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

Percentage Accurate: 91.3% → 96.7%

Time: 11.7s

Alternatives: 10

Speedup: 0.5×

• 27.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+221}:\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{2 \cdot a} - t \cdot \frac{z \cdot 9}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+221)
     (- (/ y (* 2.0 (/ a x))) (/ t (* (/ a z) 0.2222222222222222)))
     (if (<= t_1 5e+305)
       (/ (fma x (/ y 2.0) (* t (* z -4.5))) a)
       (- (* y (/ x (* 2.0 a))) (* t (/ (* z 9.0) (* 2.0 a))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	} else if (t_1 <= 5e+305) {
		tmp = fma(x, (y / 2.0), (t * (z * -4.5))) / a;
	} else {
		tmp = (y * (x / (2.0 * a))) - (t * ((z * 9.0) / (2.0 * a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+221)
		tmp = Float64(Float64(y / Float64(2.0 * Float64(a / x))) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	elseif (t_1 <= 5e+305)
		tmp = Float64(fma(x, Float64(y / 2.0), Float64(t * Float64(z * -4.5))) / a);
	else
		tmp = Float64(Float64(y * Float64(x / Float64(2.0 * a))) - Float64(t * Float64(Float64(z * 9.0) / Float64(2.0 * a))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+221], N[(N[(y / N[(2.0 * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(x * N[(y / 2.0), $MachinePrecision] + N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y * N[(x / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000002e221

   1. Initial program 69.2%

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

      1. div-sub 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-/l* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-/l* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.1%

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

      3. *-commutative 95.1%

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

      4. *-un-lft-identity 95.1%

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

      5. times-frac 95.1%

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

      6. metadata-eval 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. clear-num 95.2%

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

      2. un-div-inv 95.2%

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

      3. times-frac 95.1%

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

      4. metadata-eval 95.1%

         \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   8. Applied egg-rr 95.1%

      \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \color{blue}{\frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -5.0000000000000002e221 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.00000000000000009e305

   1. Initial program 98.6%

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

      1. associate-/l/ 99.1%

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

      2. div-sub 99.1%

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

      3. associate-/l* 99.1%

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

      4. fma-neg 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/l* 99.1%

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

      7. distribute-rgt-neg-out 99.1%

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

      8. distribute-frac-neg 99.1%

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

      9. distribute-rgt-neg-in 99.1%

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

      10. associate-/l* 99.1%

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

      11. metadata-eval 99.1%

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

      12. metadata-eval 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   if 5.00000000000000009e305 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 58.8%

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

      1. div-sub 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-/l* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-/l* 96.7%

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

   4. Applied egg-rr 96.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+221}:\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{2 \cdot a} - t \cdot \frac{z \cdot 9}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+221}:\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{2 \cdot a} - t \cdot \frac{z \cdot 9}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+221)
     (- (/ y (* 2.0 (/ a x))) (/ t (* (/ a z) 0.2222222222222222)))
     (if (<= t_1 5e+305)
       (* (fma z (* t -9.0) (* x y)) (/ 0.5 a))
       (- (* y (/ x (* 2.0 a))) (* t (/ (* z 9.0) (* 2.0 a))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	} else if (t_1 <= 5e+305) {
		tmp = fma(z, (t * -9.0), (x * y)) * (0.5 / a);
	} else {
		tmp = (y * (x / (2.0 * a))) - (t * ((z * 9.0) / (2.0 * a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+221)
		tmp = Float64(Float64(y / Float64(2.0 * Float64(a / x))) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	elseif (t_1 <= 5e+305)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(2.0 * a))) - Float64(t * Float64(Float64(z * 9.0) / Float64(2.0 * a))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+221], N[(N[(y / N[(2.0 * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000002e221

   1. Initial program 69.2%

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

      1. div-sub 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-/l* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-/l* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.1%

