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

Percentage Accurate: 91.8% → 93.1%

Time: 11.1s

Alternatives: 11

Speedup: 0.6×

• 29.2% 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: 91.8% 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: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{t}{a\_m \cdot 2}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+195}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a\_m}, \frac{x}{2}, t\_1 \cdot \left(0 - z \cdot 9\right)\right) + \mathsf{fma}\left(0 - t\_1, z \cdot 9, t\_1 \cdot \left(z \cdot 9\right)\right)\\ \end{array} \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ t (* a_m 2.0))))
   (*
    a_s
    (if (<= (* a_m 2.0) 1e+195)
      (/ (+ (* x y) (* z (* t -9.0))) (* a_m 2.0))
      (+
       (fma (/ y a_m) (/ x 2.0) (* t_1 (- 0.0 (* z 9.0))))
       (fma (- 0.0 t_1) (* z 9.0) (* t_1 (* z 9.0))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 * 2.0);
	double tmp;
	if ((a_m * 2.0) <= 1e+195) {
		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 * 9.0)))) + fma((0.0 - t_1), (z * 9.0), (t_1 * (z * 9.0)));
	}
	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])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(t / Float64(a_m * 2.0))
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+195)
		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 - Float64(z * 9.0)))) + fma(Float64(0.0 - t_1), Float64(z * 9.0), Float64(t_1 * Float64(z * 9.0))));
	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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(t / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 1e+195], 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 - N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0 - t$95$1), $MachinePrecision] * N[(z * 9.0), $MachinePrecision] + N[(t$95$1 * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 9.99999999999999977e194

   1. Initial program 93.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 93.6%

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

   3. Simplified 93.6%

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

   if 9.99999999999999977e194 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 82.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 82.5%

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

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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. *-commutative N/A

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

      13. times-frac N/A

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

      14. associate-/l* N/A

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

      15. prod-diff N/A

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

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

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

   6. Applied egg-rr 95.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+195}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, \frac{x}{2}, \frac{t}{a \cdot 2} \cdot \left(0 - z \cdot 9\right)\right) + \mathsf{fma}\left(0 - \frac{t}{a \cdot 2}, z \cdot 9, \frac{t}{a \cdot 2} \cdot \left(z \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{t}{a\_m} \cdot \left(0 - 4.5\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+195}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a\_m}, \frac{x}{2}, z \cdot t\_1\right) + \mathsf{fma}\left(t\_1, z, z \cdot \left(\frac{t}{a\_m} \cdot 4.5\right)\right)\\ \end{array} \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (/ t a_m) (- 0.0 4.5))))
   (*
    a_s
    (if (<= (* a_m 2.0) 1e+195)
      (/ (+ (* x y) (* z (* t -9.0))) (* a_m 2.0))
      (+
       (fma (/ y a_m) (/ x 2.0) (* z t_1))
       (fma t_1 z (* z (* (/ t a_m) 4.5))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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) * (0.0 - 4.5);
	double tmp;
	if ((a_m * 2.0) <= 1e+195) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a_m * 2.0);
	} else {
		tmp = fma((y / a_m), (x / 2.0), (z * t_1)) + fma(t_1, z, (z * ((t / a_m) * 4.5)));
	}
	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])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(t / a_m) * Float64(0.0 - 4.5))
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+195)
		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(z * t_1)) + fma(t_1, z, Float64(z * Float64(Float64(t / a_m) * 4.5))));
	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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(t / a$95$m), $MachinePrecision] * N[(0.0 - 4.5), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 1e+195], 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[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * z + N[(z * N[(N[(t / a$95$m), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 9.99999999999999977e194

   1. Initial program 93.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 93.6%

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

   3. Simplified 93.6%

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

   if 9.99999999999999977e194 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 82.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 82.5%

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

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 95.2%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+195}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, \frac{x}{2}, z \cdot \left(\frac{t}{a} \cdot \left(0 - 4.5\right)\right)\right) + \mathsf{fma}\left(\frac{t}{a} \cdot \left(0 - 4.5\right), z, z \cdot \left(\frac{t}{a} \cdot 4.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.6× speedup

