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

Percentage Accurate: 91.1% → 94.1%

Time: 8.6s

Alternatives: 10

Speedup: 0.6×

• 28.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \frac{0.5}{a}, y, \frac{0.5}{a} \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+245}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot t\right) \cdot 9}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+300)
   (fma (* x (/ 0.5 a)) y (* (/ 0.5 a) (* z (* t -9.0))))
   (if (<= (* x y) 1e+245)
     (/ (- (* x y) (* (* z t) 9.0)) (* a 2.0))
     (/ 1.0 (* 2.0 (/ (/ a x) y))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+300) {
		tmp = fma((x * (0.5 / a)), y, ((0.5 / a) * (z * (t * -9.0))));
	} else if ((x * y) <= 1e+245) {
		tmp = ((x * y) - ((z * t) * 9.0)) / (a * 2.0);
	} else {
		tmp = 1.0 / (2.0 * ((a / x) / y));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+300)
		tmp = fma(Float64(x * Float64(0.5 / a)), y, Float64(Float64(0.5 / a) * Float64(z * Float64(t * -9.0))));
	elseif (Float64(x * y) <= 1e+245)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * t) * 9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(1.0 / Float64(2.0 * Float64(Float64(a / x) / y)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+300], N[(N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] * y + N[(N[(0.5 / a), $MachinePrecision] * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+245], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(2.0 * N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e300

   1. Initial program 58.5%

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

      1. sub-neg 58.5%

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

      2. +-commutative 58.5%

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

      3. neg-sub0 58.5%

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

      4. associate-+l- 58.5%

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

      5. sub0-neg 58.5%

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

      6. neg-mul-1 58.5%

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

      7. associate-/l* 58.5%

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

      8. associate-/r/ 58.6%

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

      9. *-commutative 58.6%

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

      10. sub-neg 58.6%

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

      11. +-commutative 58.6%

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

      12. neg-sub0 58.6%

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

      13. associate-+l- 58.6%

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

      14. sub0-neg 58.6%

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

      15. distribute-lft-neg-out 58.6%

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

      16. distribute-rgt-neg-in 58.6%

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

   3. Simplified 64.8%

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

      1. *-commutative 64.8%

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

      2. fma-udef 58.6%

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

      3. *-commutative 58.6%

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

      4. metadata-eval 58.6%

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

      5. distribute-lft-neg-in 58.6%

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

      6. distribute-rgt-neg-in 58.6%

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

      7. distribute-lft-in 58.6%

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

      8. distribute-rgt-neg-in 58.6%

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

      9. distribute-lft-neg-in 58.6%

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

      10. metadata-eval 58.6%

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

      11. *-commutative 58.6%

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

   5. Applied egg-rr 58.6%

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

      1. associate-*r* 93.6%

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

      2. fma-def 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -2.0000000000000001e300 < (*.f64 x y) < 1.00000000000000004e245

   1. Initial program 93.2%

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

      1. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around 0 93.3%

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

      1. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   if 1.00000000000000004e245 < (*.f64 x y)

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate-+l- 73.9%

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

      5. sub0-neg 73.9%

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

      6. neg-mul-1 73.9%

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

      7. associate-/l* 73.9%

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

      8. associate-/r/ 73.9%

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

      9. *-commutative 73.9%

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

      10. sub-neg 73.9%

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

      11. +-commutative 73.9%

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

      12. neg-sub0 73.9%

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

      13. associate-+l- 73.9%

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

      14. sub0-neg 73.9%

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

      15. distribute-lft-neg-out 73.9%

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

      16. distribute-rgt-neg-in 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in x around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 99.7%

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

      3. associate-*l/ 99.7%

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

   6. Simplified 99.7%

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

      1. clear-num 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y \cdot 0.5}}} \]

      2. inv-pow 99.6%

         \[\leadsto \color{blue}{{\left(\frac{\frac{a}{x}}{y \cdot 0.5}\right)}^{-1}} \]

   8. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y \cdot 0.5}}} \]

