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

Percentage Accurate: 91.1% → 93.6%

Time: 11.7s

Alternatives: 13

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{t}{a\_m} \cdot 4.5\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 2 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a\_m}, \frac{x}{2}, t\_1 \cdot \left(0 - z\right)\right) + \mathsf{fma}\left(\frac{t}{a\_m} \cdot \left(0 - 4.5\right), z, z \cdot t\_1\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (/ t a_m) 4.5)))
   (*
    a_s
    (if (<= (* a_m 2.0) 2e+50)
      (/ (+ (* x y) (* z (* t -9.0))) (* a_m 2.0))
      (+
       (fma (/ y a_m) (/ x 2.0) (* t_1 (- 0.0 z)))
       (fma (* (/ t a_m) (- 0.0 4.5)) z (* z t_1)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (t / a_m) * 4.5;
	double tmp;
	if ((a_m * 2.0) <= 2e+50) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	} else {
		tmp = fma((y / a_m), (x / 2.0), (t_1 * (0.0 - z))) + fma(((t / a_m) * (0.0 - 4.5)), z, (z * t_1));
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(t / a_m) * 4.5)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 2e+50)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(fma(Float64(y / a_m), Float64(x / 2.0), Float64(t_1 * Float64(0.0 - z))) + fma(Float64(Float64(t / a_m) * Float64(0.0 - 4.5)), z, Float64(z * t_1)));
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(t / a$95$m), $MachinePrecision] * 4.5), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 2e+50], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision] + N[(t$95$1 * N[(0.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / a$95$m), $MachinePrecision] * N[(0.0 - 4.5), $MachinePrecision]), $MachinePrecision] * z + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 2.0000000000000002e50

   1. Initial program 93.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 93.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 93.9%

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

   if 2.0000000000000002e50 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 95.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 95.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 95.8%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. times-frac N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. frac-2neg N/A

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

      14. associate-*l* N/A

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

      15. associate-/l* N/A

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

      16. prod-diff N/A

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

   6. Applied egg-rr 94.2%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, \frac{x}{2}, \left(\frac{t}{a} \cdot 4.5\right) \cdot \left(0 - z\right)\right) + \mathsf{fma}\left(\frac{t}{a} \cdot \left(0 - 4.5\right), z, z \cdot \left(\frac{t}{a} \cdot 4.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+261}:\\ \;\;\;\;\frac{y}{a\_m} \cdot \left(-4.5 \cdot \left(t \cdot \frac{z}{y}\right) + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a\_m \cdot 2}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -4e+261)
    (* (/ y a_m) (+ (* -4.5 (* t (/ z y))) (* x 0.5)))
    (/ (+ (* x y) (* z (* t -9.0))) (* a_m 2.0)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -4e+261) {
		tmp = (y / a_m) * ((-4.5 * (t * (z / y))) + (x * 0.5));
	} else {
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-4d+261)) then
        tmp = (y / a_m) * (((-4.5d0) * (t * (z / y))) + (x * 0.5d0))
    else
        tmp = ((x * y) + (z * (t * (-9.0d0)))) / (a_m * 2.0d0)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -4e+261) {
		tmp = (y / a_m) * ((-4.5 * (t * (z / y))) + (x * 0.5));
	} else {
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -4e+261:
		tmp = (y / a_m) * ((-4.5 * (t * (z / y))) + (x * 0.5))
	else:
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -4e+261)
		tmp = Float64(Float64(y / a_m) * Float64(Float64(-4.5 * Float64(t * Float64(z / y))) + Float64(x * 0.5)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a_m * 2.0));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -4e+261)
		tmp = (y / a_m) * ((-4.5 * (t * (z / y))) + (x * 0.5));
	else
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -4e+261], N[(N[(y / a$95$m), $MachinePrecision] * N[(N[(-4.5 * N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.9999999999999997e261

   1. Initial program 74.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 74.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. fma-define N/A

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

      9. associate-*l/ N/A

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

      10. times-frac N/A

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

      11. *-inverses N/A

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

      12. *-inverses N/A

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

      13. times-frac N/A

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

      14. associate-*l/ N/A

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

      15. fma-define N/A

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

      16. associate-*l* N/A

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

   7. Simplified 99.9%

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

   if -3.9999999999999997e261 < (*.f64 x y)