Math

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

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* t (* z 9.0))))
   (*
    a_s
    (if (<= t_1 (- INFINITY))
      (* -4.5 (* z (/ t a_m)))
      (/ (- (* x y) t_1) (* 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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.5 * (z * (t / a_m));
	} else {
		tmp = ((x * y) - t_1) / (a_m * 2.0);
	}
	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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -4.5 * (z * (t / a_m));
	} else {
		tmp = ((x * y) - t_1) / (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])
def code(a_s, x, y, z, t, a_m):
	t_1 = t * (z * 9.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -4.5 * (z * (t / a_m))
	else:
		tmp = ((x * y) - t_1) / (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])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(t * Float64(z * 9.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.5 * Float64(z * Float64(t / a_m)));
	else
		tmp = Float64(Float64(Float64(x * y) - t_1) / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = t * (z * 9.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -4.5 * (z * (t / a_m));
	else
		tmp = ((x * y) - t_1) / (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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 44.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 44.9%

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

   3. Simplified 44.9%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 44.9%

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

   7. Simplified 44.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   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 99.6%

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

   9. Applied egg-rr 99.6%

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

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

   1. Initial program 95.0%

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

4. Final simplification 95.3%

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

Alternative 4: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a\_m}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{x \cdot y}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\\ \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= z -3.4e+107)
    (* (* t -4.5) (/ z a_m))
    (if (<= z 2.5e-165) (/ (* x y) (* a_m 2.0)) (* -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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -3.4e+107) {
		tmp = (t * -4.5) * (z / a_m);
	} else if (z <= 2.5e-165) {
		tmp = (x * y) / (a_m * 2.0);
	} else {
		tmp = -4.5 * (z * (t / 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.
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 (z <= (-3.4d+107)) then
        tmp = (t * (-4.5d0)) * (z / a_m)
    else if (z <= 2.5d-165) then
        tmp = (x * y) / (a_m * 2.0d0)
    else
        tmp = (-4.5d0) * (z * (t / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -3.4e+107) {
		tmp = (t * -4.5) * (z / a_m);
	} else if (z <= 2.5e-165) {
		tmp = (x * y) / (a_m * 2.0);
	} else {
		tmp = -4.5 * (z * (t / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if z <= -3.4e+107:
		tmp = (t * -4.5) * (z / a_m)
	elif z <= 2.5e-165:
		tmp = (x * y) / (a_m * 2.0)
	else:
		tmp = -4.5 * (z * (t / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (z <= -3.4e+107)
		tmp = Float64(Float64(t * -4.5) * Float64(z / a_m));
	elseif (z <= 2.5e-165)
		tmp = Float64(Float64(x * y) / Float64(a_m * 2.0));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (z <= -3.4e+107)
		tmp = (t * -4.5) * (z / a_m);
	elseif (z <= 2.5e-165)
		tmp = (x * y) / (a_m * 2.0);
	else
		tmp = -4.5 * (z * (t / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[z, -3.4e+107], N[(N[(t * -4.5), $MachinePrecision] * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-165], N[(N[(x * y), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999997e107

   1. Initial program 79.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 63.7%

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

   7. Simplified 63.7%

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. /-lowering-/.f64 79.3%

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

   9. Applied egg-rr 79.3%

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

   if -3.3999999999999997e107 < z < 2.4999999999999999e-165

   1. Initial program 97.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 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 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 72.2%

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

   7. Simplified 72.2%

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

   if 2.4999999999999999e-165 < z

   1. Initial program 88.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 88.8%

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

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 56.1%

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

   7. Simplified 56.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   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 58.1%

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

   9. Applied egg-rr 58.1%

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

Alternative 5: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+107}:\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a\_m}\\ \mathbf{elif}\;z \leq 10^{-165}:\\ \;\;\;\;\frac{y}{a\_m} \cdot \left(x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\\ \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= z -1.65e+107)
    (* (* t -4.5) (/ z a_m))
    (if (<= z 1e-165) (* (/ y a_m) (* x 0.5)) (* -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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -1.65e+107) {
		tmp = (t * -4.5) * (z / a_m);
	} else if (z <= 1e-165) {
		tmp = (y / a_m) * (x * 0.5);
	} else {
		tmp = -4.5 * (z * (t / 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.
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 (z <= (-1.65d+107)) then
        tmp = (t * (-4.5d0)) * (z / a_m)
    else if (z <= 1d-165) then
        tmp = (y / a_m) * (x * 0.5d0)
    else
        tmp = (-4.5d0) * (z * (t / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -1.65e+107) {
		tmp = (t * -4.5) * (z / a_m);
	} else if (z <= 1e-165) {
		tmp = (y / a_m) * (x * 0.5);
	} else {
		tmp = -4.5 * (z * (t / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if z <= -1.65e+107:
		tmp = (t * -4.5) * (z / a_m)
	elif z <= 1e-165:
		tmp = (y / a_m) * (x * 0.5)
	else:
		tmp = -4.5 * (z * (t / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (z <= -1.65e+107)
		tmp = Float64(Float64(t * -4.5) * Float64(z / a_m));
	elseif (z <= 1e-165)
		tmp = Float64(Float64(y / a_m) * Float64(x * 0.5));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (z <= -1.65e+107)
		tmp = (t * -4.5) * (z / a_m);
	elseif (z <= 1e-165)
		tmp = (y / a_m) * (x * 0.5);
	else
		tmp = -4.5 * (z * (t / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[z, -1.65e+107], N[(N[(t * -4.5), $MachinePrecision] * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-165], N[(N[(y / a$95$m), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000016e107

