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

Percentage Accurate: 91.4% → 97.4%

Time: 11.6s

Alternatives: 14

Speedup: 0.8×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a \cdot 2}, x, z \cdot \frac{t \cdot 4.5}{-a}\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y (* a 2.0)) x (* z (/ (* t 4.5) (- a)))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -2e+300)
     t_1
     (if (<= t_2 2e+296) (* (fma y x (* z (* t -9.0))) (/ 0.5 a)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / (a * 2.0)), x, (z * ((t * 4.5) / -a)));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -2e+300) {
		tmp = t_1;
	} else if (t_2 <= 2e+296) {
		tmp = fma(y, x, (z * (t * -9.0))) * (0.5 / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = fma(Float64(y / Float64(a * 2.0)), x, Float64(z * Float64(Float64(t * 4.5) / Float64(-a))))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -2e+300)
		tmp = t_1;
	elseif (t_2 <= 2e+296)
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * x + N[(z * N[(N[(t * 4.5), $MachinePrecision] / (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+300], t$95$1, If[LessEqual[t$95$2, 2e+296], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -2.0000000000000001e300 or 1.99999999999999996e296 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 70.6%

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

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

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

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

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

      9. associate-*l* N/A

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

      10. associate-/l* N/A

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

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

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

      12. *-commutative N/A

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

      13. associate-/r* N/A

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

      14. /-lowering-/.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-/l* N/A

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

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

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

      18. metadata-eval 96.8

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

   4. Applied egg-rr 96.8%

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

   if -2.0000000000000001e300 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.99999999999999996e296

   1. Initial program 98.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 98.4

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

   4. Applied egg-rr 98.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

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

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

      5. *-lowering-*.f64 98.4

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, z \cdot \frac{t \cdot 4.5}{-a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, z \cdot \frac{t \cdot 4.5}{-a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, z \cdot \frac{t \cdot 4.5}{-a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 5e-25)
   (* (fma y x (* z (* t -9.0))) (/ 0.5 a))
   (fma (/ x (* a 2.0)) y (* z (/ (* t 4.5) (- a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 5e-25) {
		tmp = fma(y, x, (z * (t * -9.0))) * (0.5 / a);
	} else {
		tmp = fma((x / (a * 2.0)), y, (z * ((t * 4.5) / -a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 5e-25)
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	else
		tmp = fma(Float64(x / Float64(a * 2.0)), y, Float64(z * Float64(Float64(t * 4.5) / Float64(-a))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 5e-25], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * y + N[(z * N[(N[(t * 4.5), $MachinePrecision] / (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 4.99999999999999962e-25

   1. Initial program 92.9%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 93.5

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

   4. Applied egg-rr 93.5%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

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

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

      5. *-lowering-*.f64 93.5

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

   6. Applied egg-rr 93.5%

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

   if 4.99999999999999962e-25 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 86.4%

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

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

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-/l* N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. *-commutative N/A

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

      17. associate-/l* N/A

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

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

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

      19. metadata-eval 93.5

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

   4. Applied egg-rr 93.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, z \cdot \frac{t \cdot 4.5}{-a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 3 \cdot 10^{-33}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \left(y \cdot 0.5\right) \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 3e-33)
   (/ (fma y x (* z (* t -9.0))) (* a 2.0))
   (fma -4.5 (* t (/ z a)) (* (* y 0.5) (/ x a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 3e-33) {
		tmp = fma(y, x, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = fma(-4.5, (t * (z / a)), ((y * 0.5) * (x / a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 3e-33)
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(t * Float64(z / a)), Float64(Float64(y * 0.5) * Float64(x / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 3e-33], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 3.0000000000000002e-33

   1. Initial program 92.8%

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. associate-*l* N/A

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

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

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

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

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

      7. *-commutative N/A

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

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

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

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

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

      10. metadata-eval 93.4

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

   4. Applied egg-rr 93.4%

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

   if 3.0000000000000002e-33 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. associate-/l* N/A