   1. Initial program 96.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 96.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 96.2%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+261}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-4.5 \cdot \left(t \cdot \frac{z}{y}\right) + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a\_m}{y}}{x}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -1e+106)
    (* 0.5 (* y (/ x a_m)))
    (if (<= (* x y) 2e-22) (* (* z t) (/ -4.5 a_m)) (/ 0.5 (/ (/ a_m y) x))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -1e+106) {
		tmp = 0.5 * (y * (x / a_m));
	} else if ((x * y) <= 2e-22) {
		tmp = (z * t) * (-4.5 / a_m);
	} else {
		tmp = 0.5 / ((a_m / y) / x);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-1d+106)) then
        tmp = 0.5d0 * (y * (x / a_m))
    else if ((x * y) <= 2d-22) then
        tmp = (z * t) * ((-4.5d0) / a_m)
    else
        tmp = 0.5d0 / ((a_m / y) / x)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -1e+106) {
		tmp = 0.5 * (y * (x / a_m));
	} else if ((x * y) <= 2e-22) {
		tmp = (z * t) * (-4.5 / a_m);
	} else {
		tmp = 0.5 / ((a_m / y) / x);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -1e+106:
		tmp = 0.5 * (y * (x / a_m))
	elif (x * y) <= 2e-22:
		tmp = (z * t) * (-4.5 / a_m)
	else:
		tmp = 0.5 / ((a_m / y) / x)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -1e+106)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	elseif (Float64(x * y) <= 2e-22)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a_m));
	else
		tmp = Float64(0.5 / Float64(Float64(a_m / y) / x));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -1e+106)
		tmp = 0.5 * (y * (x / a_m));
	elseif ((x * y) <= 2e-22)
		tmp = (z * t) * (-4.5 / a_m);
	else
		tmp = 0.5 / ((a_m / y) / x);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+106], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-22], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(N[(a$95$m / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000009e106

   1. Initial program 85.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 85.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 85.7%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 85.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 85.1%

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

   if -1.00000000000000009e106 < (*.f64 x y) < 2.0000000000000001e-22

   1. Initial program 97.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.1%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 74.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 73.4%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       8. /-lowering-/.f64 74.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   11. Applied egg-rr 74.9%

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

   if 2.0000000000000001e-22 < (*.f64 x y)

   1. Initial program 94.4%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 94.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   7. Simplified 72.3%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. clear-num N/A

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

      4. metadata-eval N/A

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

      5. associate-*l/ N/A

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

      6. metadata-eval N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{a}{x \cdot y}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   9. Applied egg-rr 72.3%

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

       1. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\frac{a}{y}}{\color{blue}{x}}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(\left(\frac{a}{y}\right), \color{blue}{x}\right)\right) \]

       3. /-lowering-/.f64 76.4%

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, y\right), x\right)\right) \]

   11. Applied egg-rr 76.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a\_m}{0.5}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -1e+106)
    (* 0.5 (* y (/ x a_m)))
    (if (<= (* x y) 2e-22) (* (* z t) (/ -4.5 a_m)) (* x (/ y (/ a_m 0.5)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -1e+106) {
		tmp = 0.5 * (y * (x / a_m));
	} else if ((x * y) <= 2e-22) {
		tmp = (z * t) * (-4.5 / a_m);
	} else {
		tmp = x * (y / (a_m / 0.5));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-1d+106)) then
        tmp = 0.5d0 * (y * (x / a_m))
    else if ((x * y) <= 2d-22) then
        tmp = (z * t) * ((-4.5d0) / a_m)
    else
        tmp = x * (y / (a_m / 0.5d0))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -1e+106) {
		tmp = 0.5 * (y * (x / a_m));
	} else if ((x * y) <= 2e-22) {
		tmp = (z * t) * (-4.5 / a_m);
	} else {
		tmp = x * (y / (a_m / 0.5));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -1e+106:
		tmp = 0.5 * (y * (x / a_m))
	elif (x * y) <= 2e-22:
		tmp = (z * t) * (-4.5 / a_m)
	else:
		tmp = x * (y / (a_m / 0.5))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -1e+106)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	elseif (Float64(x * y) <= 2e-22)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a_m));
	else
		tmp = Float64(x * Float64(y / Float64(a_m / 0.5)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -1e+106)
		tmp = 0.5 * (y * (x / a_m));
	elseif ((x * y) <= 2e-22)
		tmp = (z * t) * (-4.5 / a_m);
	else
		tmp = x * (y / (a_m / 0.5));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+106], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-22], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(a$95$m / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000009e106

