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

Percentage Accurate: 91.4% → 97.2%

Time: 9.9s

Alternatives: 10

Speedup: 0.6×

• 28.3% 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: 91.4% 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: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{\frac{x}{2}}{\frac{a}{y}} + z \cdot \frac{-4.5}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+299)))
     (+ (/ (/ x 2.0) (/ a y)) (* z (/ -4.5 (/ a t))))
     (/ (fma x y (* z (* t -9.0))) (* 2.0 a)))))

C

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 <= -((double) INFINITY)) || !(t_1 <= 4e+299)) {
		tmp = ((x / 2.0) / (a / y)) + (z * (-4.5 / (a / t)));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) / (2.0 * a);
	}
	return tmp;
}

Julia

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 <= Float64(-Inf)) || !(t_1 <= 4e+299))
		tmp = Float64(Float64(Float64(x / 2.0) / Float64(a / y)) + Float64(z * Float64(-4.5 / Float64(a / t))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -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.
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, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+299]], $MachinePrecision]], N[(N[(N[(x / 2.0), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 4.0000000000000002e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 58.4%

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

      1. div-inv 58.4%

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

      2. fma-neg 58.4%

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

      3. *-commutative 58.4%

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

      4. distribute-rgt-neg-in 58.4%

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

      5. distribute-rgt-neg-in 58.4%

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

      6. metadata-eval 58.4%

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

      7. *-commutative 58.4%

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

      8. associate-/r* 58.4%

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

      9. metadata-eval 58.4%

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

   4. Applied egg-rr 58.4%

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

      1. fma-undefine 58.4%

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

   6. Applied egg-rr 58.4%

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

      1. *-commutative 58.4%

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

      2. distribute-lft-in 55.0%

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

      3. associate-*l/ 55.0%

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

      4. *-commutative 55.0%

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

      5. associate-*r* 55.0%

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

      6. associate-*l* 55.0%

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

      7. metadata-eval 55.0%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \frac{\left(t \cdot z\right) \cdot \color{blue}{-4.5}}{a} \]

      8. *-commutative 55.0%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \frac{\color{blue}{\left(z \cdot t\right)} \cdot -4.5}{a} \]

      9. associate-*r/ 55.0%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

      10. associate-*r* 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{-4.5}{a}\right)} \]

      11. associate-*r/ 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\frac{t \cdot -4.5}{a}} \]

      12. associate-*l/ 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\left(\frac{t}{a} \cdot -4.5\right)} \]

      13. clear-num 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \left(\color{blue}{\frac{1}{\frac{a}{t}}} \cdot -4.5\right) \]

      14. associate-*l/ 74.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\frac{1 \cdot -4.5}{\frac{a}{t}}} \]

      15. metadata-eval 74.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \frac{\color{blue}{-4.5}}{\frac{a}{t}} \]

   8. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \frac{-4.5}{\frac{a}{t}}} \]
   9. Step-by-step derivation

      1. *-commutative 74.3%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      2. associate-*r* 94.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      3. associate-/l* 94.7%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      4. clear-num 94.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y \cdot 0.5}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      5. un-div-inv 94.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      6. *-un-lft-identity 94.7%

         \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot a}}{y \cdot 0.5}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      7. *-commutative 94.7%

         \[\leadsto \frac{x}{\frac{1 \cdot a}{\color{blue}{0.5 \cdot y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      8. times-frac 94.7%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{0.5} \cdot \frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      9. metadata-eval 94.7%

         \[\leadsto \frac{x}{\color{blue}{2} \cdot \frac{a}{y}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

   10. Applied egg-rr 94.7%

       \[\leadsto \color{blue}{\frac{x}{2 \cdot \frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]
   11. Step-by-step derivation

       1. associate-/r* 94.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{2}}{\frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

   12. Simplified 94.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{2}}{\frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.0000000000000002e299