      2. *-un-lft-identity 99.6%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \frac{a}{x}}}{y \cdot 0.5}} \]

      3. *-commutative 99.6%

         \[\leadsto \frac{1}{\frac{1 \cdot \frac{a}{x}}{\color{blue}{0.5 \cdot y}}} \]

      4. times-frac 99.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{0.5} \cdot \frac{\frac{a}{x}}{y}}} \]

      5. metadata-eval 99.6%

         \[\leadsto \frac{1}{\color{blue}{2} \cdot \frac{\frac{a}{x}}{y}} \]

   10. Applied egg-rr 99.6%

       \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \frac{0.5}{a}, y, \frac{0.5}{a} \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+245}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot t\right) \cdot 9}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}\\ \end{array} \]

Alternative 2: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+245}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* (* y 0.5) (/ x a))
   (if (<= (* x y) 1e+245)
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
     (/ 1.0 (* 2.0 (/ (/ a x) y))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+245) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 1.0 / (2.0 * ((a / x) / y));
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+245) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 1.0 / (2.0 * ((a / x) / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = (y * 0.5) * (x / a)
	elif (x * y) <= 1e+245:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = 1.0 / (2.0 * ((a / x) / y))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (Float64(x * y) <= 1e+245)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(1.0 / Float64(2.0 * Float64(Float64(a / x) / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = (y * 0.5) * (x / a);
	elseif ((x * y) <= 1e+245)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = 1.0 / (2.0 * ((a / x) / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+245], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(2.0 * N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 55.8%

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

      1. sub-neg 55.8%

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

      2. +-commutative 55.8%

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

      3. neg-sub0 55.8%

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

      4. associate-+l- 55.8%

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

      5. sub0-neg 55.8%

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

      6. neg-mul-1 55.8%

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

      7. associate-/l* 55.8%

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

      8. associate-/r/ 55.8%

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

      9. *-commutative 55.8%

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

      10. sub-neg 55.8%

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

      11. +-commutative 55.8%

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

      12. neg-sub0 55.8%

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

      13. associate-+l- 55.8%

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

      14. sub0-neg 55.8%

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

      15. distribute-lft-neg-out 55.8%

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

      16. distribute-rgt-neg-in 55.8%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in x around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 93.1%

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

      3. associate-*l/ 93.1%

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

   6. Simplified 93.1%

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

      1. div-inv 93.1%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   8. Applied egg-rr 93.1%

      \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   9. Taylor expanded in a around 0 93.1%

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

   if -inf.0 < (*.f64 x y) < 1.00000000000000004e245

   1. Initial program 93.3%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   if 1.00000000000000004e245 < (*.f64 x y)

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate-+l- 73.9%

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

      5. sub0-neg 73.9%

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

      6. neg-mul-1 73.9%

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

      7. associate-/l* 73.9%

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

      8. associate-/r/ 73.9%

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

      9. *-commutative 73.9%

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

      10. sub-neg 73.9%

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

      11. +-commutative 73.9%

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

      12. neg-sub0 73.9%

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

      13. associate-+l- 73.9%

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

      14. sub0-neg 73.9%

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

      15. distribute-lft-neg-out 73.9%

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

      16. distribute-rgt-neg-in 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in x around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 99.7%

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

      3. associate-*l/ 99.7%

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

   6. Simplified 99.7%

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

      1. clear-num 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y \cdot 0.5}}} \]

      2. inv-pow 99.6%

         \[\leadsto \color{blue}{{\left(\frac{\frac{a}{x}}{y \cdot 0.5}\right)}^{-1}} \]

   8. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y \cdot 0.5}}} \]

      2. *-un-lft-identity 99.6%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \frac{a}{x}}}{y \cdot 0.5}} \]

      3. *-commutative 99.6%

         \[\leadsto \frac{1}{\frac{1 \cdot \frac{a}{x}}{\color{blue}{0.5 \cdot y}}} \]

      4. times-frac 99.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{0.5} \cdot \frac{\frac{a}{x}}{y}}} \]