   1. Initial program 85.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 85.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 85.7%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 85.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 85.1%

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

   if -1.00000000000000009e106 < (*.f64 x y) < 2.0000000000000001e-22

   1. Initial program 97.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.1%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 74.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 73.4%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       8. /-lowering-/.f64 74.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   11. Applied egg-rr 74.9%

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

   if 2.0000000000000001e-22 < (*.f64 x y)

   1. Initial program 94.4%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 94.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   7. Simplified 72.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot \frac{1}{\frac{1}{2}}\right)\right), x\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{\frac{1}{2}}\right)\right), x\right) \]

      7. /-lowering-/.f64 76.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \frac{1}{2}\right)\right), x\right) \]

   9. Applied egg-rr 76.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+305}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a\_m}{y}}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a\_m \cdot 2}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -2e+305)
    (/ 0.5 (/ (/ a_m y) x))
    (/ (+ (* x y) (* z (* t -9.0))) (* a_m 2.0)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -2e+305) {
		tmp = 0.5 / ((a_m / y) / x);
	} else {
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((x * y) <= (-2d+305)) then
        tmp = 0.5d0 / ((a_m / y) / x)
    else
        tmp = ((x * y) + (z * (t * (-9.0d0)))) / (a_m * 2.0d0)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -2e+305) {
		tmp = 0.5 / ((a_m / y) / x);
	} else {
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -2e+305:
		tmp = 0.5 / ((a_m / y) / x)
	else:
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0)
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -2e+305)
		tmp = Float64(0.5 / Float64(Float64(a_m / y) / x));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a_m * 2.0));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -2e+305)
		tmp = 0.5 / ((a_m / y) / x);
	else
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -2e+305], N[(0.5 / N[(N[(a$95$m / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e305

   1. Initial program 72.3%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 72.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 72.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   7. Simplified 72.3%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. clear-num N/A

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

      4. metadata-eval N/A

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

      5. associate-*l/ N/A

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

      6. metadata-eval N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{a}{x \cdot y}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   9. Applied egg-rr 72.4%

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

       1. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\frac{a}{y}}{\color{blue}{x}}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(\left(\frac{a}{y}\right), \color{blue}{x}\right)\right) \]

       3. /-lowering-/.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, y\right), x\right)\right) \]

   11. Applied egg-rr 99.9%

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

   if -1.9999999999999999e305 < (*.f64 x y)

   1. Initial program 95.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 95.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 95.8%

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

Alternative 6: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a\_m}{y}}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a\_m} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) (- INFINITY))
    (/ 0.5 (/ (/ a_m y) x))
    (* (/ 0.5 a_m) (+ (* x y) (* -9.0 (* z t)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 / ((a_m / y) / x);
	} else {
		tmp = (0.5 / a_m) * ((x * y) + (-9.0 * (z * t)));
	}
	return a_s * tmp;
}

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 / ((a_m / y) / x);
	} else {
		tmp = (0.5 / a_m) * ((x * y) + (-9.0 * (z * t)));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 / ((a_m / y) / x)
	else:
		tmp = (0.5 / a_m) * ((x * y) + (-9.0 * (z * t)))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 / Float64(Float64(a_m / y) / x));
	else
		tmp = Float64(Float64(0.5 / a_m) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t))));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 / ((a_m / y) / x);
	else
		tmp = (0.5 / a_m) * ((x * y) + (-9.0 * (z * t)));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 / N[(N[(a$95$m / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / a$95$m), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 70.6%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 70.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 70.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   7. Simplified 70.6%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. clear-num N/A

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

      4. metadata-eval N/A

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

      5. associate-*l/ N/A

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

      6. metadata-eval N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{a}{x \cdot y}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   9. Applied egg-rr 70.6%

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

       1. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\frac{a}{y}}{\color{blue}{x}}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(\left(\frac{a}{y}\right), \color{blue}{x}\right)\right) \]

       3. /-lowering-/.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, y\right), x\right)\right) \]

   11. Applied egg-rr 99.9%

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

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

   1. Initial program 95.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 95.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 95.8%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

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

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

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

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

      11. frac-2neg N/A

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

      12. div-sub N/A

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

      13. div-inv N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a \cdot 2}\right), \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), \left(x \cdot \color{blue}{y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(\color{blue}{x} \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \]