   1. Initial program 98.1%

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

      1. div-sub 96.1%

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

      2. *-commutative 96.1%

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

      3. div-sub 98.1%

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

      4. cancel-sign-sub-inv 98.1%

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

      5. *-commutative 98.1%

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

      6. fma-define 98.1%

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

      7. distribute-rgt-neg-in 98.1%

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

      8. associate-*r* 98.2%

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

      9. distribute-lft-neg-in 98.2%

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

      10. *-commutative 98.2%

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

      11. distribute-rgt-neg-in 98.2%

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

      12. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{\frac{x}{2}}{\frac{a}{y}} + z \cdot \frac{-4.5}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{\frac{x}{2}}{\frac{a}{y}} + z \cdot \frac{-4.5}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+299)))
     (+ (/ (/ x 2.0) (/ a y)) (* z (/ -4.5 (/ a t))))
     (/ t_1 (* 2.0 a)))))

C

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 <= -((double) INFINITY)) || !(t_1 <= 4e+299)) {
		tmp = ((x / 2.0) / (a / y)) + (z * (-4.5 / (a / t)));
	} else {
		tmp = t_1 / (2.0 * a);
	}
	return tmp;
}

Java

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+299)) {
		tmp = ((x / 2.0) / (a / y)) + (z * (-4.5 / (a / t)));
	} else {
		tmp = t_1 / (2.0 * a);
	}
	return tmp;
}

Python

[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 <= -math.inf) or not (t_1 <= 4e+299):
		tmp = ((x / 2.0) / (a / y)) + (z * (-4.5 / (a / t)))
	else:
		tmp = t_1 / (2.0 * a)
	return tmp

Julia

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 <= Float64(-Inf)) || !(t_1 <= 4e+299))
		tmp = Float64(Float64(Float64(x / 2.0) / Float64(a / y)) + Float64(z * Float64(-4.5 / Float64(a / t))));
	else
		tmp = Float64(t_1 / Float64(2.0 * a));
	end
	return tmp
end

MATLAB

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 <= -Inf) || ~((t_1 <= 4e+299)))
		tmp = ((x / 2.0) / (a / y)) + (z * (-4.5 / (a / t)));
	else
		tmp = t_1 / (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.
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, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+299]], $MachinePrecision]], N[(N[(N[(x / 2.0), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 4.0000000000000002e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 58.4%

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

      1. div-inv 58.4%

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

      2. fma-neg 58.4%

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

      3. *-commutative 58.4%

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

      4. distribute-rgt-neg-in 58.4%

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

      5. distribute-rgt-neg-in 58.4%

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

      6. metadata-eval 58.4%

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

      7. *-commutative 58.4%

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

      8. associate-/r* 58.4%

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

      9. metadata-eval 58.4%

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

   4. Applied egg-rr 58.4%

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

      1. fma-undefine 58.4%

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

   6. Applied egg-rr 58.4%

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

      1. *-commutative 58.4%

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

      2. distribute-lft-in 55.0%

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

      3. associate-*l/ 55.0%

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

      4. *-commutative 55.0%

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

      5. associate-*r* 55.0%

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

      6. associate-*l* 55.0%

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

      7. metadata-eval 55.0%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \frac{\left(t \cdot z\right) \cdot \color{blue}{-4.5}}{a} \]

      8. *-commutative 55.0%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \frac{\color{blue}{\left(z \cdot t\right)} \cdot -4.5}{a} \]

      9. associate-*r/ 55.0%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

      10. associate-*r* 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{-4.5}{a}\right)} \]

      11. associate-*r/ 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\frac{t \cdot -4.5}{a}} \]

      12. associate-*l/ 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\left(\frac{t}{a} \cdot -4.5\right)} \]

      13. clear-num 74.2%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \left(\color{blue}{\frac{1}{\frac{a}{t}}} \cdot -4.5\right) \]

      14. associate-*l/ 74.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\frac{1 \cdot -4.5}{\frac{a}{t}}} \]

      15. metadata-eval 74.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \frac{\color{blue}{-4.5}}{\frac{a}{t}} \]

   8. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \frac{-4.5}{\frac{a}{t}}} \]
   9. Step-by-step derivation

