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

Percentage Accurate: 91.6% → 95.4%

Time: 10.8s

Alternatives: 10

Speedup: 0.8×

• 27.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.6% 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: 95.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, \frac{z \cdot 4.5}{a}, x \cdot \frac{y}{a \cdot 2}\right)\\ t_2 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+95}:\\ \;\;\;\;\frac{t\_2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (fma (- t) (/ (* z 4.5) a) (* x (/ y (* a 2.0)))))
        (t_2 (- (* x y) (* t (* z 9.0)))))
   (if (<= t_2 -5e+170) t_1 (if (<= t_2 1e+95) (/ t_2 (* a 2.0)) t_1))))

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 = fma(-t, ((z * 4.5) / a), (x * (y / (a * 2.0))));
	double t_2 = (x * y) - (t * (z * 9.0));
	double tmp;
	if (t_2 <= -5e+170) {
		tmp = t_1;
	} else if (t_2 <= 1e+95) {
		tmp = t_2 / (a * 2.0);
	} else {
		tmp = t_1;
	}
	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 = fma(Float64(-t), Float64(Float64(z * 4.5) / a), Float64(x * Float64(y / Float64(a * 2.0))))
	t_2 = Float64(Float64(x * y) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if (t_2 <= -5e+170)
		tmp = t_1;
	elseif (t_2 <= 1e+95)
		tmp = Float64(t_2 / Float64(a * 2.0));
	else
		tmp = t_1;
	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[((-t) * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision] + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+170], t$95$1, If[LessEqual[t$95$2, 1e+95], N[(t$95$2 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -4.99999999999999977e170 or 1.00000000000000002e95 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 85.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. lower-fma.f64 N/A

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

   4. Applied egg-rr 96.2%

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

   if -4.99999999999999977e170 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000002e95

   1. Initial program 97.9%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -5 \cdot 10^{+170}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z \cdot 4.5}{a}, x \cdot \frac{y}{a \cdot 2}\right)\\ \mathbf{elif}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq 10^{+95}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z \cdot 4.5}{a}, x \cdot \frac{y}{a \cdot 2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ t_2 := t \cdot \frac{z \cdot -4.5}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, -4.5 \cdot \frac{z \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (* z 9.0))) (t_2 (* t (/ (* z -4.5) a))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 2e+282) (fma (/ y (* a 2.0)) x (* -4.5 (/ (* z t) a))) t_2))))

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 = t * (z * 9.0);
	double t_2 = t * ((z * -4.5) / a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 2e+282) {
		tmp = fma((y / (a * 2.0)), x, (-4.5 * ((z * t) / a)));
	} else {
		tmp = t_2;
	}
	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(t * Float64(z * 9.0))
	t_2 = Float64(t * Float64(Float64(z * -4.5) / a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 2e+282)
		tmp = fma(Float64(y / Float64(a * 2.0)), x, Float64(-4.5 * Float64(Float64(z * t) / a)));
	else
		tmp = t_2;
	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[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 2e+282], N[(N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * x + N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0 or 2.00000000000000007e282 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 60.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 96.3

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

   5. Simplified 96.3%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-lft-identity N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. metadata-eval N/A

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

      17. lower-*.f64 93.1

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

   7. Applied egg-rr 93.1%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2.00000000000000007e282

   1. Initial program 95.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. lower-fma.f64 N/A

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

   4. Applied egg-rr 91.0%

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

   6. Applied egg-rr 93.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -\infty:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, -4.5 \cdot \frac{z \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{+24}:\\ \;\;\;\;\frac{0.5}{\frac{a}{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, -z \cdot 4.5, x \cdot \frac{y}{a \cdot 2}\right)\\ \end{array} \end{array} \]

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 (<= (* a 2.0) 2e+24)
   (/ 0.5 (/ a (fma z (* t -9.0) (* x y))))
   (fma (/ t a) (- (* z 4.5)) (* x (/ y (* a 2.0))))))

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 ((a * 2.0) <= 2e+24) {
		tmp = 0.5 / (a / fma(z, (t * -9.0), (x * y)));
	} else {
		tmp = fma((t / a), -(z * 4.5), (x * (y / (a * 2.0))));
	}
	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(a * 2.0) <= 2e+24)
		tmp = Float64(0.5 / Float64(a / fma(z, Float64(t * -9.0), Float64(x * y))));
	else
		tmp = fma(Float64(t / a), Float64(-Float64(z * 4.5)), Float64(x * Float64(y / Float64(a * 2.0))));
	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_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 2e+24], N[(0.5 / N[(a / N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-N[(z * 4.5), $MachinePrecision]) + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 2e24