      20. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(z \cdot 9\right)\right) \cdot t}\right)\right) \]

   6. Applied egg-rr 95.8%

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

Alternative 7: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a\_m}{z}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= t -2.7e-150)
    (* (* z t) (/ -4.5 a_m))
    (if (<= t 9e-24) (* x (* y (/ 0.5 a_m))) (* t (/ -4.5 (/ a_m z)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if (t <= 9e-24) {
		tmp = x * (y * (0.5 / a_m));
	} else {
		tmp = t * (-4.5 / (a_m / z));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (t <= (-2.7d-150)) then
        tmp = (z * t) * ((-4.5d0) / a_m)
    else if (t <= 9d-24) then
        tmp = x * (y * (0.5d0 / a_m))
    else
        tmp = t * ((-4.5d0) / (a_m / z))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if (t <= 9e-24) {
		tmp = x * (y * (0.5 / a_m));
	} else {
		tmp = t * (-4.5 / (a_m / z));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= -2.7e-150:
		tmp = (z * t) * (-4.5 / a_m)
	elif t <= 9e-24:
		tmp = x * (y * (0.5 / a_m))
	else:
		tmp = t * (-4.5 / (a_m / z))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= -2.7e-150)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a_m));
	elseif (t <= 9e-24)
		tmp = Float64(x * Float64(y * Float64(0.5 / a_m)));
	else
		tmp = Float64(t * Float64(-4.5 / Float64(a_m / z)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= -2.7e-150)
		tmp = (z * t) * (-4.5 / a_m);
	elseif (t <= 9e-24)
		tmp = x * (y * (0.5 / a_m));
	else
		tmp = t * (-4.5 / (a_m / z));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, -2.7e-150], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-24], N[(x * N[(y * N[(0.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.5 / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e-150

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 61.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 62.8%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       8. /-lowering-/.f64 61.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   11. Applied egg-rr 61.0%

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

   if -2.7000000000000001e-150 < t < 8.9999999999999995e-24

   1. Initial program 93.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 93.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 73.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   7. Simplified 73.5%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a} \cdot y\right), \color{blue}{x}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), y\right), x\right) \]

      10. /-lowering-/.f64 75.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), y\right), x\right) \]

   9. Applied egg-rr 75.6%

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

   if 8.9999999999999995e-24 < t

   1. Initial program 89.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 89.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 89.9%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 73.3%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{t}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 75.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 75.8%

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

       1. *-commutative N/A

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

       2. associate-/r/ N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. associate-/l* N/A

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

       6. associate-*l/ N/A

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

       7. associate-*r/ N/A

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

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \frac{\frac{-9}{2}}{a}\right), \color{blue}{t}\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{z \cdot \frac{-9}{2}}{a}\right), t\right) \]

       10. clear-num N/A

           \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{a}{z \cdot \frac{-9}{2}}}\right), t\right) \]

       11. associate-/r* N/A

           \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{\frac{a}{z}}{\frac{-9}{2}}}\right), t\right) \]

       12. clear-num N/A

           \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-9}{2}}{\frac{a}{z}}\right), t\right) \]

       13. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-9}{2}, \left(\frac{a}{z}\right)\right), t\right) \]

       14. /-lowering-/.f64 75.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(a, z\right)\right), t\right) \]

   11. Applied egg-rr 75.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a\_m}\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= t -2.7e-150)
    (* (* z t) (/ -4.5 a_m))
    (if (<= t 3.9e-25) (* x (* y (/ 0.5 a_m))) (* t (* z (/ -4.5 a_m)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if (t <= 3.9e-25) {
		tmp = x * (y * (0.5 / a_m));
	} else {
		tmp = t * (z * (-4.5 / a_m));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (t <= (-2.7d-150)) then
        tmp = (z * t) * ((-4.5d0) / a_m)
    else if (t <= 3.9d-25) then
        tmp = x * (y * (0.5d0 / a_m))
    else
        tmp = t * (z * ((-4.5d0) / a_m))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if (t <= 3.9e-25) {
		tmp = x * (y * (0.5 / a_m));
	} else {
		tmp = t * (z * (-4.5 / a_m));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= -2.7e-150:
		tmp = (z * t) * (-4.5 / a_m)
	elif t <= 3.9e-25:
		tmp = x * (y * (0.5 / a_m))
	else:
		tmp = t * (z * (-4.5 / a_m))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= -2.7e-150)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a_m));
	elseif (t <= 3.9e-25)
		tmp = Float64(x * Float64(y * Float64(0.5 / a_m)));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / a_m)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= -2.7e-150)
		tmp = (z * t) * (-4.5 / a_m);
	elseif (t <= 3.9e-25)
		tmp = x * (y * (0.5 / a_m));
	else
		tmp = t * (z * (-4.5 / a_m));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, -2.7e-150], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-25], N[(x * N[(y * N[(0.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e-150

