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

Percentage Accurate: 91.4% → 97.3%

Time: 13.4s

Alternatives: 14

Speedup: 0.7×

• 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: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{z \cdot 4.5}{a}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-t, t\_1, \frac{x \cdot 0.5}{\frac{a}{y}}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, t\_1, x \cdot \frac{y}{a \cdot 2}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z 4.5) a)) (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 (- INFINITY))
     (fma (- t) t_1 (/ (* x 0.5) (/ a y)))
     (if (<= t_2 2e+299)
       (/ (fma (* z t) -9.0 (* x y)) (* a 2.0))
       (fma (- t) t_1 (* 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 t_1 = (z * 4.5) / a;
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(-t, t_1, ((x * 0.5) / (a / y)));
	} else if (t_2 <= 2e+299) {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	} else {
		tmp = fma(-t, t_1, (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)
	t_1 = Float64(Float64(z * 4.5) / a)
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(-t), t_1, Float64(Float64(x * 0.5) / Float64(a / y)));
	elseif (t_2 <= 2e+299)
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(-t), t_1, Float64(x * Float64(y / Float64(a * 2.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[((-t) * t$95$1 + N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+299], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-t) * t$95$1 + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 62.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

      15. lower-/.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. associate-/l* N/A

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

      22. lower-*.f64 N/A

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

   4. Applied rewrites 99.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 N/A

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

      10. div-inv N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 99.9

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

   6. Applied rewrites 99.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.0000000000000001e299

   1. Initial program 98.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 98.6

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

   4. Applied rewrites 98.6%

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

   if 2.0000000000000001e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 56.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

      15. lower-/.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. associate-/l* N/A

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

      22. lower-*.f64 N/A

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

   4. Applied rewrites 91.5%

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

Alternative 2: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, \frac{z \cdot 4.5}{a}, x \cdot \frac{y}{a \cdot 2}\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t) (/ (* z 4.5) a) (* x (/ y (* a 2.0)))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e+299) (/ (fma (* z t) -9.0 (* x y)) (* a 2.0)) 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(-t, ((z * 4.5) / a), (x * (y / (a * 2.0))));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+299) {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	} 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(-t), Float64(Float64(z * 4.5) / a), Float64(x * Float64(y / Float64(a * 2.0))))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+299)
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision] + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+299], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 2.0000000000000001e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 60.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

      15. lower-/.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. associate-/l* N/A

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

      22. lower-*.f64 N/A

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

   4. Applied rewrites 96.5%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.0000000000000001e299

   1. Initial program 98.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 98.6

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

   4. Applied rewrites 98.6%

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

Alternative 3: 92.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot -9, z, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y \cdot 0.5, \frac{z \cdot \left(t \cdot -4.5\right)}{a}\right)\\ \end{array} \end{array} \]

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) 4e+18)
   (/ (fma (* t -9.0) z (* x y)) (* a 2.0))
   (fma (/ x a) (* y 0.5) (/ (* 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) <= 4e+18) {
		tmp = fma((t * -9.0), z, (x * y)) / (a * 2.0);
	} else {
		tmp = fma((x / a), (y * 0.5), ((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) <= 4e+18)
		tmp = Float64(fma(Float64(t * -9.0), z, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(x / a), Float64(y * 0.5), Float64(Float64(z * Float64(t * -4.5)) / 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[(a * 2.0), $MachinePrecision], 4e+18], N[(N[(N[(t * -9.0), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(y * 0.5), $MachinePrecision] + N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 4e18

   1. Initial program 91.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 92.6

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

   4. Applied rewrites 92.6%

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

   if 4e18 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 81.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 81.5

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

   4. Applied rewrites 81.5%

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

   6. Applied rewrites 88.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot -9, z, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y \cdot 0.5, \frac{z \cdot \left(t \cdot -4.5\right)}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot -9, z, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \frac{z \cdot \left(t \cdot -4.5\right)}{a}\right)\\ \end{array} \end{array} \]