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

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

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r/ N/A

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

      12. associate-*r* N/A

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

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

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. *-commutative N/A

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

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

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

      18. *-commutative N/A

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

      19. *-lowering-*.f64 91.0

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

   5. Simplified 91.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 95.4

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

   7. Applied egg-rr 95.4%

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

Alternative 4: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -5e-63)
     (* -4.5 (* t (/ z a)))
     (if (<= t_1 2e+77) (* (* x y) (/ 0.5 a)) (* t (* z (/ -4.5 a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e-63) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 2e+77) {
		tmp = (x * y) * (0.5 / a);
	} else {
		tmp = t * (z * (-4.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-5d-63)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if (t_1 <= 2d+77) then
        tmp = (x * y) * (0.5d0 / a)
    else
        tmp = t * (z * ((-4.5d0) / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e-63) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 2e+77) {
		tmp = (x * y) * (0.5 / a);
	} else {
		tmp = t * (z * (-4.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -5e-63:
		tmp = -4.5 * (t * (z / a))
	elif t_1 <= 2e+77:
		tmp = (x * y) * (0.5 / a)
	else:
		tmp = t * (z * (-4.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -5e-63)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t_1 <= 2e+77)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -5e-63)
		tmp = -4.5 * (t * (z / a));
	elseif (t_1 <= 2e+77)
		tmp = (x * y) * (0.5 / a);
	else
		tmp = t * (z * (-4.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-63], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+77], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -5.0000000000000002e-63

   1. Initial program 89.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 66.5

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

   5. Simplified 66.5%

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

   if -5.0000000000000002e-63 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999997e77

   1. Initial program 95.5%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 95.5

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

   4. Applied egg-rr 95.5%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 81.3

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

   7. Simplified 81.3%

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

   if 1.99999999999999997e77 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 78.4

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

   5. Simplified 78.4%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. times-frac N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. metadata-eval N/A

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

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

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

      15. /-lowering-/.f64 80.1

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

   7. Applied egg-rr 80.1%

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 78.5

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

   9. Applied egg-rr 78.5%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{-63}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-8)
   (* x (/ y (* a 2.0)))
   (if (<= (* x y) 1e-13) (/ (* z (* t -4.5)) a) (/ 0.5 (/ a (* x y))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = 0.5 / (a / (x * y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-8)) then
        tmp = x * (y / (a * 2.0d0))
    else if ((x * y) <= 1d-13) then
        tmp = (z * (t * (-4.5d0))) / a
    else
        tmp = 0.5d0 / (a / (x * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = 0.5 / (a / (x * y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-8:
		tmp = x * (y / (a * 2.0))
	elif (x * y) <= 1e-13:
		tmp = (z * (t * -4.5)) / a
	else:
		tmp = 0.5 / (a / (x * y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-8)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 1e-13)
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	else
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-8)
		tmp = x * (y / (a * 2.0));
	elseif ((x * y) <= 1e-13)
		tmp = (z * (t * -4.5)) / a;
	else
		tmp = 0.5 / (a / (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-8], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-13], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000001e-8

   1. Initial program 86.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 86.5

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 70.4

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

   7. Simplified 70.4%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

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

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 73.6

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

   9. Applied egg-rr 73.6%

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

   if -4.0000000000000001e-8 < (*.f64 x y) < 1e-13

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 81.4

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

   5. Simplified 81.4%

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

      1. associate-*r* N/A

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

      2. associate-*r/ N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 81.7

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

   7. Applied egg-rr 81.7%

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

   if 1e-13 < (*.f64 x y)

   1. Initial program 90.4%

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

      1. clear-num N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

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

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

      6. metadata-eval N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-lowering-*.f64 91.7

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 75.6

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

   7. Simplified 75.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 0.7× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (/ 0.5 (* (/ a y) (/ 1.0 x)))
   (* (fma y x (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 / ((a / y) * (1.0 / x));
	} else {
		tmp = fma(y, x, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 / Float64(Float64(a / y) * Float64(1.0 / x)));
	else
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 / N[(N[(a / y), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 67.4%

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

      1. clear-num N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

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

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

      6. metadata-eval N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-lowering-*.f64 67.7

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

   4. Applied egg-rr 67.7%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 67.7

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

   7. Simplified 67.7%

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

      1. associate-/l/ N/A

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

      2. div-inv N/A

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

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

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

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

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

      5. /-lowering-/.f64 98.1

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

   9. Applied egg-rr 98.1%

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

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

   1. Initial program 93.1%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 94.0

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

   4. Applied egg-rr 94.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

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

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

      5. *-lowering-*.f64 94.0

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

   6. Applied egg-rr 94.0%

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

Alternative 7: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-8)
   (* x (/ y (* a 2.0)))
   (if (<= (* x y) 1e-13) (/ (* z (* t -4.5)) a) (/ (* x y) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = (x * y) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-8)) then
        tmp = x * (y / (a * 2.0d0))
    else if ((x * y) <= 1d-13) then
        tmp = (z * (t * (-4.5d0))) / a
    else
        tmp = (x * y) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = (x * y) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-8:
		tmp = x * (y / (a * 2.0))
	elif (x * y) <= 1e-13:
		tmp = (z * (t * -4.5)) / a
	else:
		tmp = (x * y) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-8)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 1e-13)
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	else
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-8)
		tmp = x * (y / (a * 2.0));
	elseif ((x * y) <= 1e-13)
		tmp = (z * (t * -4.5)) / a;
	else
		tmp = (x * y) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-8], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-13], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000001e-8