   1. Initial program 79.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 63.7%

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

   7. Simplified 63.7%

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. /-lowering-/.f64 79.3%

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

   9. Applied egg-rr 79.3%

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

   if -1.65000000000000016e107 < z < 1e-165

   1. Initial program 97.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 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 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 85.8%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 69.5%

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

   10. Simplified 69.5%

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

   if 1e-165 < z

   1. Initial program 88.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 88.8%

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

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 56.1%

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

   7. Simplified 56.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   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 58.1%

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

   9. Applied egg-rr 58.1%

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

Alternative 6: 63.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+107}:\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a\_m}\\ \mathbf{elif}\;z \leq 10^{-165}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\\ \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= z -2.75e+107)
    (* (* t -4.5) (/ z a_m))
    (if (<= z 1e-165) (* 0.5 (* y (/ x a_m))) (* -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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -2.75e+107) {
		tmp = (t * -4.5) * (z / a_m);
	} else if (z <= 1e-165) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = -4.5 * (z * (t / 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.
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 (z <= (-2.75d+107)) then
        tmp = (t * (-4.5d0)) * (z / a_m)
    else if (z <= 1d-165) then
        tmp = 0.5d0 * (y * (x / a_m))
    else
        tmp = (-4.5d0) * (z * (t / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -2.75e+107) {
		tmp = (t * -4.5) * (z / a_m);
	} else if (z <= 1e-165) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = -4.5 * (z * (t / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if z <= -2.75e+107:
		tmp = (t * -4.5) * (z / a_m)
	elif z <= 1e-165:
		tmp = 0.5 * (y * (x / a_m))
	else:
		tmp = -4.5 * (z * (t / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (z <= -2.75e+107)
		tmp = Float64(Float64(t * -4.5) * Float64(z / a_m));
	elseif (z <= 1e-165)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (z <= -2.75e+107)
		tmp = (t * -4.5) * (z / a_m);
	elseif (z <= 1e-165)
		tmp = 0.5 * (y * (x / a_m));
	else
		tmp = -4.5 * (z * (t / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[z, -2.75e+107], N[(N[(t * -4.5), $MachinePrecision] * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-165], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.7500000000000002e107

   1. Initial program 79.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 63.7%

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

   7. Simplified 63.7%

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. /-lowering-/.f64 79.3%

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

   9. Applied egg-rr 79.3%

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

   if -2.7500000000000002e107 < z < 1e-165

   1. Initial program 97.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 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 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 67.6%

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

   7. Simplified 67.6%

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

   if 1e-165 < z

   1. Initial program 88.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 88.8%

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

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 56.1%

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

   7. Simplified 56.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   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 58.1%