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

      3. *-commutative 95.1%

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

      4. *-un-lft-identity 95.1%

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

      5. times-frac 95.1%

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

      6. metadata-eval 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. clear-num 95.2%

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

      2. un-div-inv 95.2%

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

      3. times-frac 95.1%

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

      4. metadata-eval 95.1%

         \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   8. Applied egg-rr 95.1%

      \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \color{blue}{\frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -5.0000000000000002e221 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.00000000000000009e305

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 99.1%

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

      1. associate-*r/ 99.1%

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

      2. fma-neg 99.1%

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

      3. *-commutative 99.1%

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

      4. distribute-lft-neg-in 99.1%

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

      5. metadata-eval 99.1%

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

      6. *-commutative 99.1%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

      9. associate-*r/ 99.0%

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

      10. fma-define 99.0%

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

      11. +-commutative 99.0%

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

      12. fma-define 99.0%

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

   5. Simplified 99.0%

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

   if 5.00000000000000009e305 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 58.8%

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

      1. div-sub 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-/l* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-/l* 96.7%

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

   4. Applied egg-rr 96.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+221}:\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{2 \cdot a} - t \cdot \frac{z \cdot 9}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+221}:\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{2 \cdot a} - t \cdot \frac{z \cdot 9}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+221)
     (- (/ y (* 2.0 (/ a x))) (/ t (* (/ a z) 0.2222222222222222)))
     (if (<= t_1 5e+305)
       (* (/ 0.5 a) (+ (* x y) (* -9.0 (* z t))))
       (- (* y (/ x (* 2.0 a))) (* t (/ (* z 9.0) (* 2.0 a))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	} else if (t_1 <= 5e+305) {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	} else {
		tmp = (y * (x / (2.0 * a))) - (t * ((z * 9.0) / (2.0 * a)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-5d+221)) then
        tmp = (y / (2.0d0 * (a / x))) - (t / ((a / z) * 0.2222222222222222d0))
    else if (t_1 <= 5d+305) then
        tmp = (0.5d0 / a) * ((x * y) + ((-9.0d0) * (z * t)))
    else
        tmp = (y * (x / (2.0d0 * a))) - (t * ((z * 9.0d0) / (2.0d0 * a)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	} else if (t_1 <= 5e+305) {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	} else {
		tmp = (y * (x / (2.0 * a))) - (t * ((z * 9.0) / (2.0 * a)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -5e+221:
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222))
	elif t_1 <= 5e+305:
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)))
	else:
		tmp = (y * (x / (2.0 * a))) - (t * ((z * 9.0) / (2.0 * a)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+221)
		tmp = Float64(Float64(y / Float64(2.0 * Float64(a / x))) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t))));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(2.0 * a))) - Float64(t * Float64(Float64(z * 9.0) / Float64(2.0 * a))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -5e+221)
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	elseif (t_1 <= 5e+305)
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	else
		tmp = (y * (x / (2.0 * a))) - (t * ((z * 9.0) / (2.0 * a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+221], N[(N[(y / N[(2.0 * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000002e221

   1. Initial program 69.2%

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

      1. div-sub 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-/l* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-/l* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.1%

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

      3. *-commutative 95.1%

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

      4. *-un-lft-identity 95.1%

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

      5. times-frac 95.1%

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

      6. metadata-eval 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. clear-num 95.2%

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

      2. un-div-inv 95.2%

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

      3. times-frac 95.1%

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

      4. metadata-eval 95.1%

         \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   8. Applied egg-rr 95.1%

      \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \color{blue}{\frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -5.0000000000000002e221 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.00000000000000009e305

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 99.1%

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

      1. associate-*r/ 99.1%

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

      2. fma-neg 99.1%

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

      3. *-commutative 99.1%

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

      4. distribute-lft-neg-in 99.1%

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

      5. metadata-eval 99.1%

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

      6. *-commutative 99.1%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

      9. associate-*r/ 99.0%

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

      10. fma-define 99.0%

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

      11. +-commutative 99.0%

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

      12. fma-define 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in z around 0 99.0%