   1. Initial program 86.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 86.5

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 70.4

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

   7. Simplified 70.4%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

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

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 73.6

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

   9. Applied egg-rr 73.6%

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

   if -4.0000000000000001e-8 < (*.f64 x y) < 1e-13

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 81.4

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

   5. Simplified 81.4%

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

      1. associate-*r* N/A

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

      2. associate-*r/ N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 81.7

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

   7. Applied egg-rr 81.7%

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

   if 1e-13 < (*.f64 x y)

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 75.6

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

   5. Simplified 75.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-8)
   (* x (/ y (* a 2.0)))
   (if (<= (* x y) 1e-13) (* t (* z (/ -4.5 a))) (/ (* x y) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (x * y) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-8)) then
        tmp = x * (y / (a * 2.0d0))
    else if ((x * y) <= 1d-13) then
        tmp = t * (z * ((-4.5d0) / a))
    else
        tmp = (x * y) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (x * y) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-8:
		tmp = x * (y / (a * 2.0))
	elif (x * y) <= 1e-13:
		tmp = t * (z * (-4.5 / a))
	else:
		tmp = (x * y) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-8)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 1e-13)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	else
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-8)
		tmp = x * (y / (a * 2.0));
	elseif ((x * y) <= 1e-13)
		tmp = t * (z * (-4.5 / a));
	else
		tmp = (x * y) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-8], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-13], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000001e-8

   1. Initial program 86.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 86.5

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 70.4

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

   7. Simplified 70.4%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

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

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 73.6

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

   9. Applied egg-rr 73.6%

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

   if -4.0000000000000001e-8 < (*.f64 x y) < 1e-13

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 81.4

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

   5. Simplified 81.4%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. times-frac N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. metadata-eval N/A

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

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

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

      15. /-lowering-/.f64 77.0

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

   7. Applied egg-rr 77.0%

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 81.3

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

   9. Applied egg-rr 81.3%

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

   if 1e-13 < (*.f64 x y)

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 75.6

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

   5. Simplified 75.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-8)
   (* x (/ y (* a 2.0)))
   (if (<= (* x y) 1e-13) (* t (* z (/ -4.5 a))) (* (* x y) (/ 0.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-8)) then
        tmp = x * (y / (a * 2.0d0))
    else if ((x * y) <= 1d-13) then
        tmp = t * (z * ((-4.5d0) / a))
    else
        tmp = (x * y) * (0.5d0 / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y / (a * 2.0));
	} else if ((x * y) <= 1e-13) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-8:
		tmp = x * (y / (a * 2.0))
	elif (x * y) <= 1e-13:
		tmp = t * (z * (-4.5 / a))
	else:
		tmp = (x * y) * (0.5 / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-8)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 1e-13)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	else
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-8)
		tmp = x * (y / (a * 2.0));
	elseif ((x * y) <= 1e-13)
		tmp = t * (z * (-4.5 / a));
	else
		tmp = (x * y) * (0.5 / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-8], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-13], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000001e-8

   1. Initial program 86.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 86.5

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 70.4

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

   7. Simplified 70.4%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

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

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 73.6

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

   9. Applied egg-rr 73.6%

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

   if -4.0000000000000001e-8 < (*.f64 x y) < 1e-13

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 81.4

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

   5. Simplified 81.4%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. times-frac N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. metadata-eval N/A

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

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

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

      15. /-lowering-/.f64 77.0

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

   7. Applied egg-rr 77.0%

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 81.3

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

   9. Applied egg-rr 81.3%

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

   if 1e-13 < (*.f64 x y)