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) 4e+18)
   (/ (fma (* t -9.0) z (* x y)) (* a 2.0))
   (fma (* y (/ 0.5 a)) x (/ (* 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) <= 4e+18) {
		tmp = fma((t * -9.0), z, (x * y)) / (a * 2.0);
	} else {
		tmp = fma((y * (0.5 / a)), x, ((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) <= 4e+18)
		tmp = Float64(fma(Float64(t * -9.0), z, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(y * Float64(0.5 / a)), x, Float64(Float64(z * Float64(t * -4.5)) / 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[(a * 2.0), $MachinePrecision], 4e+18], N[(N[(N[(t * -9.0), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] * x + N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 4e18

   1. Initial program 91.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 92.6

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

   4. Applied rewrites 92.6%

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

   if 4e18 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 81.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 81.5

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

   4. Applied rewrites 81.5%

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

   6. Applied rewrites 88.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 88.1

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

   8. Applied rewrites 88.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot -9, z, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \frac{z \cdot \left(t \cdot -4.5\right)}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \left(t \cdot \frac{1}{a}\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -5e+98)
     (* -4.5 (* z (* t (/ 1.0 a))))
     (if (<= t_1 5e-49) (/ (* x y) (* a 2.0)) (* 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 t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = -4.5 * (z * (t * (1.0 / a)));
	} else if (t_1 <= 5e-49) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-5d+98)) then
        tmp = (-4.5d0) * (z * (t * (1.0d0 / a)))
    else if (t_1 <= 5d-49) then
        tmp = (x * y) / (a * 2.0d0)
    else
        tmp = z * ((t * (-4.5d0)) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = -4.5 * (z * (t * (1.0 / a)));
	} else if (t_1 <= 5e-49) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -5e+98:
		tmp = -4.5 * (z * (t * (1.0 / a)))
	elif t_1 <= 5e-49:
		tmp = (x * y) / (a * 2.0)
	else:
		tmp = z * ((t * -4.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -5e+98)
		tmp = Float64(-4.5 * Float64(z * Float64(t * Float64(1.0 / a))));
	elseif (t_1 <= 5e-49)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(Float64(t * -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+98)
		tmp = -4.5 * (z * (t * (1.0 / a)));
	elseif (t_1 <= 5e-49)
		tmp = (x * y) / (a * 2.0);
	else
		tmp = z * ((t * -4.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+98], N[(-4.5 * N[(z * N[(t * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-49], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -4.9999999999999998e98

   1. Initial program 87.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 85.2

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

   5. Applied rewrites 85.2%

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

   7. Applied rewrites 80.1%

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

   if -4.9999999999999998e98 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999999e-49

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if 4.9999999999999999e-49 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 82.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 77.8

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

   5. Applied rewrites 77.8%

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

   7. Applied rewrites 77.8%

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

   9. Applied rewrites 78.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \left(t \cdot \frac{1}{a}\right)\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -5e+98)
     (* -4.5 (* z (/ t a)))
     (if (<= t_1 5e-49) (/ (* x y) (* a 2.0)) (* 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 t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = -4.5 * (z * (t / a));
	} else if (t_1 <= 5e-49) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-5d+98)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t_1 <= 5d-49) then
        tmp = (x * y) / (a * 2.0d0)
    else
        tmp = z * ((t * (-4.5d0)) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = -4.5 * (z * (t / a));
	} else if (t_1 <= 5e-49) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -5e+98:
		tmp = -4.5 * (z * (t / a))
	elif t_1 <= 5e-49:
		tmp = (x * y) / (a * 2.0)
	else:
		tmp = z * ((t * -4.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -5e+98)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t_1 <= 5e-49)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(Float64(t * -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+98)
		tmp = -4.5 * (z * (t / a));
	elseif (t_1 <= 5e-49)
		tmp = (x * y) / (a * 2.0);
	else
		tmp = z * ((t * -4.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+98], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-49], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -4.9999999999999998e98

   1. Initial program 87.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 85.2

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

   5. Applied rewrites 85.2%

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

   7. Applied rewrites 80.1%

      \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\left(\frac{1}{a} \cdot t\right)}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 80.1%

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

   if -4.9999999999999998e98 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999999e-49

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if 4.9999999999999999e-49 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 82.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 77.8