      5. metadata-eval 99.6%

         \[\leadsto \frac{1}{\color{blue}{2} \cdot \frac{\frac{a}{x}}{y}} \]

   10. Applied egg-rr 99.6%

       \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+245}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}\\ \end{array} \]

Alternative 3: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+245}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot t\right) \cdot 9}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* (* y 0.5) (/ x a))
   (if (<= (* x y) 1e+245)
     (/ (- (* x y) (* (* z t) 9.0)) (* a 2.0))
     (/ 1.0 (* 2.0 (/ (/ a x) y))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+245) {
		tmp = ((x * y) - ((z * t) * 9.0)) / (a * 2.0);
	} else {
		tmp = 1.0 / (2.0 * ((a / x) / y));
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+245) {
		tmp = ((x * y) - ((z * t) * 9.0)) / (a * 2.0);
	} else {
		tmp = 1.0 / (2.0 * ((a / x) / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = (y * 0.5) * (x / a)
	elif (x * y) <= 1e+245:
		tmp = ((x * y) - ((z * t) * 9.0)) / (a * 2.0)
	else:
		tmp = 1.0 / (2.0 * ((a / x) / y))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (Float64(x * y) <= 1e+245)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * t) * 9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(1.0 / Float64(2.0 * Float64(Float64(a / x) / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = (y * 0.5) * (x / a);
	elseif ((x * y) <= 1e+245)
		tmp = ((x * y) - ((z * t) * 9.0)) / (a * 2.0);
	else
		tmp = 1.0 / (2.0 * ((a / x) / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+245], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(2.0 * N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 55.8%

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

      1. sub-neg 55.8%

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

      2. +-commutative 55.8%

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

      3. neg-sub0 55.8%

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

      4. associate-+l- 55.8%

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

      5. sub0-neg 55.8%

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

      6. neg-mul-1 55.8%

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

      7. associate-/l* 55.8%

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

      8. associate-/r/ 55.8%

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

      9. *-commutative 55.8%

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

      10. sub-neg 55.8%

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

      11. +-commutative 55.8%

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

      12. neg-sub0 55.8%

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

      13. associate-+l- 55.8%

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

      14. sub0-neg 55.8%

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

      15. distribute-lft-neg-out 55.8%

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

      16. distribute-rgt-neg-in 55.8%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in x around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 93.1%

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

      3. associate-*l/ 93.1%

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

   6. Simplified 93.1%

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

      1. div-inv 93.1%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   8. Applied egg-rr 93.1%

      \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   9. Taylor expanded in a around 0 93.1%

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

   if -inf.0 < (*.f64 x y) < 1.00000000000000004e245

   1. Initial program 93.3%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 93.3%

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

      1. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   if 1.00000000000000004e245 < (*.f64 x y)

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate-+l- 73.9%

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

      5. sub0-neg 73.9%

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

      6. neg-mul-1 73.9%

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

      7. associate-/l* 73.9%

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

      8. associate-/r/ 73.9%

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

      9. *-commutative 73.9%

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

      10. sub-neg 73.9%

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

      11. +-commutative 73.9%

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

      12. neg-sub0 73.9%

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

      13. associate-+l- 73.9%

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

      14. sub0-neg 73.9%

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

      15. distribute-lft-neg-out 73.9%

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

      16. distribute-rgt-neg-in 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in x around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 99.7%

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

      3. associate-*l/ 99.7%

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

   6. Simplified 99.7%

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

      1. clear-num 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y \cdot 0.5}}} \]

      2. inv-pow 99.6%

         \[\leadsto \color{blue}{{\left(\frac{\frac{a}{x}}{y \cdot 0.5}\right)}^{-1}} \]

   8. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y \cdot 0.5}}} \]

      2. *-un-lft-identity 99.6%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \frac{a}{x}}}{y \cdot 0.5}} \]

      3. *-commutative 99.6%

         \[\leadsto \frac{1}{\frac{1 \cdot \frac{a}{x}}{\color{blue}{0.5 \cdot y}}} \]