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

   if 5.00000000000000009e305 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 58.8%

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

      1. div-sub 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-/l* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-/l* 96.7%

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

   4. Applied egg-rr 96.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+221}:\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{2 \cdot a} - t \cdot \frac{z \cdot 9}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+221} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 -5e+221) (not (<= t_1 2e+304)))
     (- (/ y (* 2.0 (/ a x))) (/ t (* (/ a z) 0.2222222222222222)))
     (* (/ 0.5 a) (+ (* x y) (* -9.0 (* z t)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+221) || !(t_1 <= 2e+304)) {
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	} else {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if ((t_1 <= (-5d+221)) .or. (.not. (t_1 <= 2d+304))) then
        tmp = (y / (2.0d0 * (a / x))) - (t / ((a / z) * 0.2222222222222222d0))
    else
        tmp = (0.5d0 / a) * ((x * y) + ((-9.0d0) * (z * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+221) || !(t_1 <= 2e+304)) {
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	} else {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -5e+221) or not (t_1 <= 2e+304):
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222))
	else:
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -5e+221) || !(t_1 <= 2e+304))
		tmp = Float64(Float64(y / Float64(2.0 * Float64(a / x))) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	else
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -5e+221) || ~((t_1 <= 2e+304)))
		tmp = (y / (2.0 * (a / x))) - (t / ((a / z) * 0.2222222222222222));
	else
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+221], N[Not[LessEqual[t$95$1, 2e+304]], $MachinePrecision]], N[(N[(y / N[(2.0 * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000002e221 or 1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 65.7%

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

      1. div-sub 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-/l* 78.7%

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

      4. *-commutative 78.7%

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

      5. associate-/l* 95.8%

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

   4. Applied egg-rr 95.8%

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

      1. clear-num 95.8%

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

      2. un-div-inv 95.9%

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

      3. *-commutative 95.9%

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

      4. *-un-lft-identity 95.9%

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

      5. times-frac 95.9%

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

      6. metadata-eval 95.9%

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

   6. Applied egg-rr 95.9%

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

      1. clear-num 95.9%

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

      2. un-div-inv 95.9%

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

      3. times-frac 95.8%

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

      4. metadata-eval 95.8%

         \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   8. Applied egg-rr 95.8%

      \[\leadsto \frac{y}{2 \cdot \frac{a}{x}} - \color{blue}{\frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -5.0000000000000002e221 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 1.9999999999999999e304

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 99.1%

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

      1. associate-*r/ 99.1%

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

      2. fma-neg 99.1%

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

      3. *-commutative 99.1%

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

      4. distribute-lft-neg-in 99.1%

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

      5. metadata-eval 99.1%

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

      6. *-commutative 99.1%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

      9. associate-*r/ 99.0%

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

      10. fma-define 99.0%

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

      11. +-commutative 99.0%

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

      12. fma-define 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in z around 0 99.0%

      \[\leadsto \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)} \cdot \frac{0.5}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+221} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;\frac{y}{2 \cdot \frac{a}{x}} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) (- INFINITY)) (not (<= (* x y) 2e+226)))
   (/ (* y 0.5) (/ a x))
   (* (/ 0.5 a) (+ (* x y) (* -9.0 (* z t))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -((double) INFINITY)) || !((x * y) <= 2e+226)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -Double.POSITIVE_INFINITY) || !((x * y) <= 2e+226)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -math.inf) or not ((x * y) <= 2e+226):
		tmp = (y * 0.5) / (a / x)
	else:
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= Float64(-Inf)) || !(Float64(x * y) <= 2e+226))
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	else
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -Inf) || ~(((x * y) <= 2e+226)))
		tmp = (y * 0.5) / (a / x);
	else
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+226]], $MachinePrecision]], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 1.99999999999999992e226 < (*.f64 x y)