      1. *-commutative 74.3%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      2. associate-*r* 94.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      3. associate-/l* 94.7%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      4. clear-num 94.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{y \cdot 0.5}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      5. un-div-inv 94.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      6. *-un-lft-identity 94.7%

         \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot a}}{y \cdot 0.5}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      7. *-commutative 94.7%

         \[\leadsto \frac{x}{\frac{1 \cdot a}{\color{blue}{0.5 \cdot y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      8. times-frac 94.7%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{0.5} \cdot \frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

      9. metadata-eval 94.7%

         \[\leadsto \frac{x}{\color{blue}{2} \cdot \frac{a}{y}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

   10. Applied egg-rr 94.7%

       \[\leadsto \color{blue}{\frac{x}{2 \cdot \frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]
   11. Step-by-step derivation

       1. associate-/r* 94.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{2}}{\frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

   12. Simplified 94.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{2}}{\frac{a}{y}}} + z \cdot \frac{-4.5}{\frac{a}{t}} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.0000000000000002e299

   1. Initial program 98.1%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{\frac{x}{2}}{\frac{a}{y}} + z \cdot \frac{-4.5}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-145}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-259} \lor \neg \left(y \leq 2.15 \cdot 10^{-218}\right) \land y \leq 2.2 \cdot 10^{+78}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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 (* y (* 0.5 (/ x a)))))
   (if (<= y -5e-62)
     t_1
     (if (<= y -5.6e-145)
       (* t (* z (/ -4.5 a)))
       (if (<= y -9.2e-166)
         (* x (/ (* y 0.5) a))
         (if (or (<= y 9.2e-259) (and (not (<= y 2.15e-218)) (<= y 2.2e+78)))
           (* -4.5 (/ (* z t) a))
           t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if (y <= -5e-62) {
		tmp = t_1;
	} else if (y <= -5.6e-145) {
		tmp = t * (z * (-4.5 / a));
	} else if (y <= -9.2e-166) {
		tmp = x * ((y * 0.5) / a);
	} else if ((y <= 9.2e-259) || (!(y <= 2.15e-218) && (y <= 2.2e+78))) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = y * (0.5d0 * (x / a))
    if (y <= (-5d-62)) then
        tmp = t_1
    else if (y <= (-5.6d-145)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (y <= (-9.2d-166)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((y <= 9.2d-259) .or. (.not. (y <= 2.15d-218)) .and. (y <= 2.2d+78)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 = y * (0.5 * (x / a));
	double tmp;
	if (y <= -5e-62) {
		tmp = t_1;
	} else if (y <= -5.6e-145) {
		tmp = t * (z * (-4.5 / a));
	} else if (y <= -9.2e-166) {
		tmp = x * ((y * 0.5) / a);
	} else if ((y <= 9.2e-259) || (!(y <= 2.15e-218) && (y <= 2.2e+78))) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (0.5 * (x / a))
	tmp = 0
	if y <= -5e-62:
		tmp = t_1
	elif y <= -5.6e-145:
		tmp = t * (z * (-4.5 / a))
	elif y <= -9.2e-166:
		tmp = x * ((y * 0.5) / a)
	elif (y <= 9.2e-259) or (not (y <= 2.15e-218) and (y <= 2.2e+78)):
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(0.5 * Float64(x / a)))
	tmp = 0.0
	if (y <= -5e-62)
		tmp = t_1;
	elseif (y <= -5.6e-145)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (y <= -9.2e-166)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif ((y <= 9.2e-259) || (!(y <= 2.15e-218) && (y <= 2.2e+78)))
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (0.5 * (x / a));
	tmp = 0.0;
	if (y <= -5e-62)
		tmp = t_1;
	elseif (y <= -5.6e-145)
		tmp = t * (z * (-4.5 / a));
	elseif (y <= -9.2e-166)
		tmp = x * ((y * 0.5) / a);
	elseif ((y <= 9.2e-259) || (~((y <= 2.15e-218)) && (y <= 2.2e+78)))
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-62], t$95$1, If[LessEqual[y, -5.6e-145], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.2e-166], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 9.2e-259], And[N[Not[LessEqual[y, 2.15e-218]], $MachinePrecision], LessEqual[y, 2.2e+78]]], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.0000000000000002e-62 or 9.1999999999999997e-259 < y < 2.15e-218 or 2.20000000000000014e78 < y

