   1. Initial program 97.6%

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

      1. sub-neg 97.6%

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

      2. +-commutative 97.6%

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

      3. neg-sub0 97.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.6%

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

      6. neg-mul-1 97.6%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.5%

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

      9. *-commutative 97.5%

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

      10. sub-neg 97.5%

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

      11. +-commutative 97.5%

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

      12. neg-sub0 97.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.5%

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

      15. distribute-lft-neg-out 97.5%

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

      16. distribute-rgt-neg-in 97.5%

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

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.7%

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

      2. clear-num 98.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 98.6%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around inf 73.3%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

   if -5.00000000000000026e-102 < y < 1.20000000000000007e44

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. +-commutative 97.0%

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

      3. neg-sub0 97.0%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.0%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.0%

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

      6. neg-mul-1 97.0%

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

      7. associate-/l* 96.7%

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

      8. associate-/r/ 96.9%

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

      9. *-commutative 96.9%

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

      10. sub-neg 96.9%

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

      11. +-commutative 96.9%

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

      12. neg-sub0 96.9%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 96.9%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 96.9%

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

      15. distribute-lft-neg-out 96.9%

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

      16. distribute-rgt-neg-in 96.9%

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

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 97.0%

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

      2. clear-num 96.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 96.8%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around 0 72.9%

      \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right)\right)}}} \]
   7. Step-by-step derivation

      1. *-commutative 72.9%

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

      2. associate-*l* 72.9%

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

   8. Simplified 73.0%

      \[\leadsto \frac{1}{\frac{a}{0.5 \cdot \color{blue}{\left(t \cdot \left(z \cdot -9\right)\right)}}} \]

   if 1.20000000000000007e44 < y < 1.7000000000000001e87 or 1.02000000000000002e101 < y

   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. sub-neg 98.1%

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

      2. +-commutative 98.1%

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

      3. neg-sub0 98.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 98.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-/l* 98.0%

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

      8. associate-/r/ 98.0%

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

      9. *-commutative 98.0%

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

      10. sub-neg 98.0%

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

      11. +-commutative 98.0%

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

      12. neg-sub0 98.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 98.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 98.0%

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

      15. distribute-lft-neg-out 98.0%

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

      16. distribute-rgt-neg-in 98.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.2%

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

   if 1.7000000000000001e87 < y < 1.02000000000000002e101

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

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

      7. associate-/l* 100.0%

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

      8. associate-/r/ 99.6%

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

      9. *-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. +-commutative 99.6%

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

      12. neg-sub0 99.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 99.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 99.6%

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

      15. distribute-lft-neg-out 99.6%

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

      16. distribute-rgt-neg-in 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 75.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-102}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{\frac{a}{0.5 \cdot \left(t \cdot \left(z \cdot -9\right)\right)}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+87} \lor \neg \left(y \leq 1.02 \cdot 10^{+101}\right):\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 7: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
end

Wolfram

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

Derivation

1. Initial program 97.5%

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

   1. associate-*l* 97.5%

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

3. Simplified 97.5%

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

4. Final simplification 97.5%

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

Alternative 8: 53.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+194}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

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 5.2e+194) (* -4.5 (* z (/ t a))) (* -4.5 (/ t (/ a z)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.2e+194) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	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 <= 5.2d+194) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = (-4.5d0) * (t / (a / z))
    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 <= 5.2e+194) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.2e+194:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.2e+194)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	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 <= 5.2e+194)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = -4.5 * (t / (a / z));
	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, 5.2e+194], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.1999999999999998e194

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. +-commutative 97.7%

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

      3. neg-sub0 97.7%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.7%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.7%

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

      6. neg-mul-1 97.7%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.6%

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

      9. *-commutative 97.6%

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

      10. sub-neg 97.6%

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

      11. +-commutative 97.6%

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

      12. neg-sub0 97.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.6%

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

      15. distribute-lft-neg-out 97.6%

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

      16. distribute-rgt-neg-in 97.6%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around 0 47.3%