      4. times-frac 99.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{0.5} \cdot \frac{\frac{a}{x}}{y}}} \]

      5. metadata-eval 99.6%

         \[\leadsto \frac{1}{\color{blue}{2} \cdot \frac{\frac{a}{x}}{y}} \]

   10. Applied egg-rr 99.6%

       \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+245}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot t\right) \cdot 9}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}\\ \end{array} \]

Alternative 4: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.45 \cdot 10^{-17}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ t (/ a z)))))
   (if (<= z -4.2e+57)
     t_1
     (if (<= z -4.45e-17)
       (* (* y 0.5) (/ x a))
       (if (<= z -1.2e-40)
         (* -4.5 (* t (/ z a)))
         (if (<= z 1.3e-130) (* x (/ (* y 0.5) a)) t_1))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * (t / (a / z));
	double tmp;
	if (z <= -4.2e+57) {
		tmp = t_1;
	} else if (z <= -4.45e-17) {
		tmp = (y * 0.5) * (x / a);
	} else if (z <= -1.2e-40) {
		tmp = -4.5 * (t * (z / a));
	} else if (z <= 1.3e-130) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.5d0) * (t / (a / z))
    if (z <= (-4.2d+57)) then
        tmp = t_1
    else if (z <= (-4.45d-17)) then
        tmp = (y * 0.5d0) * (x / a)
    else if (z <= (-1.2d-40)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if (z <= 1.3d-130) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * (t / (a / z));
	double tmp;
	if (z <= -4.2e+57) {
		tmp = t_1;
	} else if (z <= -4.45e-17) {
		tmp = (y * 0.5) * (x / a);
	} else if (z <= -1.2e-40) {
		tmp = -4.5 * (t * (z / a));
	} else if (z <= 1.3e-130) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = -4.5 * (t / (a / z))
	tmp = 0
	if z <= -4.2e+57:
		tmp = t_1
	elif z <= -4.45e-17:
		tmp = (y * 0.5) * (x / a)
	elif z <= -1.2e-40:
		tmp = -4.5 * (t * (z / a))
	elif z <= 1.3e-130:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(t / Float64(a / z)))
	tmp = 0.0
	if (z <= -4.2e+57)
		tmp = t_1;
	elseif (z <= -4.45e-17)
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (z <= -1.2e-40)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (z <= 1.3e-130)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * (t / (a / z));
	tmp = 0.0;
	if (z <= -4.2e+57)
		tmp = t_1;
	elseif (z <= -4.45e-17)
		tmp = (y * 0.5) * (x / a);
	elseif (z <= -1.2e-40)
		tmp = -4.5 * (t * (z / a));
	elseif (z <= 1.3e-130)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+57], t$95$1, If[LessEqual[z, -4.45e-17], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-40], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-130], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.19999999999999982e57 or 1.3e-130 < z

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. +-commutative 86.8%

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

      3. neg-sub0 86.8%

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

      4. associate-+l- 86.8%

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

      5. sub0-neg 86.8%

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

      6. neg-mul-1 86.8%

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

      7. associate-/l* 86.8%

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

      8. associate-/r/ 86.7%

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

      9. *-commutative 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. neg-sub0 86.7%

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

      13. associate-+l- 86.7%

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

      14. sub0-neg 86.7%

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

      15. distribute-lft-neg-out 86.7%

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

      16. distribute-rgt-neg-in 86.7%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 58.0%

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

      1. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   if -4.19999999999999982e57 < z < -4.4500000000000002e-17

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. +-commutative 92.2%

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

      3. neg-sub0 92.2%

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

      4. associate-+l- 92.2%

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

      5. sub0-neg 92.2%

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

      6. neg-mul-1 92.2%

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

      7. associate-/l* 91.5%

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

      8. associate-/r/ 91.8%

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

      9. *-commutative 91.8%

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

      10. sub-neg 91.8%

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

      11. +-commutative 91.8%

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

      12. neg-sub0 91.8%

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

      13. associate-+l- 91.8%

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

      14. sub0-neg 91.8%

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

      15. distribute-lft-neg-out 91.8%

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

      16. distribute-rgt-neg-in 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-/l* 55.4%