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

   9. Applied egg-rr 58.1%

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

Alternative 7: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a\_m}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-167}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\\ \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= z -6.5e+109)
    (* -4.5 (/ (* z t) a_m))
    (if (<= z 6.5e-167) (* 0.5 (* y (/ x a_m))) (* -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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -6.5e+109) {
		tmp = -4.5 * ((z * t) / a_m);
	} else if (z <= 6.5e-167) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = -4.5 * (z * (t / 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.
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 (z <= (-6.5d+109)) then
        tmp = (-4.5d0) * ((z * t) / a_m)
    else if (z <= 6.5d-167) then
        tmp = 0.5d0 * (y * (x / a_m))
    else
        tmp = (-4.5d0) * (z * (t / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (z <= -6.5e+109) {
		tmp = -4.5 * ((z * t) / a_m);
	} else if (z <= 6.5e-167) {
		tmp = 0.5 * (y * (x / a_m));
	} else {
		tmp = -4.5 * (z * (t / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if z <= -6.5e+109:
		tmp = -4.5 * ((z * t) / a_m)
	elif z <= 6.5e-167:
		tmp = 0.5 * (y * (x / a_m))
	else:
		tmp = -4.5 * (z * (t / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (z <= -6.5e+109)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a_m));
	elseif (z <= 6.5e-167)
		tmp = Float64(0.5 * Float64(y * Float64(x / a_m)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (z <= -6.5e+109)
		tmp = -4.5 * ((z * t) / a_m);
	elseif (z <= 6.5e-167)
		tmp = 0.5 * (y * (x / a_m));
	else
		tmp = -4.5 * (z * (t / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[z, -6.5e+109], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-167], N[(0.5 * N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e109

   1. Initial program 79.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 63.7%

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

   7. Simplified 63.7%

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

   if -6.5e109 < z < 6.49999999999999973e-167

   1. Initial program 97.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   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 67.4%

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

   7. Simplified 67.4%

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

   if 6.49999999999999973e-167 < z

   1. Initial program 89.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 89.0%

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

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 55.6%

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

   7. Simplified 55.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   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 57.5%

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

   9. Applied egg-rr 57.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-167}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a\_m \cdot 2} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (/ (+ (* 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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (((x * y) + (z * (t * -9.0))) / (a_m * 2.0));
}

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.
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 * (((x * y) + (z * (t * (-9.0d0)))) / (a_m * 2.0d0))
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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (((x * y) + (z * (t * -9.0))) / (a_m * 2.0));
}

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])
def code(a_s, x, y, z, t, a_m):
	return a_s * (((x * y) + (z * (t * -9.0))) / (a_m * 2.0))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
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(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a_m * 2.0)))
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])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (((x * y) + (z * (t * -9.0))) / (a_m * 2.0));
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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * 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. 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. Add Preprocessing

Alternative 9: 91.7% accurate, 1.0× speedup

Math

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

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (* (/ 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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * ((0.5 / a_m) * ((x * y) + (-9.0 * (z * t))));
}

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.
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 * ((0.5d0 / a_m) * ((x * y) + ((-9.0d0) * (z * t))))
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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * ((0.5 / a_m) * ((x * y) + (-9.0 * (z * t))));
}

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])
def code(a_s, x, y, z, t, a_m):
	return a_s * ((0.5 / a_m) * ((x * y) + (-9.0 * (z * t))))

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
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(Float64(0.5 / a_m) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t)))))
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])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * ((0.5 / a_m) * ((x * y) + (-9.0 * (z * t))));
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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * 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. 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. 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 92.6%

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

Alternative 10: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{+45}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\\ \end{array} \end{array} \]

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.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= t 8.2e+45) (* -4.5 (/ (* z t) a_m)) (* -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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= 8.2e+45) {
		tmp = -4.5 * ((z * t) / a_m);
	} else {
		tmp = -4.5 * (z * (t / 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.
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 <= 8.2d+45) then
        tmp = (-4.5d0) * ((z * t) / a_m)
    else
        tmp = (-4.5d0) * (z * (t / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= 8.2e+45) {
		tmp = -4.5 * ((z * t) / a_m);
	} else {
		tmp = -4.5 * (z * (t / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= 8.2e+45:
		tmp = -4.5 * ((z * t) / a_m)
	else:
		tmp = -4.5 * (z * (t / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= 8.2e+45)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a_m));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= 8.2e+45)
		tmp = -4.5 * ((z * t) / a_m);
	else
		tmp = -4.5 * (z * (t / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, 8.2e+45], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 8.20000000000000025e45

   1. Initial program 94.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 94.8%

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

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 42.5%

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

   7. Simplified 42.5%

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

   if 8.20000000000000025e45 < t

   1. Initial program 86.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in x around 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 62.3%

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

   7. Simplified 62.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   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 68.6%

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

   9. Applied egg-rr 68.6%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{+45}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(-4.5 \cdot \left(z \cdot \frac{t}{a\_m}\right)\right) \end{array} \]

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.
(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);
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.
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;
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])
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])
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])){:}
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.
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 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 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 47.4%

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

7. Simplified 47.4%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
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 48.1%

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

9. Applied egg-rr 48.1%

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

Developer Target 1: 94.2% 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 2024161 
(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)))