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 61.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 62.8%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       8. /-lowering-/.f64 61.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   11. Applied egg-rr 61.0%

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

   if -2.7000000000000001e-150 < t < 3.9e-25

   1. Initial program 93.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 93.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 73.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   7. Simplified 73.5%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a} \cdot y\right), \color{blue}{x}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), y\right), x\right) \]

      10. /-lowering-/.f64 75.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), y\right), x\right) \]

   9. Applied egg-rr 75.6%

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

   if 3.9e-25 < t

   1. Initial program 89.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 89.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 89.9%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 73.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 73.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 73.0%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-commutative N/A

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

       6. associate-*l* N/A

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

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(z \cdot \frac{\frac{-9}{2}}{a}\right)}\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right)\right) \]

       9. /-lowering-/.f64 75.9%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right)\right) \]

   11. Applied egg-rr 75.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a\_m}\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= t -2.7e-150)
    (* (* z t) (/ -4.5 a_m))
    (if (<= t 2.9e+81) (* 0.5 (* y (/ x a_m))) (* t (* z (/ -4.5 a_m)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if (t <= 2.9e+81) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = t * (z * (-4.5 / a_m));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (t <= (-2.7d-150)) then
        tmp = (z * t) * ((-4.5d0) / a_m)
    else if (t <= 2.9d+81) then
        tmp = 0.5d0 * (y * (x / a_m))
    else
        tmp = t * (z * ((-4.5d0) / a_m))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if (t <= 2.9e+81) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = t * (z * (-4.5 / a_m));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= -2.7e-150:
		tmp = (z * t) * (-4.5 / a_m)
	elif t <= 2.9e+81:
		tmp = 0.5 * (y * (x / a_m))
	else:
		tmp = t * (z * (-4.5 / a_m))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= -2.7e-150)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a_m));
	elseif (t <= 2.9e+81)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / a_m)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= -2.7e-150)
		tmp = (z * t) * (-4.5 / a_m);
	elseif (t <= 2.9e+81)
		tmp = 0.5 * (y * (x / a_m));
	else
		tmp = t * (z * (-4.5 / a_m));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, -2.7e-150], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+81], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e-150

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 61.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 62.8%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

       8. /-lowering-/.f64 61.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   11. Applied egg-rr 61.0%

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

   if -2.7000000000000001e-150 < t < 2.9e81

   1. Initial program 92.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 92.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 71.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 71.7%

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

   if 2.9e81 < t

   1. Initial program 90.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 90.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 90.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 83.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 79.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 79.1%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-commutative N/A

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

       6. associate-*l* N/A

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

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(z \cdot \frac{\frac{-9}{2}}{a}\right)}\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right)\right) \]

       9. /-lowering-/.f64 83.4%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right)\right) \]

   11. Applied egg-rr 83.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a\_m}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+81}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a\_m}\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= t -2.7e-150)
    (* -4.5 (/ (* z t) a_m))
    (if (<= t 3.4e+81) (* 0.5 (* y (/ x a_m))) (* t (* z (/ -4.5 a_m)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = -4.5 * ((z * t) / a_m);
	} else if (t <= 3.4e+81) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = t * (z * (-4.5 / a_m));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (t <= (-2.7d-150)) then
        tmp = (-4.5d0) * ((z * t) / a_m)
    else if (t <= 3.4d+81) then
        tmp = 0.5d0 * (y * (x / a_m))
    else
        tmp = t * (z * ((-4.5d0) / a_m))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = -4.5 * ((z * t) / a_m);
	} else if (t <= 3.4e+81) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = t * (z * (-4.5 / a_m));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= -2.7e-150:
		tmp = -4.5 * ((z * t) / a_m)
	elif t <= 3.4e+81:
		tmp = 0.5 * (y * (x / a_m))
	else:
		tmp = t * (z * (-4.5 / a_m))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= -2.7e-150)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a_m));
	elseif (t <= 3.4e+81)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / a_m)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= -2.7e-150)
		tmp = -4.5 * ((z * t) / a_m);
	elseif (t <= 3.4e+81)
		tmp = 0.5 * (y * (x / a_m));
	else
		tmp = t * (z * (-4.5 / a_m));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, -2.7e-150], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+81], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e-150