   1. Initial program 62.7%

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

   3. Taylor expanded in a around 0 64.8%

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

      1. associate-*r/ 64.8%

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

      2. fma-neg 64.8%

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

      3. *-commutative 64.8%

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

      4. distribute-lft-neg-in 64.8%

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

      5. metadata-eval 64.8%

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

      6. *-commutative 64.8%

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

      7. associate-*r* 64.8%

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

      8. *-commutative 64.8%

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

      9. associate-*r/ 64.8%

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

      10. fma-define 64.8%

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

      11. +-commutative 64.8%

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

      12. fma-define 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in z around 0 64.8%

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

   7. Taylor expanded in t around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*l/ 97.9%

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

      4. associate-/r/ 98.0%

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

      5. metadata-eval 98.0%

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

      6. times-frac 98.0%

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

      7. *-rgt-identity 98.0%

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

      8. associate-/r* 98.0%

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

      9. associate-/r/ 97.9%

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

      10. associate-*l/ 64.9%

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

      11. *-commutative 64.9%

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

      12. associate-/r* 62.9%

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

      13. associate-/l* 95.9%

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

   9. Simplified 95.9%

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

       1. associate-*r/ 62.9%

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

       2. times-frac 97.8%

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

       3. div-inv 97.8%

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

       4. metadata-eval 97.8%

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

       5. *-commutative 97.8%

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

       6. clear-num 97.8%

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

       7. un-div-inv 98.0%

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

   11. Applied egg-rr 98.0%

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

   if -inf.0 < (*.f64 x y) < 1.99999999999999992e226

   1. Initial program 94.7%

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

   3. Taylor expanded in a around 0 94.6%

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

      1. associate-*r/ 94.6%

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

      2. fma-neg 94.6%

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

      3. *-commutative 94.6%

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

      4. distribute-lft-neg-in 94.6%

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

      5. metadata-eval 94.6%

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

      6. *-commutative 94.6%

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

      7. associate-*r* 94.7%

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

      8. *-commutative 94.7%

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

      9. associate-*r/ 94.6%

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

      10. fma-define 94.6%

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

      11. +-commutative 94.6%

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

      12. fma-define 94.6%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in z around 0 94.5%

      \[\leadsto \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)} \cdot \frac{0.5}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) (- INFINITY)) (not (<= (* x y) 2e+226)))
   (/ (* y 0.5) (/ a x))
   (/ (- (* x y) (* (* z 9.0) t)) (* 2.0 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -((double) INFINITY)) || !((x * y) <= 2e+226)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -Double.POSITIVE_INFINITY) || !((x * y) <= 2e+226)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -math.inf) or not ((x * y) <= 2e+226):
		tmp = (y * 0.5) / (a / x)
	else:
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= Float64(-Inf)) || !(Float64(x * y) <= 2e+226))
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(2.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -Inf) || ~(((x * y) <= 2e+226)))
		tmp = (y * 0.5) / (a / x);
	else
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+226]], $MachinePrecision]], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 1.99999999999999992e226 < (*.f64 x y)

   1. Initial program 62.7%

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

   3. Taylor expanded in a around 0 64.8%

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

      1. associate-*r/ 64.8%

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

      2. fma-neg 64.8%

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

      3. *-commutative 64.8%

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

      4. distribute-lft-neg-in 64.8%

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

      5. metadata-eval 64.8%

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

      6. *-commutative 64.8%

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

      7. associate-*r* 64.8%

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

      8. *-commutative 64.8%

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

      9. associate-*r/ 64.8%

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

      10. fma-define 64.8%

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

      11. +-commutative 64.8%

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

      12. fma-define 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in z around 0 64.8%