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 79.1%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 63.8%

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

   if -5.0000000000000002e-62 < y < -5.6000000000000002e-145

   1. Initial program 99.8%

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

      1. div-inv 99.4%

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

      2. fma-neg 99.4%

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

      3. *-commutative 99.4%

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

      4. distribute-rgt-neg-in 99.4%

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

      5. distribute-rgt-neg-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around 0 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/l* 57.9%

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

      3. associate-*r* 57.7%

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

      4. metadata-eval 57.7%

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

      5. times-frac 57.8%

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

      6. times-frac 57.7%

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

      7. metadata-eval 57.7%

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

      8. associate-*l/ 57.8%

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

      9. associate-/l* 58.0%

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

   7. Simplified 58.0%

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

   if -5.6000000000000002e-145 < y < -9.19999999999999995e-166

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.5%

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

      1. *-commutative 80.5%

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

      2. associate-/l* 80.2%

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

      3. associate-*r* 80.2%

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

      4. *-commutative 80.2%

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

      5. associate-*r/ 80.2%

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

   5. Simplified 80.2%

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

   if -9.19999999999999995e-166 < y < 9.1999999999999997e-259 or 2.15e-218 < y < 2.20000000000000014e78

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 66.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-145}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-259} \lor \neg \left(y \leq 2.15 \cdot 10^{-218}\right) \land y \leq 2.2 \cdot 10^{+78}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* t (* z (/ -4.5 a)))
     (if (<= t_1 2e+208)
       (/ (- (* x y) t_1) (* 2.0 a))
       (* (/ t a) (* z -4.5))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 2e+208) {
		tmp = ((x * y) - t_1) / (2.0 * a);
	} else {
		tmp = (t / a) * (z * -4.5);
	}
	return tmp;
}

Java

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 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 2e+208) {
		tmp = ((x * y) - t_1) / (2.0 * a);
	} else {
		tmp = (t / a) * (z * -4.5);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t * (z * (-4.5 / a))
	elif t_1 <= 2e+208:
		tmp = ((x * y) - t_1) / (2.0 * a)
	else:
		tmp = (t / a) * (z * -4.5)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_1 <= 2e+208)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t * (z * (-4.5 / a));
	elseif (t_1 <= 2e+208)
		tmp = ((x * y) - t_1) / (2.0 * a);
	else
		tmp = (t / a) * (z * -4.5);
	end
	tmp_2 = tmp;
end

Wolfram

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[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+208], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0

   1. Initial program 55.4%

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

      1. div-inv 55.4%

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

      2. fma-neg 55.4%

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

      3. *-commutative 55.4%

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

      4. distribute-rgt-neg-in 55.4%

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

      5. distribute-rgt-neg-in 55.4%

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

      6. metadata-eval 55.4%

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

      7. *-commutative 55.4%

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

      8. associate-/r* 55.4%

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

      9. metadata-eval 55.4%

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

   4. Applied egg-rr 55.4%

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

   5. Taylor expanded in x around 0 55.4%

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

      1. *-commutative 55.4%

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

      2. associate-/l* 86.6%

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

      3. associate-*r* 86.6%

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

      4. metadata-eval 86.6%

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

      5. times-frac 86.6%

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

      6. times-frac 86.6%

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

      7. metadata-eval 86.6%

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

      8. associate-*l/ 86.6%

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

      9. associate-/l* 86.7%

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

   7. Simplified 86.7%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2e208

   1. Initial program 93.5%

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

   if 2e208 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. associate-*r* 71.6%

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

      3. associate-*l/ 99.7%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*l* 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-145}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-165} \lor \neg \left(y \leq 1.12 \cdot 10^{+77}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