   1. Initial program 91.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/r* N/A

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

      6. clear-num N/A

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

      7. associate-/l/ N/A

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

      8. associate-/r* N/A

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

      9. lower-/.f64 N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 91.1

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-*l* N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied egg-rr 91.6%

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

   if 2e24 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 90.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. times-frac N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

   4. Applied egg-rr 97.8%

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

Alternative 4: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, 0.5 \cdot y, -4.5 \cdot \frac{z \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -2e+192)
   (fma (/ x a) (* 0.5 y) (* -4.5 (/ (* z t) a)))
   (* (fma z (* t -9.0) (* x y)) (/ 0.5 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) <= -2e+192) {
		tmp = fma((x / a), (0.5 * y), (-4.5 * ((z * t) / a)));
	} else {
		tmp = fma(z, (t * -9.0), (x * y)) * (0.5 / 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) <= -2e+192)
		tmp = fma(Float64(x / a), Float64(0.5 * y), Float64(-4.5 * Float64(Float64(z * t) / a)));
	else
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) * Float64(0.5 / 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_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+192], N[(N[(x / a), $MachinePrecision] * N[(0.5 * y), $MachinePrecision] + N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000008e192

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. lower-fma.f64 N/A

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

   4. Applied egg-rr 99.9%

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

   6. Applied egg-rr 97.1%

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

   if -2.00000000000000008e192 < (*.f64 x y)

   1. Initial program 92.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. distribute-rgt-neg-in N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 93.2

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

   4. Applied egg-rr 93.2%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, 0.5 \cdot y, -4.5 \cdot \frac{z \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;\frac{x}{a} \cdot \left(0.5 \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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) -50000000000000.0)
   (* (/ x a) (* 0.5 y))
   (if (<= (* x y) 2e-23) (* z (* (/ t a) -4.5)) (/ (* 0.5 x) (/ a y)))))

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) <= -50000000000000.0) {
		tmp = (x / a) * (0.5 * y);
	} else if ((x * y) <= 2e-23) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = (0.5 * x) / (a / y);
	}
	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) <= (-50000000000000.0d0)) then
        tmp = (x / a) * (0.5d0 * y)
    else if ((x * y) <= 2d-23) then
        tmp = z * ((t / a) * (-4.5d0))
    else
        tmp = (0.5d0 * x) / (a / y)
    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) <= -50000000000000.0) {
		tmp = (x / a) * (0.5 * y);
	} else if ((x * y) <= 2e-23) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = (0.5 * x) / (a / y);
	}
	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) <= -50000000000000.0:
		tmp = (x / a) * (0.5 * y)
	elif (x * y) <= 2e-23:
		tmp = z * ((t / a) * -4.5)
	else:
		tmp = (0.5 * x) / (a / y)
	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) <= -50000000000000.0)
		tmp = Float64(Float64(x / a) * Float64(0.5 * y));
	elseif (Float64(x * y) <= 2e-23)
		tmp = Float64(z * Float64(Float64(t / a) * -4.5));
	else
		tmp = Float64(Float64(0.5 * x) / Float64(a / y));
	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) <= -50000000000000.0)
		tmp = (x / a) * (0.5 * y);
	elseif ((x * y) <= 2e-23)
		tmp = z * ((t / a) * -4.5);
	else
		tmp = (0.5 * x) / (a / y);
	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], -50000000000000.0], N[(N[(x / a), $MachinePrecision] * N[(0.5 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-23], N[(z * N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e13

   1. Initial program 88.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 81.2

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

   5. Simplified 81.2%

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

      1. lift-*.f64 N/A

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

      2. associate-*l/ N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 84.3

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 84.3

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

   7. Applied egg-rr 84.3%

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

   if -5e13 < (*.f64 x y) < 1.99999999999999992e-23

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.7

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

   5. Simplified 76.7%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-/l* N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. times-frac N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 N/A

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

      21. lower-/.f64 77.7

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

   7. Applied egg-rr 77.7%

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

   if 1.99999999999999992e-23 < (*.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 79.5