   1. Initial program 90.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 91.8

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

   4. Applied egg-rr 91.8%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 75.6

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

   7. Simplified 75.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-8)
   (* x (* y (/ 0.5 a)))
   (if (<= (* x y) 1e-13) (* t (* z (/ -4.5 a))) (* (* x y) (/ 0.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y * (0.5 / a));
	} else if ((x * y) <= 1e-13) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-8)) then
        tmp = x * (y * (0.5d0 / a))
    else if ((x * y) <= 1d-13) then
        tmp = t * (z * ((-4.5d0) / a))
    else
        tmp = (x * y) * (0.5d0 / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-8) {
		tmp = x * (y * (0.5 / a));
	} else if ((x * y) <= 1e-13) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-8:
		tmp = x * (y * (0.5 / a))
	elif (x * y) <= 1e-13:
		tmp = t * (z * (-4.5 / a))
	else:
		tmp = (x * y) * (0.5 / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-8)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (Float64(x * y) <= 1e-13)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	else
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-8)
		tmp = x * (y * (0.5 / a));
	elseif ((x * y) <= 1e-13)
		tmp = t * (z * (-4.5 / a));
	else
		tmp = (x * y) * (0.5 / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-8], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-13], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000001e-8

   1. Initial program 86.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 86.5

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 70.4

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

   7. Simplified 70.4%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

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

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lowering-*.f64 73.6

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

   9. Applied egg-rr 73.6%

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

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

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

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

       4. *-commutative N/A

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

       5. associate-/r* N/A

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

       6. metadata-eval N/A

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

       7. /-lowering-/.f64 73.5

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

   11. Applied egg-rr 73.5%

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

   if -4.0000000000000001e-8 < (*.f64 x y) < 1e-13

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 81.4

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

   5. Simplified 81.4%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. times-frac N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. metadata-eval N/A

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

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

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

      15. /-lowering-/.f64 77.0

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

   7. Applied egg-rr 77.0%

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 81.3

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

   9. Applied egg-rr 81.3%

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

   if 1e-13 < (*.f64 x y)

   1. Initial program 90.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 91.8

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

   4. Applied egg-rr 91.8%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 75.6

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

   7. Simplified 75.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-13}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.2% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (/ (* y 0.5) (/ a x))
   (* (fma y x (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = fma(y, x, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 67.4%

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

      1. div-inv N/A

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*l* N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. metadata-eval 67.7

          \[\leadsto \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{\color{blue}{0.5}}{a} \]

   4. Applied egg-rr 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{\frac{1}{2}}{a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 67.7

         \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{0.5}{a} \]

   7. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{0.5}{a} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a} \cdot \left(x \cdot y\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{\frac{1}{2}}{a} \cdot x\right) \cdot y} \]

      3. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{x}}} \cdot y \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot y}{\frac{a}{x}}} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{\frac{a}{x}}} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      8. /-lowering-/.f64 98.1

         \[\leadsto \frac{y \cdot 0.5}{\color{blue}{\frac{a}{x}}} \]

   9. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]

   if -inf.0 < (*.f64 x y)

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{a \cdot 2}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{a \cdot 2}} \]

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right)} \cdot \frac{1}{a \cdot 2} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right) + x \cdot y\right)} \cdot \frac{1}{a \cdot 2} \]

      5. associate-*l* N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \left(9 \cdot t\right)}\right)\right) + x \cdot y\right) \cdot \frac{1}{a \cdot 2} \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)} + x \cdot y\right) \cdot \frac{1}{a \cdot 2} \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{neg}\left(9 \cdot t\right), x \cdot y\right)} \cdot \frac{1}{a \cdot 2} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(z, \mathsf{neg}\left(\color{blue}{t \cdot 9}\right), x \cdot y\right) \cdot \frac{1}{a \cdot 2} \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{t \cdot \left(\mathsf{neg}\left(9\right)\right)}, x \cdot y\right) \cdot \frac{1}{a \cdot 2} \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{t \cdot \left(\mathsf{neg}\left(9\right)\right)}, x \cdot y\right) \cdot \frac{1}{a \cdot 2} \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(z, t \cdot \color{blue}{-9}, x \cdot y\right) \cdot \frac{1}{a \cdot 2} \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, t \cdot -9, \color{blue}{x \cdot y}\right) \cdot \frac{1}{a \cdot 2} \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} \]

      14. associate-/r* N/A

          \[\leadsto \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

      16. metadata-eval 94.0

          \[\leadsto \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{\color{blue}{0.5}}{a} \]

   4. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}} \]
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)} \cdot \frac{\frac{1}{2}}{a} \]

      2. *-commutative N/A

         \[\leadsto \left(\color{blue}{y \cdot x} + z \cdot \left(t \cdot -9\right)\right) \cdot \frac{\frac{1}{2}}{a} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)} \cdot \frac{\frac{1}{2}}{a} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{z \cdot \left(t \cdot -9\right)}\right) \cdot \frac{\frac{1}{2}}{a} \]