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

      3. associate-*l/ 55.4%

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

   6. Simplified 55.4%

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

      1. div-inv 55.4%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   8. Applied egg-rr 55.4%

      \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   9. Taylor expanded in a around 0 55.3%

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

   if -4.4500000000000002e-17 < z < -1.19999999999999996e-40

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. neg-sub0 99.2%

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

      4. associate-+l- 99.2%

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

      5. sub0-neg 99.2%

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

      6. neg-mul-1 99.2%

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

      7. associate-/l* 98.8%

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

      8. associate-/r/ 99.2%

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

      9. *-commutative 99.2%

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

      10. sub-neg 99.2%

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

      11. +-commutative 99.2%

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

      12. neg-sub0 99.2%

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

      13. associate-+l- 99.2%

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

      14. sub0-neg 99.2%

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

      15. distribute-lft-neg-out 99.2%

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

      16. distribute-rgt-neg-in 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 72.8%

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

      1. associate-/l* 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in t around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 72.8%

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

      3. associate-/r/ 72.8%

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

   9. Simplified 72.8%

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

   if -1.19999999999999996e-40 < z < 1.3e-130

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. +-commutative 93.2%

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

      3. neg-sub0 93.2%

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

      4. associate-+l- 93.2%

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

      5. sub0-neg 93.2%

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

      6. neg-mul-1 93.2%

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

      7. associate-/l* 92.3%

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

      8. associate-/r/ 93.1%

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

      9. *-commutative 93.1%

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

      10. sub-neg 93.1%

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

      11. +-commutative 93.1%

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

      12. neg-sub0 93.1%

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

      13. associate-+l- 93.1%

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

      14. sub0-neg 93.1%

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

      15. distribute-lft-neg-out 93.1%

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

      16. distribute-rgt-neg-in 93.1%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/l* 65.7%

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

      3. associate-*l/ 65.7%

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

   6. Simplified 65.7%

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

      1. associate-/r/ 59.8%

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

   8. Applied egg-rr 59.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -4.45 \cdot 10^{-17}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ t (/ a z)))))
   (if (<= z -3e+57)
     t_1
     (if (<= z -3.7e-14)
       (* (* y 0.5) (/ x a))
       (if (<= z -1.2e-37)
         (* -4.5 (* t (/ z a)))
         (if (<= z 6.8e-130) (/ (* x y) (* a 2.0)) t_1))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * (t / (a / z));
	double tmp;
	if (z <= -3e+57) {
		tmp = t_1;
	} else if (z <= -3.7e-14) {
		tmp = (y * 0.5) * (x / a);
	} else if (z <= -1.2e-37) {
		tmp = -4.5 * (t * (z / a));
	} else if (z <= 6.8e-130) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.5d0) * (t / (a / z))
    if (z <= (-3d+57)) then
        tmp = t_1
    else if (z <= (-3.7d-14)) then
        tmp = (y * 0.5d0) * (x / a)
    else if (z <= (-1.2d-37)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if (z <= 6.8d-130) then
        tmp = (x * y) / (a * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * (t / (a / z));
	double tmp;
	if (z <= -3e+57) {
		tmp = t_1;
	} else if (z <= -3.7e-14) {
		tmp = (y * 0.5) * (x / a);
	} else if (z <= -1.2e-37) {
		tmp = -4.5 * (t * (z / a));
	} else if (z <= 6.8e-130) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = -4.5 * (t / (a / z))
	tmp = 0
	if z <= -3e+57:
		tmp = t_1
	elif z <= -3.7e-14:
		tmp = (y * 0.5) * (x / a)
	elif z <= -1.2e-37:
		tmp = -4.5 * (t * (z / a))
	elif z <= 6.8e-130:
		tmp = (x * y) / (a * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(t / Float64(a / z)))
	tmp = 0.0
	if (z <= -3e+57)
		tmp = t_1;
	elseif (z <= -3.7e-14)
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (z <= -1.2e-37)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (z <= 6.8e-130)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * (t / (a / z));
	tmp = 0.0;
	if (z <= -3e+57)
		tmp = t_1;
	elseif (z <= -3.7e-14)
		tmp = (y * 0.5) * (x / a);
	elseif (z <= -1.2e-37)
		tmp = -4.5 * (t * (z / a));
	elseif (z <= 6.8e-130)
		tmp = (x * y) / (a * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+57], t$95$1, If[LessEqual[z, -3.7e-14], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-37], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-130], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3e57 or 6.8000000000000001e-130 < z