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

      1. associate-/l* 43.9%

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

      2. associate-/r/ 48.2%

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

   6. Simplified 48.2%

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

   if 5.1999999999999998e194 < t

   1. Initial program 95.2%

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

      1. sub-neg 95.2%

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

      2. +-commutative 95.2%

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

      3. neg-sub0 95.2%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 95.2%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 95.2%

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

      6. neg-mul-1 95.2%

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

      7. associate-/l* 95.0%

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

      8. associate-/r/ 94.9%

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

      9. *-commutative 94.9%

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

      10. sub-neg 94.9%

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

      11. +-commutative 94.9%

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

      12. neg-sub0 94.9%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 94.9%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 94.9%

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

      15. distribute-lft-neg-out 94.9%

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

      16. distribute-rgt-neg-in 94.9%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. clear-num 99.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot 0.5}}} \]

      3. *-commutative 99.8%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{0.5 \cdot \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   6. Taylor expanded in x around 0 91.0%

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

      1. associate-/l* 91.0%

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

   8. Simplified 91.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+194}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 53.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{+193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 8e+193) (* -4.5 (* z (/ t 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 (t <= 8e+193) {
		tmp = -4.5 * (z * (t / 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 (t <= 8d+193) then
        tmp = (-4.5d0) * (z * (t / 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 (t <= 8e+193) {
		tmp = -4.5 * (z * (t / 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 t <= 8e+193:
		tmp = -4.5 * (z * (t / 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 (t <= 8e+193)
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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 (t <= 8e+193)
		tmp = -4.5 * (z * (t / 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[LessEqual[t, 8e+193], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.00000000000000053e193

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. +-commutative 97.7%

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

      3. neg-sub0 97.7%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 97.7%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 97.7%

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

      6. neg-mul-1 97.7%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.6%

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

      9. *-commutative 97.6%

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

      10. sub-neg 97.6%

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

      11. +-commutative 97.6%

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

      12. neg-sub0 97.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 97.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 97.6%

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

      15. distribute-lft-neg-out 97.6%

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

      16. distribute-rgt-neg-in 97.6%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around 0 47.3%

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

      1. associate-/l* 43.9%

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

      2. associate-/r/ 48.2%

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

   6. Simplified 48.2%

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

   if 8.00000000000000053e193 < t

   1. Initial program 95.2%

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

      1. sub-neg 95.2%

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

      2. +-commutative 95.2%

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

      3. neg-sub0 95.2%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 95.2%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 95.2%

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

      6. neg-mul-1 95.2%

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

      7. associate-/l* 95.0%

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

      8. associate-/r/ 94.9%

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

      9. *-commutative 94.9%

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

      10. sub-neg 94.9%

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

      11. +-commutative 94.9%

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

      12. neg-sub0 94.9%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 94.9%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 94.9%

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

      15. distribute-lft-neg-out 94.9%

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

      16. distribute-rgt-neg-in 94.9%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 91.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{+193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 10: 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 97.5%

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

   1. sub-neg 97.5%

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

   2. +-commutative 97.5%

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

   3. neg-sub0 97.5%

      \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

   4. associate-+l- 97.5%

      \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

   5. sub0-neg 97.5%

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

   6. neg-mul-1 97.5%

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

   7. associate-/l* 97.3%

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

   8. associate-/r/ 97.4%

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

   9. *-commutative 97.4%

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

   10. sub-neg 97.4%

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

   11. +-commutative 97.4%

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

   12. neg-sub0 97.4%

       \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

   13. associate-+l- 97.4%

       \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

   14. sub0-neg 97.4%

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

   15. distribute-lft-neg-out 97.4%

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

   16. distribute-rgt-neg-in 97.4%

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

3. Simplified 98.2%

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

4. Taylor expanded in x around 0 50.9%

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

   1. associate-/l* 47.7%

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

   2. associate-/r/ 50.6%

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

6. Simplified 50.6%

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

7. Final simplification 50.6%

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

Developer target: 98.2% 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 2023278 
(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)))