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 0.5) a))))
   (if (<= y -2.05e-61)
     t_1
     (if (<= y -5.6e-145)
       (* t (* z (/ -4.5 a)))
       (if (or (<= y -4.2e-165) (not (<= y 1.12e+77)))
         t_1
         (* -4.5 (/ (* z t) a)))))))

C

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 * 0.5) / a);
	double tmp;
	if (y <= -2.05e-61) {
		tmp = t_1;
	} else if (y <= -5.6e-145) {
		tmp = t * (z * (-4.5 / a));
	} else if ((y <= -4.2e-165) || !(y <= 1.12e+77)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

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 * 0.5d0) / a)
    if (y <= (-2.05d-61)) then
        tmp = t_1
    else if (y <= (-5.6d-145)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if ((y <= (-4.2d-165)) .or. (.not. (y <= 1.12d+77))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

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 * 0.5) / a);
	double tmp;
	if (y <= -2.05e-61) {
		tmp = t_1;
	} else if (y <= -5.6e-145) {
		tmp = t * (z * (-4.5 / a));
	} else if ((y <= -4.2e-165) || !(y <= 1.12e+77)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if y <= -2.05e-61:
		tmp = t_1
	elif y <= -5.6e-145:
		tmp = t * (z * (-4.5 / a))
	elif (y <= -4.2e-165) or not (y <= 1.12e+77):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (y <= -2.05e-61)
		tmp = t_1;
	elseif (y <= -5.6e-145)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif ((y <= -4.2e-165) || !(y <= 1.12e+77))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

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 * 0.5) / a);
	tmp = 0.0;
	if (y <= -2.05e-61)
		tmp = t_1;
	elseif (y <= -5.6e-145)
		tmp = t * (z * (-4.5 / a));
	elseif ((y <= -4.2e-165) || ~((y <= 1.12e+77)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e-61], t$95$1, If[LessEqual[y, -5.6e-145], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.2e-165], N[Not[LessEqual[y, 1.12e+77]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.04999999999999999e-61 or -5.6000000000000002e-145 < y < -4.1999999999999999e-165 or 1.1199999999999999e77 < y

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 67.5%

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

      3. associate-*r* 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*r/ 67.5%

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

   5. Simplified 67.5%

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

   if -2.04999999999999999e-61 < y < -5.6000000000000002e-145

   1. Initial program 99.8%

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

      1. div-inv 99.4%

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

      2. fma-neg 99.4%

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

      3. *-commutative 99.4%

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

      4. distribute-rgt-neg-in 99.4%

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

      5. distribute-rgt-neg-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around 0 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/l* 57.9%

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

      3. associate-*r* 57.7%

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

      4. metadata-eval 57.7%

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

      5. times-frac 57.8%

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

      6. times-frac 57.7%

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

      7. metadata-eval 57.7%

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

      8. associate-*l/ 57.8%

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

      9. associate-/l* 58.0%

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

   7. Simplified 58.0%

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

   if -4.1999999999999999e-165 < y < 1.1199999999999999e77

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 65.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-145}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-165} \lor \neg \left(y \leq 1.12 \cdot 10^{+77}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+301} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+181}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + t \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

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) -2e+301) (not (<= (* x y) 4e+181)))
   (* x (/ (* y 0.5) a))
   (* (/ 0.5 a) (+ (* x y) (* t (* z -9.0))))))

C

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) <= -2e+301) || !((x * y) <= 4e+181)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = (0.5 / a) * ((x * y) + (t * (z * -9.0)));
	}
	return tmp;
}

Fortran

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) <= (-2d+301)) .or. (.not. ((x * y) <= 4d+181))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (0.5d0 / a) * ((x * y) + (t * (z * (-9.0d0))))
    end if
    code = tmp
end function

Java

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) <= -2e+301) || !((x * y) <= 4e+181)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = (0.5 / a) * ((x * y) + (t * (z * -9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+301) or not ((x * y) <= 4e+181):
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = (0.5 / a) * ((x * y) + (t * (z * -9.0)))
	return tmp