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. +-commutative 86.8%

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

      3. neg-sub0 86.8%

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

      4. associate-+l- 86.8%

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

      5. sub0-neg 86.8%

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

      6. neg-mul-1 86.8%

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

      7. associate-/l* 86.8%

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

      8. associate-/r/ 86.7%

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

      9. *-commutative 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. neg-sub0 86.7%

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

      13. associate-+l- 86.7%

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

      14. sub0-neg 86.7%

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

      15. distribute-lft-neg-out 86.7%

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

      16. distribute-rgt-neg-in 86.7%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 58.0%

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

      1. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   if -3e57 < z < -3.70000000000000001e-14

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. +-commutative 92.2%

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

      3. neg-sub0 92.2%

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

      4. associate-+l- 92.2%

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

      5. sub0-neg 92.2%

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

      6. neg-mul-1 92.2%

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

      7. associate-/l* 91.5%

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

      8. associate-/r/ 91.8%

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

      9. *-commutative 91.8%

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

      10. sub-neg 91.8%

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

      11. +-commutative 91.8%

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

      12. neg-sub0 91.8%

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

      13. associate-+l- 91.8%

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

      14. sub0-neg 91.8%

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

      15. distribute-lft-neg-out 91.8%

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

      16. distribute-rgt-neg-in 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-/l* 55.4%

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

      3. associate-*l/ 55.4%

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

   6. Simplified 55.4%

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

      1. div-inv 55.4%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   8. Applied egg-rr 55.4%

      \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   9. Taylor expanded in a around 0 55.3%

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

   if -3.70000000000000001e-14 < z < -1.19999999999999995e-37

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. neg-sub0 99.2%

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

      4. associate-+l- 99.2%

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

      5. sub0-neg 99.2%

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

      6. neg-mul-1 99.2%

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

      7. associate-/l* 98.8%

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

      8. associate-/r/ 99.2%

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

      9. *-commutative 99.2%

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

      10. sub-neg 99.2%

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

      11. +-commutative 99.2%

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

      12. neg-sub0 99.2%

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

      13. associate-+l- 99.2%

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

      14. sub0-neg 99.2%

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

      15. distribute-lft-neg-out 99.2%

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

      16. distribute-rgt-neg-in 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 72.8%

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

      1. associate-/l* 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in t around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 72.8%

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

      3. associate-/r/ 72.8%

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

   9. Simplified 72.8%

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

   if -1.19999999999999995e-37 < z < 6.8000000000000001e-130

   1. Initial program 93.2%

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

      1. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 66.5%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+57}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 65.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+57} \lor \neg \left(z \leq 6.8 \cdot 10^{-130}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e+57) (not (<= z 6.8e-130)))
   (* -4.5 (/ t (/ a z)))
   (* (* y 0.5) (/ x a))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+57) || !(z <= 6.8e-130)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((z <= (-4.3d+57)) .or. (.not. (z <= 6.8d-130))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (y * 0.5d0) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+57) || !(z <= 6.8e-130)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e+57) or not (z <= 6.8e-130):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = (y * 0.5) * (x / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e+57) || !(z <= 6.8e-130))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e+57) || ~((z <= 6.8e-130)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = (y * 0.5) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e+57], N[Not[LessEqual[z, 6.8e-130]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.30000000000000033e57 or 6.8000000000000001e-130 < z