      5. *-lowering-*.f64 94.0

         \[\leadsto \mathsf{fma}\left(y, x, z \cdot \color{blue}{\left(t \cdot -9\right)}\right) \cdot \frac{0.5}{a} \]

   6. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)} \cdot \frac{0.5}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 7e+133) (* t (* z (/ -4.5 a))) (* z (* -4.5 (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7e+133) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = z * (-4.5 * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 7d+133) then
        tmp = t * (z * ((-4.5d0) / a))
    else
        tmp = z * ((-4.5d0) * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7e+133) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = z * (-4.5 * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 7e+133:
		tmp = t * (z * (-4.5 / a))
	else:
		tmp = z * (-4.5 * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 7e+133)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	else
		tmp = Float64(z * Float64(-4.5 * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 7e+133)
		tmp = t * (z * (-4.5 / a));
	else
		tmp = z * (-4.5 * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 7e+133], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.9999999999999997e133

   1. Initial program 92.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]

      2. associate-/l* N/A

         \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

      4. /-lowering-/.f64 48.2

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-9}{2}} \cdot \left(t \cdot \frac{z}{a}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \frac{-9}{2} \cdot \color{blue}{\frac{t \cdot z}{a}} \]

      3. times-frac N/A

         \[\leadsto \color{blue}{\frac{-9 \cdot \left(t \cdot z\right)}{2 \cdot a}} \]

      4. *-commutative N/A

         \[\leadsto \frac{-9 \cdot \left(t \cdot z\right)}{\color{blue}{a \cdot 2}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-9 \cdot t\right) \cdot z}}{a \cdot 2} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(t \cdot -9\right)} \cdot z}{a \cdot 2} \]

      7. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

      8. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -9}{a \cdot 2}} \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -9}{a \cdot 2}} \]

      10. *-commutative N/A

          \[\leadsto z \cdot \frac{\color{blue}{-9 \cdot t}}{a \cdot 2} \]

      11. *-commutative N/A

          \[\leadsto z \cdot \frac{-9 \cdot t}{\color{blue}{2 \cdot a}} \]

      12. times-frac N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right)} \]

      13. metadata-eval N/A

          \[\leadsto z \cdot \left(\color{blue}{\frac{-9}{2}} \cdot \frac{t}{a}\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right)} \]

      15. /-lowering-/.f64 45.8

          \[\leadsto z \cdot \left(-4.5 \cdot \color{blue}{\frac{t}{a}}\right) \]

   7. Applied egg-rr 45.8%

      \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-9}{2} \cdot t}{a}} \cdot z \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot \frac{-9}{2}}}{a} \cdot z \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(t \cdot \frac{\frac{-9}{2}}{a}\right)} \cdot z \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\frac{\frac{-9}{2}}{a} \cdot z\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(\frac{\frac{-9}{2}}{a} \cdot z\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{\frac{-9}{2}}{a} \cdot z\right)} \]

      8. /-lowering-/.f64 48.2

         \[\leadsto t \cdot \left(\color{blue}{\frac{-4.5}{a}} \cdot z\right) \]

   9. Applied egg-rr 48.2%

      \[\leadsto \color{blue}{t \cdot \left(\frac{-4.5}{a} \cdot z\right)} \]

   if 6.9999999999999997e133 < t

   1. Initial program 80.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]

      2. associate-/l* N/A

         \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

      4. /-lowering-/.f64 72.4

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

   5. Simplified 72.4%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-9}{2}} \cdot \left(t \cdot \frac{z}{a}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \frac{-9}{2} \cdot \color{blue}{\frac{t \cdot z}{a}} \]

      3. times-frac N/A

         \[\leadsto \color{blue}{\frac{-9 \cdot \left(t \cdot z\right)}{2 \cdot a}} \]

      4. *-commutative N/A

         \[\leadsto \frac{-9 \cdot \left(t \cdot z\right)}{\color{blue}{a \cdot 2}} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-9 \cdot t\right) \cdot z}}{a \cdot 2} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(t \cdot -9\right)} \cdot z}{a \cdot 2} \]

      7. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

      8. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -9}{a \cdot 2}} \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \frac{t \cdot -9}{a \cdot 2}} \]

      10. *-commutative N/A

          \[\leadsto z \cdot \frac{\color{blue}{-9 \cdot t}}{a \cdot 2} \]

      11. *-commutative N/A

          \[\leadsto z \cdot \frac{-9 \cdot t}{\color{blue}{2 \cdot a}} \]