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 61.0%

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

   if -2.7000000000000001e-150 < t < 3.40000000000000003e81

   1. Initial program 92.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 92.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 71.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 71.7%

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

   if 3.40000000000000003e81 < t

   1. Initial program 90.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 90.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 90.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 83.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 79.1%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 79.1%

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

       1. associate-*r/ N/A

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

       2. associate-/l* N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. *-commutative N/A

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

       6. associate-*l* N/A

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

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(z \cdot \frac{\frac{-9}{2}}{a}\right)}\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right)\right) \]

       9. /-lowering-/.f64 83.4%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right)\right) \]

   11. Applied egg-rr 83.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+81}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a\_m}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a\_m}{z}}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= t -2.7e-150)
    (* -4.5 (/ (* z t) a_m))
    (if (<= t 2.9e+81) (* 0.5 (* y (/ x a_m))) (* -4.5 (/ t (/ a_m z)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = -4.5 * ((z * t) / a_m);
	} else if (t <= 2.9e+81) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (t <= (-2.7d-150)) then
        tmp = (-4.5d0) * ((z * t) / a_m)
    else if (t <= 2.9d+81) then
        tmp = 0.5d0 * (y * (x / a_m))
    else
        tmp = (-4.5d0) * (t / (a_m / z))
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= -2.7e-150) {
		tmp = -4.5 * ((z * t) / a_m);
	} else if (t <= 2.9e+81) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= -2.7e-150:
		tmp = -4.5 * ((z * t) / a_m)
	elif t <= 2.9e+81:
		tmp = 0.5 * (y * (x / a_m))
	else:
		tmp = -4.5 * (t / (a_m / z))
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= -2.7e-150)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a_m));
	elseif (t <= 2.9e+81)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a_m / z)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= -2.7e-150)
		tmp = -4.5 * ((z * t) / a_m);
	elseif (t <= 2.9e+81)
		tmp = 0.5 * (y * (x / a_m));
	else
		tmp = -4.5 * (t / (a_m / z));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, -2.7e-150], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+81], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e-150

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 61.0%

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

   if -2.7000000000000001e-150 < t < 2.9e81

   1. Initial program 92.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 92.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 71.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 71.7%

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

   if 2.9e81 < t

   1. Initial program 90.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 90.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 90.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 83.5%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{t}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 83.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(-4.5 \cdot \frac{t}{\frac{a\_m}{z}}\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* -4.5 (/ t (/ a_m z)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (-4.5 * (t / (a_m / z)));
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * ((-4.5d0) * (t / (a_m / z)))
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (-4.5 * (t / (a_m / z)));
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (-4.5 * (t / (a_m / z)))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(-4.5 * Float64(t / Float64(a_m / z))))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (-4.5 * (t / (a_m / z)));
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.3%

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

   5. associate-*l* N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

   12. *-lowering-*.f64 94.3%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

3. Simplified 94.3%

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

5. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

   3. *-lowering-*.f64 52.8%

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

7. Simplified 52.8%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{t}{\color{blue}{\frac{a}{z}}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

   5. /-lowering-/.f64 53.1%

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

9. Applied egg-rr 53.1%

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

Alternative 13: 52.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* -4.5 (* z (/ t a_m)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (-4.5 * (z * (t / a_m)));
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * ((-4.5d0) * (z * (t / a_m)))
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (-4.5 * (z * (t / a_m)));
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (-4.5 * (z * (t / a_m)))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(-4.5 * Float64(z * Float64(t / a_m))))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (-4.5 * (z * (t / a_m)));
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.3%

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

   5. associate-*l* N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

   12. *-lowering-*.f64 94.3%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

3. Simplified 94.3%

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

5. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

   3. *-lowering-*.f64 52.8%

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

7. Simplified 52.8%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z \cdot t}{a}\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(z \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

   4. /-lowering-/.f64 52.4%

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

9. Applied egg-rr 52.4%

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

Developer Target 1: 94.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024160 
(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)))