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. +-commutative 86.8%

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

      3. neg-sub0 86.8%

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

      4. associate-+l- 86.8%

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

      5. sub0-neg 86.8%

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

      6. neg-mul-1 86.8%

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

      7. associate-/l* 86.8%

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

      8. associate-/r/ 86.7%

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

      9. *-commutative 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. neg-sub0 86.7%

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

      13. associate-+l- 86.7%

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

      14. sub0-neg 86.7%

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

      15. distribute-lft-neg-out 86.7%

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

      16. distribute-rgt-neg-in 86.7%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 58.0%

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

      1. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   if -4.30000000000000033e57 < z < 6.8000000000000001e-130

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. +-commutative 93.2%

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

      3. neg-sub0 93.2%

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

      4. associate-+l- 93.2%

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

      5. sub0-neg 93.2%

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

      6. neg-mul-1 93.2%

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

      7. associate-/l* 92.4%

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

      8. associate-/r/ 93.0%

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

      9. *-commutative 93.0%

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

      10. sub-neg 93.0%

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

      11. +-commutative 93.0%

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

      12. neg-sub0 93.0%

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

      13. associate-+l- 93.0%

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

      14. sub0-neg 93.0%

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

      15. distribute-lft-neg-out 93.0%

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

      16. distribute-rgt-neg-in 93.0%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 63.5%

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

      3. associate-*l/ 63.5%

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

   6. Simplified 63.5%

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

      1. div-inv 63.4%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   8. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{1}{\frac{a}{x}}} \]

   9. Taylor expanded in a around 0 63.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+57} \lor \neg \left(z \leq 6.8 \cdot 10^{-130}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]

Alternative 7: 52.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.35e+133) (* -4.5 (* t (/ z a))) (* -4.5 (* z (/ t a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.35e+133) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 1.35d+133) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.35e+133) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.35e+133:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.35e+133)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.35e+133)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.35e+133], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.3500000000000001e133

   1. Initial program 90.3%

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

      1. sub-neg 90.3%

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

      2. +-commutative 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate-+l- 90.3%

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

      5. sub0-neg 90.3%

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

      6. neg-mul-1 90.3%

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

      7. associate-/l* 89.9%

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

      8. associate-/r/ 90.2%

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

      9. *-commutative 90.2%

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

      10. sub-neg 90.2%

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

      11. +-commutative 90.2%

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

      12. neg-sub0 90.2%

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

      13. associate-+l- 90.2%

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

      14. sub0-neg 90.2%

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

      15. distribute-lft-neg-out 90.2%

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

      16. distribute-rgt-neg-in 90.2%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 45.1%

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

      1. associate-/l* 45.2%

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

   6. Simplified 45.2%

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

   7. Taylor expanded in t around 0 45.1%

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

      1. *-commutative 45.1%

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

      2. associate-/l* 46.8%

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

      3. associate-/r/ 45.2%

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

   9. Simplified 45.2%

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

   if 1.3500000000000001e133 < t

   1. Initial program 86.9%

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

      1. sub-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. neg-sub0 86.9%

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

      4. associate-+l- 86.9%

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

      5. sub0-neg 86.9%

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

      6. neg-mul-1 86.9%

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

      7. associate-/l* 86.7%

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

      8. associate-/r/ 86.7%

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

      9. *-commutative 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. neg-sub0 86.7%

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

      13. associate-+l- 86.7%

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

      14. sub0-neg 86.7%

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

      15. distribute-lft-neg-out 86.7%

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

      16. distribute-rgt-neg-in 86.7%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in x around 0 68.4%

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

      1. associate-/l* 68.4%

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

      2. associate-/r/ 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 8: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+134}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 5.2e+134) (* -4.5 (/ t (/ a z))) (* -4.5 (* z (/ t a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.2e+134) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x and y 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+134) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.2e+134) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.2e+134:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.2e+134)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 5.2e+134)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 5.2e+134], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.2000000000000003e134