Julia

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) <= -2e+301) || !(Float64(x * y) <= 4e+181))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(t * Float64(z * -9.0))));
	end
	return tmp
end

MATLAB

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) <= -2e+301) || ~(((x * y) <= 4e+181)))
		tmp = x * ((y * 0.5) / a);
	else
		tmp = (0.5 / a) * ((x * y) + (t * (z * -9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

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], -2e+301], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+181]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000011e301 or 3.9999999999999997e181 < (*.f64 x y)

   1. Initial program 69.8%

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

   3. Taylor expanded in x around inf 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-/l* 97.3%

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

      3. associate-*r* 97.3%

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

      4. *-commutative 97.3%

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

      5. associate-*r/ 97.3%

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

   5. Simplified 97.3%

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

   if -2.00000000000000011e301 < (*.f64 x y) < 3.9999999999999997e181

   1. Initial program 93.0%

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

      1. div-inv 92.8%

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

      2. fma-neg 92.8%

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

      3. *-commutative 92.8%

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

      4. distribute-rgt-neg-in 92.8%

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

      5. distribute-rgt-neg-in 92.8%

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

      6. metadata-eval 92.8%

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

      7. *-commutative 92.8%

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

      8. associate-/r* 92.8%

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

      9. metadata-eval 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. fma-undefine 92.8%

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

   6. Applied egg-rr 92.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+301} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+181}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + t \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 10^{+79}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}} + \left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

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 (<= (* 2.0 a) 1e+79)
   (/ (- (* x y) (* (* z 9.0) t)) (* 2.0 a))
   (+ (* z (/ -4.5 (/ a t))) (* (* x y) (/ 0.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((2.0 * a) <= 1e+79) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a);
	} else {
		tmp = (z * (-4.5 / (a / t))) + ((x * y) * (0.5 / a));
	}
	return tmp;
}

Fortran

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 ((2.0d0 * a) <= 1d+79) then
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (2.0d0 * a)
    else
        tmp = (z * ((-4.5d0) / (a / t))) + ((x * y) * (0.5d0 / a))
    end if
    code = tmp
end function

Java

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 ((2.0 * a) <= 1e+79) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a);
	} else {
		tmp = (z * (-4.5 / (a / t))) + ((x * y) * (0.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (2.0 * a) <= 1e+79:
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a)
	else:
		tmp = (z * (-4.5 / (a / t))) + ((x * y) * (0.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(2.0 * a) <= 1e+79)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(z * Float64(-4.5 / Float64(a / t))) + Float64(Float64(x * y) * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

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 ((2.0 * a) <= 1e+79)
		tmp = ((x * y) - ((z * 9.0) * t)) / (2.0 * a);
	else
		tmp = (z * (-4.5 / (a / t))) + ((x * y) * (0.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

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[(2.0 * a), $MachinePrecision], 1e+79], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 9.99999999999999967e78

   1. Initial program 92.9%

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

   if 9.99999999999999967e78 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 70.8%

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

      1. div-inv 70.8%

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

      2. fma-neg 70.8%

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

      3. *-commutative 70.8%

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

      4. distribute-rgt-neg-in 70.8%

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

      5. distribute-rgt-neg-in 70.8%

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

      6. metadata-eval 70.8%

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

      7. *-commutative 70.8%

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

      8. associate-/r* 70.8%

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

      9. metadata-eval 70.8%

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

   4. Applied egg-rr 70.8%

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

      1. fma-undefine 70.8%

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

   6. Applied egg-rr 70.8%

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

      1. *-commutative 70.8%

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

      2. distribute-lft-in 70.8%

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

      3. associate-*l/ 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-*r* 70.9%

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

      6. associate-*l* 70.9%

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

      7. metadata-eval 70.9%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \frac{\left(t \cdot z\right) \cdot \color{blue}{-4.5}}{a} \]

      8. *-commutative 70.9%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \frac{\color{blue}{\left(z \cdot t\right)} \cdot -4.5}{a} \]