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

   5. Simplified 79.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. lift-/.f64 N/A

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

      7. lift-/.f64 74.2

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;\frac{x}{a} \cdot \left(0.5 \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;\frac{x}{a} \cdot \left(0.5 \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -50000000000000.0)
   (* (/ x a) (* 0.5 y))
   (if (<= (* x y) 2e-23) (* z (* (/ t a) -4.5)) (* x (* y (/ 0.5 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) <= -50000000000000.0) {
		tmp = (x / a) * (0.5 * y);
	} else if ((x * y) <= 2e-23) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = 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.
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) <= (-50000000000000.0d0)) then
        tmp = (x / a) * (0.5d0 * y)
    else if ((x * y) <= 2d-23) then
        tmp = z * ((t / a) * (-4.5d0))
    else
        tmp = x * (y * (0.5d0 / 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) <= -50000000000000.0) {
		tmp = (x / a) * (0.5 * y);
	} else if ((x * y) <= 2e-23) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = x * (y * (0.5 / 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) <= -50000000000000.0:
		tmp = (x / a) * (0.5 * y)
	elif (x * y) <= 2e-23:
		tmp = z * ((t / a) * -4.5)
	else:
		tmp = x * (y * (0.5 / 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) <= -50000000000000.0)
		tmp = Float64(Float64(x / a) * Float64(0.5 * y));
	elseif (Float64(x * y) <= 2e-23)
		tmp = Float64(z * Float64(Float64(t / a) * -4.5));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / 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) <= -50000000000000.0)
		tmp = (x / a) * (0.5 * y);
	elseif ((x * y) <= 2e-23)
		tmp = z * ((t / a) * -4.5);
	else
		tmp = 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.
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], -50000000000000.0], N[(N[(x / a), $MachinePrecision] * N[(0.5 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-23], N[(z * N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e13

   1. Initial program 88.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 81.2

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

   5. Simplified 81.2%

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

      1. lift-*.f64 N/A

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

      2. associate-*l/ N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 84.3

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 84.3

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

   7. Applied egg-rr 84.3%

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

   if -5e13 < (*.f64 x y) < 1.99999999999999992e-23

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.7

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

   5. Simplified 76.7%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-/l* N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. times-frac N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 N/A

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

      21. lower-/.f64 77.7

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

   7. Applied egg-rr 77.7%

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

   if 1.99999999999999992e-23 < (*.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 79.5

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

   5. Simplified 79.5%

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

      1. associate-*r* N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-/r/ N/A

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

      9. lift-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. div-inv N/A

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

      12. lift-/.f64 N/A

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

      13. clear-num N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

      16. associate-/l* N/A

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

      17. clear-num N/A

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

      18. un-div-inv N/A

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

      19. lower-/.f64 N/A

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

      20. div-inv N/A

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

      21. metadata-eval N/A

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

      22. lower-*.f64 75.2

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

   7. Applied egg-rr 75.2%

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

      1. associate-/l/ N/A

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

      2. div-inv N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 75.3

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

   9. Applied egg-rr 75.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;\frac{x}{a} \cdot \left(0.5 \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -50000000000000.0)
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) 2e-23) (* z (* (/ t a) -4.5)) (* x (* y (/ 0.5 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) <= -50000000000000.0) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= 2e-23) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = 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.
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) <= (-50000000000000.0d0)) then
        tmp = y * (x * (0.5d0 / a))
    else if ((x * y) <= 2d-23) then
        tmp = z * ((t / a) * (-4.5d0))
    else
        tmp = x * (y * (0.5d0 / 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) <= -50000000000000.0) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= 2e-23) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = x * (y * (0.5 / 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) <= -50000000000000.0:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= 2e-23:
		tmp = z * ((t / a) * -4.5)
	else:
		tmp = x * (y * (0.5 / 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) <= -50000000000000.0)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= 2e-23)
		tmp = Float64(z * Float64(Float64(t / a) * -4.5));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / 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) <= -50000000000000.0)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= 2e-23)
		tmp = z * ((t / a) * -4.5);
	else
		tmp = 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.
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], -50000000000000.0], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-23], N[(z * N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e13

   1. Initial program 88.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 81.2

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

   5. Simplified 81.2%

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

      1. associate-*r* N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 84.3

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

   7. Applied egg-rr 84.3%

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

   if -5e13 < (*.f64 x y) < 1.99999999999999992e-23

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.7

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

   5. Simplified 76.7%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-/l* N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. times-frac N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 N/A