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

   7. Taylor expanded in t around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*l/ 97.9%

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

      4. associate-/r/ 98.0%

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

      5. metadata-eval 98.0%

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

      6. times-frac 98.0%

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

      7. *-rgt-identity 98.0%

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

      8. associate-/r* 98.0%

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

      9. associate-/r/ 97.9%

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

      10. associate-*l/ 64.9%

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

      11. *-commutative 64.9%

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

      12. associate-/r* 62.9%

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

      13. associate-/l* 95.9%

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

   9. Simplified 95.9%

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

       1. associate-*r/ 62.9%

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

       2. times-frac 97.8%

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

       3. div-inv 97.8%

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

       4. metadata-eval 97.8%

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

       5. *-commutative 97.8%

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

       6. clear-num 97.8%

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

       7. un-div-inv 98.0%

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

   11. Applied egg-rr 98.0%

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

   if -inf.0 < (*.f64 x y) < 1.99999999999999992e226

   1. Initial program 94.7%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-77}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+14}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e-77)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 2e+14) (* -4.5 (* t (/ z a))) (* x (* 0.5 (/ y a))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-77) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+14) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x * (0.5 * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d-77)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= 2d+14) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = x * (0.5d0 * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-77) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+14) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x * (0.5 * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e-77:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 2e+14:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = x * (0.5 * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e-77)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 2e+14)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(x * Float64(0.5 * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e-77)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 2e+14)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = x * (0.5 * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-77], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+14], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999993e-78

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   if -9.9999999999999993e-78 < (*.f64 x y) < 2e14

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 78.3%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   if 2e14 < (*.f64 x y)

   1. Initial program 86.1%

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

      1. associate-/l/ 87.6%

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

      2. div-sub 87.6%

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

      3. associate-/l* 87.6%

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

      4. fma-neg 87.6%

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

      5. *-commutative 87.6%

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

      6. associate-/l* 87.6%

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

      7. distribute-rgt-neg-out 87.6%

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

      8. distribute-frac-neg 87.6%

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

      9. distribute-rgt-neg-in 87.6%

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

      10. associate-/l* 87.6%

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

      11. metadata-eval 87.6%

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

      12. metadata-eval 87.6%

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

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*r* 73.4%

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

      3. *-commutative 73.4%

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

   7. Simplified 73.4%

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

      1. associate-/l* 76.3%

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

      2. *-un-lft-identity 76.3%

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

      3. times-frac 76.3%

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

      4. metadata-eval 76.3%

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

   9. Applied egg-rr 76.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-77}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+14}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-149} \lor \neg \left(y \leq 6.2 \cdot 10^{+57}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4e-149) (not (<= y 6.2e+57)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (* t (/ z a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4e-149) || !(y <= 6.2e+57)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4d-149)) .or. (.not. (y <= 6.2d+57))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4e-149) || !(y <= 6.2e+57)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4e-149) or not (y <= 6.2e+57):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4e-149) || !(y <= 6.2e+57))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4e-149) || ~((y <= 6.2e+57)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4e-149], N[Not[LessEqual[y, 6.2e+57]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999992e-149 or 6.20000000000000026e57 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 55.7%

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

      1. associate-/l* 65.8%

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

   5. Simplified 65.8%

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

   if -3.99999999999999992e-149 < y < 6.20000000000000026e57

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 64.0%

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

      1. associate-/l* 64.1%

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

   5. Simplified 64.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-149} \lor \neg \left(y \leq 6.2 \cdot 10^{+57}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

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

3. Taylor expanded in x around 0 48.6%

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

   1. associate-/l* 48.0%

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

5. Simplified 48.0%

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

6. Final simplification 48.0%

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

Alternative 10: 50.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

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

3. Taylor expanded in x around 0 48.6%

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

   1. associate-/l* 48.0%

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

5. Simplified 48.0%

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

   1. clear-num 47.8%

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

   2. un-div-inv 47.8%

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

7. Applied egg-rr 47.8%

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

8. Final simplification 47.8%

   \[\leadsto -4.5 \cdot \frac{t}{\frac{a}{z}} \]
9. Add Preprocessing

Developer target: 93.3% accurate, 0.5× 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 2024047 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (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)))