   1. Initial program 90.3%

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

      1. sub-neg 90.3%

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

      2. +-commutative 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate-+l- 90.3%

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

      5. sub0-neg 90.3%

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

      6. neg-mul-1 90.3%

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

      7. associate-/l* 89.9%

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

      8. associate-/r/ 90.2%

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

      9. *-commutative 90.2%

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

      10. sub-neg 90.2%

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

      11. +-commutative 90.2%

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

      12. neg-sub0 90.2%

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

      13. associate-+l- 90.2%

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

      14. sub0-neg 90.2%

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

      15. distribute-lft-neg-out 90.2%

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

      16. distribute-rgt-neg-in 90.2%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 45.1%

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

      1. associate-/l* 45.2%

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

   6. Simplified 45.2%

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

   if 5.2000000000000003e134 < t

   1. Initial program 86.9%

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

      1. sub-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. neg-sub0 86.9%

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

      4. associate-+l- 86.9%

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

      5. sub0-neg 86.9%

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

      6. neg-mul-1 86.9%

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

      7. associate-/l* 86.7%

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

      8. associate-/r/ 86.7%

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

      9. *-commutative 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. neg-sub0 86.7%

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

      13. associate-+l- 86.7%

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

      14. sub0-neg 86.7%

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

      15. distribute-lft-neg-out 86.7%

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

      16. distribute-rgt-neg-in 86.7%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in x around 0 68.4%

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

      1. associate-/l* 68.4%

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

      2. associate-/r/ 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+134}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 9: 52.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.4 \cdot 10^{+131}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 5.4e+131) (* -4.5 (/ t (/ a z))) (* -4.5 (/ z (/ a t)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.4e+131) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= 5.4d+131) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5.4e+131) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 5.4e+131:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5.4e+131)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 5.4e+131)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 5.4e+131], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.40000000000000008e131

   1. Initial program 90.3%

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

      1. sub-neg 90.3%

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

      2. +-commutative 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate-+l- 90.3%

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

      5. sub0-neg 90.3%

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

      6. neg-mul-1 90.3%

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

      7. associate-/l* 89.9%

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

      8. associate-/r/ 90.2%

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

      9. *-commutative 90.2%

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

      10. sub-neg 90.2%

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

      11. +-commutative 90.2%

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

      12. neg-sub0 90.2%

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

      13. associate-+l- 90.2%

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

      14. sub0-neg 90.2%

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

      15. distribute-lft-neg-out 90.2%

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

      16. distribute-rgt-neg-in 90.2%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 45.1%

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

      1. associate-/l* 45.2%

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

   6. Simplified 45.2%

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

   if 5.40000000000000008e131 < t

   1. Initial program 86.9%

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

      1. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around 0 86.8%

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

      1. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-/l* 81.2%

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

   9. Simplified 81.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.4 \cdot 10^{+131}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 10: 52.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y 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 89.7%

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

   1. sub-neg 89.7%

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

   2. +-commutative 89.7%

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

   3. neg-sub0 89.7%

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

   4. associate-+l- 89.7%

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

   5. sub0-neg 89.7%

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

   6. neg-mul-1 89.7%

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

   7. associate-/l* 89.4%

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

   8. associate-/r/ 89.6%

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

   9. *-commutative 89.6%

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

   10. sub-neg 89.6%

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

   11. +-commutative 89.6%

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

   12. neg-sub0 89.6%

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

   13. associate-+l- 89.6%

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

   14. sub0-neg 89.6%

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

   15. distribute-lft-neg-out 89.6%

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

   16. distribute-rgt-neg-in 89.6%

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

3. Simplified 89.3%

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

4. Taylor expanded in x around 0 49.1%

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

   1. associate-/l* 49.2%

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

   2. associate-/r/ 52.4%

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

6. Simplified 52.4%

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

7. Final simplification 52.4%

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

Developer target: 93.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023182 
(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)))