      12. times-frac N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right)} \]

      13. metadata-eval N/A

          \[\leadsto z \cdot \left(\color{blue}{\frac{-9}{2}} \cdot \frac{t}{a}\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right)} \]

      15. /-lowering-/.f64 79.8

          \[\leadsto z \cdot \left(-4.5 \cdot \color{blue}{\frac{t}{a}}\right) \]

   7. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ t \cdot \left(z \cdot \frac{-4.5}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* t (* z (/ -4.5 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return t * (z * (-4.5 / a));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t * (z * ((-4.5d0) / a))
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return t * (z * (-4.5 / a));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return t * (z * (-4.5 / a))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(t * Float64(z * Float64(-4.5 / a)))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = t * (z * (-4.5 / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.1%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]

   2. associate-/l* N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   4. /-lowering-/.f64 51.4

      \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

5. Simplified 51.4%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto \color{blue}{\frac{-9}{2}} \cdot \left(t \cdot \frac{z}{a}\right) \]

   2. associate-*r/ N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\frac{t \cdot z}{a}} \]

   3. times-frac N/A

      \[\leadsto \color{blue}{\frac{-9 \cdot \left(t \cdot z\right)}{2 \cdot a}} \]

   4. *-commutative N/A

      \[\leadsto \frac{-9 \cdot \left(t \cdot z\right)}{\color{blue}{a \cdot 2}} \]

   5. associate-*r* N/A

      \[\leadsto \frac{\color{blue}{\left(-9 \cdot t\right) \cdot z}}{a \cdot 2} \]

   6. *-commutative N/A

      \[\leadsto \frac{\color{blue}{\left(t \cdot -9\right)} \cdot z}{a \cdot 2} \]

   7. *-commutative N/A

      \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

   8. associate-/l* N/A

      \[\leadsto \color{blue}{z \cdot \frac{t \cdot -9}{a \cdot 2}} \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{z \cdot \frac{t \cdot -9}{a \cdot 2}} \]

   10. *-commutative N/A

       \[\leadsto z \cdot \frac{\color{blue}{-9 \cdot t}}{a \cdot 2} \]

   11. *-commutative N/A

       \[\leadsto z \cdot \frac{-9 \cdot t}{\color{blue}{2 \cdot a}} \]

   12. times-frac N/A

       \[\leadsto z \cdot \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right)} \]

   13. metadata-eval N/A

       \[\leadsto z \cdot \left(\color{blue}{\frac{-9}{2}} \cdot \frac{t}{a}\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto z \cdot \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right)} \]

   15. /-lowering-/.f64 50.3

       \[\leadsto z \cdot \left(-4.5 \cdot \color{blue}{\frac{t}{a}}\right) \]

7. Applied egg-rr 50.3%

   \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]
8. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(\frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z} \]

   2. associate-*r/ N/A

      \[\leadsto \color{blue}{\frac{\frac{-9}{2} \cdot t}{a}} \cdot z \]

   3. *-commutative N/A

      \[\leadsto \frac{\color{blue}{t \cdot \frac{-9}{2}}}{a} \cdot z \]

   4. associate-/l* N/A

      \[\leadsto \color{blue}{\left(t \cdot \frac{\frac{-9}{2}}{a}\right)} \cdot z \]

   5. associate-*l* N/A

      \[\leadsto \color{blue}{t \cdot \left(\frac{\frac{-9}{2}}{a} \cdot z\right)} \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{t \cdot \left(\frac{\frac{-9}{2}}{a} \cdot z\right)} \]

   7. *-lowering-*.f64 N/A

      \[\leadsto t \cdot \color{blue}{\left(\frac{\frac{-9}{2}}{a} \cdot z\right)} \]

   8. /-lowering-/.f64 51.4

      \[\leadsto t \cdot \left(\color{blue}{\frac{-4.5}{a}} \cdot z\right) \]

9. Applied egg-rr 51.4%

   \[\leadsto \color{blue}{t \cdot \left(\frac{-4.5}{a} \cdot z\right)} \]

10. Final simplification 51.4%

    \[\leadsto t \cdot \left(z \cdot \frac{-4.5}{a}\right) \]
11. Add Preprocessing

Alternative 14: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (t * (z / a))
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * (t * (z / a))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t * Float64(z / a)))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.1%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]

   2. associate-/l* N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   4. /-lowering-/.f64 51.4

      \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

5. Simplified 51.4%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Add Preprocessing

Developer Target 1: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024204 
(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)))