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

      21. lower-/.f64 77.7

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

   7. Applied egg-rr 77.7%

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

   if 1.99999999999999992e-23 < (*.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 79.5

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

   5. Simplified 79.5%

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

      1. associate-*r* N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-/r/ N/A

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

      9. lift-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. div-inv N/A

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

      12. lift-/.f64 N/A

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

      13. clear-num N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

      16. associate-/l* N/A

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

      17. clear-num N/A

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

      18. un-div-inv N/A

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

      19. lower-/.f64 N/A

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

      20. div-inv N/A

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

      21. metadata-eval N/A

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

      22. lower-*.f64 75.2

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

   7. Applied egg-rr 75.2%

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

      1. associate-/l/ N/A

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

      2. div-inv N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 75.3

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

   9. Applied egg-rr 75.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* x (/ 0.5 a)))))
   (if (<= (* x y) -50000000000000.0)
     t_1
     (if (<= (* x y) 2e-17) (* z (* (/ t a) -4.5)) t_1))))

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 = y * (x * (0.5 / a));
	double tmp;
	if ((x * y) <= -50000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e-17) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = t_1;
	}
	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 = y * (x * (0.5d0 / a))
    if ((x * y) <= (-50000000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 2d-17) then
        tmp = z * ((t / a) * (-4.5d0))
    else
        tmp = t_1
    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 = y * (x * (0.5 / a));
	double tmp;
	if ((x * y) <= -50000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e-17) {
		tmp = z * ((t / a) * -4.5);
	} else {
		tmp = t_1;
	}
	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 = y * (x * (0.5 / a))
	tmp = 0
	if (x * y) <= -50000000000000.0:
		tmp = t_1
	elif (x * y) <= 2e-17:
		tmp = z * ((t / a) * -4.5)
	else:
		tmp = t_1
	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(y * Float64(x * Float64(0.5 / a)))
	tmp = 0.0
	if (Float64(x * y) <= -50000000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-17)
		tmp = Float64(z * Float64(Float64(t / a) * -4.5));
	else
		tmp = t_1;
	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 = y * (x * (0.5 / a));
	tmp = 0.0;
	if ((x * y) <= -50000000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 2e-17)
		tmp = z * ((t / a) * -4.5);
	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.
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[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -50000000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-17], N[(z * N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5e13 or 2.00000000000000014e-17 < (*.f64 x y)

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 80.7

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

   5. Simplified 80.7%

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

      1. associate-*r* N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 83.0

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

   7. Applied egg-rr 83.0%

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

   if -5e13 < (*.f64 x y) < 2.00000000000000014e-17

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 75.7

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

   5. Simplified 75.7%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-/l* N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. times-frac N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 N/A

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

      21. lower-/.f64 76.7

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

   7. Applied egg-rr 76.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -50000000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(\frac{t}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.6% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) (- INFINITY))
   (* x (* y (/ 0.5 a)))
   (* (fma z (* t -9.0) (* x y)) (/ 0.5 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)) {
		tmp = x * (y * (0.5 / a));
	} else {
		tmp = fma(z, (t * -9.0), (x * y)) * (0.5 / 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))
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	else
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) * Float64(0.5 / 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_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.8

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

   5. Simplified 71.8%

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

      1. associate-*r* N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-/r/ N/A

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

      9. lift-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. div-inv N/A

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

      12. lift-/.f64 N/A

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

      13. clear-num N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

      16. associate-/l* N/A

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

      17. clear-num N/A

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

      18. un-div-inv N/A

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

      19. lower-/.f64 N/A

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

      20. div-inv N/A

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

      21. metadata-eval N/A

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

      22. lower-*.f64 99.8

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

   7. Applied egg-rr 99.8%

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

      1. associate-/l/ N/A

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

      2. div-inv N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 99.8

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 92.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. distribute-rgt-neg-in N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 93.2

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

   4. Applied egg-rr 93.2%

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

4. Final simplification 93.7%

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

Alternative 10: 51.1% accurate, 1.6× speedup

Math

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

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 91.1%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 46.1

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

5. Simplified 46.1%

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

Developer Target 1: 93.4% accurate, 0.6× 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 2024207 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))