      9. associate-*r/ 70.9%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \color{blue}{\left(z \cdot t\right) \cdot \frac{-4.5}{a}} \]

      10. associate-*r* 81.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + \color{blue}{z \cdot \left(t \cdot \frac{-4.5}{a}\right)} \]

      11. associate-*r/ 81.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\frac{t \cdot -4.5}{a}} \]

      12. associate-*l/ 81.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\left(\frac{t}{a} \cdot -4.5\right)} \]

      13. clear-num 81.3%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \left(\color{blue}{\frac{1}{\frac{a}{t}}} \cdot -4.5\right) \]

      14. associate-*l/ 81.4%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \color{blue}{\frac{1 \cdot -4.5}{\frac{a}{t}}} \]

      15. metadata-eval 81.4%

          \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \frac{\color{blue}{-4.5}}{\frac{a}{t}} \]

   8. Applied egg-rr 81.4%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right) + z \cdot \frac{-4.5}{\frac{a}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 10^{+79}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}} + \left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-70} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+110}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

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) -1e-70) (not (<= (* x y) 4e+110)))
   (* y (* 0.5 (/ x a)))
   (* z (* t (/ -4.5 a)))))

C

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-70) || !((x * y) <= 4e+110)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Fortran

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-70)) .or. (.not. ((x * y) <= 4d+110))) then
        tmp = y * (0.5d0 * (x / a))
    else
        tmp = z * (t * ((-4.5d0) / a))
    end if
    code = tmp
end function

Java

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-70) || !((x * y) <= 4e+110)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -1e-70) or not ((x * y) <= 4e+110):
		tmp = y * (0.5 * (x / a))
	else:
		tmp = z * (t * (-4.5 / a))
	return tmp

Julia

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-70) || !(Float64(x * y) <= 4e+110))
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

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-70) || ~(((x * y) <= 4e+110)))
		tmp = y * (0.5 * (x / a));
	else
		tmp = z * (t * (-4.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

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], -1e-70], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+110]], $MachinePrecision]], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.99999999999999996e-71 or 4.0000000000000001e110 < (*.f64 x y)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 76.3%

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

   if -9.99999999999999996e-71 < (*.f64 x y) < 4.0000000000000001e110

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 72.8%

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

      1. associate-*r/ 72.9%

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

      2. associate-*r* 72.9%

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

      3. associate-*l/ 74.2%

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

      4. associate-*r/ 74.2%

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

      5. *-commutative 74.2%

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

      6. associate-*r/ 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around 0 74.2%

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

      1. associate-*r/ 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r/ 74.2%

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

   8. Simplified 74.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-70} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+110}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.0%

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

3. Taylor expanded in x around 0 47.7%

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

   1. associate-/l* 48.5%

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

5. Simplified 48.5%

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

6. Final simplification 48.5%

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

Alternative 10: 50.7% accurate, 1.9× speedup

Math

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

FPCore

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 (* t (* z (/ -4.5 a))))

C

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

Fortran

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 = t * (z * ((-4.5d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. div-inv 88.8%

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

   2. fma-neg 88.8%

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

   3. *-commutative 88.8%

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

   4. distribute-rgt-neg-in 88.8%

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

   5. distribute-rgt-neg-in 88.8%

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

   6. metadata-eval 88.8%

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

   7. *-commutative 88.8%

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

   8. associate-/r* 88.8%

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

   9. metadata-eval 88.8%

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

4. Applied egg-rr 88.8%

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

5. Taylor expanded in x around 0 47.7%

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

   1. *-commutative 47.7%

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

   2. associate-/l* 48.5%

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

   3. associate-*r* 48.5%

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

   4. metadata-eval 48.5%

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

   5. times-frac 48.5%

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

   6. times-frac 48.5%

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

   7. metadata-eval 48.5%

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

   8. associate-*l/ 48.5%

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

   9. associate-/l* 48.5%

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

7. Simplified 48.5%

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

8. Final simplification 48.5%

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

Developer target: 93.4% 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 2024082 
(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)))