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

   5. Applied rewrites 77.8%

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

   7. Applied rewrites 77.8%

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

   9. Applied rewrites 78.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -5e+98)
     (* -4.5 (* z (/ t a)))
     (if (<= t_1 5e-49) (* (/ 0.5 a) (* x 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 t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = -4.5 * (z * (t / a));
	} else if (t_1 <= 5e-49) {
		tmp = (0.5 / a) * (x * y);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-5d+98)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t_1 <= 5d-49) then
        tmp = (0.5d0 / a) * (x * y)
    else
        tmp = z * ((t * (-4.5d0)) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = -4.5 * (z * (t / a));
	} else if (t_1 <= 5e-49) {
		tmp = (0.5 / a) * (x * y);
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -5e+98:
		tmp = -4.5 * (z * (t / a))
	elif t_1 <= 5e-49:
		tmp = (0.5 / a) * (x * y)
	else:
		tmp = z * ((t * -4.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -5e+98)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t_1 <= 5e-49)
		tmp = Float64(Float64(0.5 / a) * Float64(x * y));
	else
		tmp = Float64(z * Float64(Float64(t * -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+98)
		tmp = -4.5 * (z * (t / a));
	elseif (t_1 <= 5e-49)
		tmp = (0.5 / a) * (x * y);
	else
		tmp = z * ((t * -4.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+98], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-49], N[(N[(0.5 / a), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -4.9999999999999998e98

   1. Initial program 87.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 85.2

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

   5. Applied rewrites 85.2%

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

   7. Applied rewrites 80.1%

      \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\left(\frac{1}{a} \cdot t\right)}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 80.1%

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

   if -4.9999999999999998e98 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999999e-49

   1. Initial program 92.8%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 92.7

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

   4. Applied rewrites 92.7%

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

   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. lower-*.f64 74.7

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

   7. Applied rewrites 74.7%

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

   if 4.9999999999999999e-49 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 82.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 77.8

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

   5. Applied rewrites 77.8%

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

   7. Applied rewrites 77.8%

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

   9. Applied rewrites 78.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+98}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* (* z 9.0) t) 5e+268)
   (/ (fma (* z t) -9.0 (* x y)) (* a 2.0))
   (* 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 tmp;
	if (((z * 9.0) * t) <= 5e+268) {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	} 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)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 5e+268)
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / 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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 5e+268], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.0000000000000002e268

   1. Initial program 92.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 92.1

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

   4. Applied rewrites 92.1%

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

   if 5.0000000000000002e268 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 57.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 89.7

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

   5. Applied rewrites 89.7%

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

   7. Applied rewrites 89.7%

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

   9. Applied rewrites 89.8%

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

   11. Applied rewrites 89.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot -9, z, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* (* z 9.0) t) 5e+268)
   (/ (fma (* t -9.0) z (* x y)) (* a 2.0))
   (* 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 tmp;
	if (((z * 9.0) * t) <= 5e+268) {
		tmp = fma((t * -9.0), z, (x * y)) / (a * 2.0);
	} 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)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 5e+268)
		tmp = Float64(fma(Float64(t * -9.0), z, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / 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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 5e+268], N[(N[(N[(t * -9.0), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.0000000000000002e268

   1. Initial program 92.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

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

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 92.1

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

   4. Applied rewrites 92.1%

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

   if 5.0000000000000002e268 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 57.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 89.7

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

   5. Applied rewrites 89.7%

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

   7. Applied rewrites 89.7%

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

   9. Applied rewrites 89.8%

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

   11. Applied rewrites 89.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot -9, z, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{0.5}{a} \cdot \mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* (* z 9.0) t) 5e+268)
   (* (/ 0.5 a) (fma (* z t) -9.0 (* x y)))
   (* 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 tmp;
	if (((z * 9.0) * t) <= 5e+268) {
		tmp = (0.5 / a) * fma((z * t), -9.0, (x * y));
	} 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)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 5e+268)
		tmp = Float64(Float64(0.5 / a) * fma(Float64(z * t), -9.0, Float64(x * y)));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / 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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 5e+268], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.0000000000000002e268

   1. Initial program 92.0%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 92.0

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

   4. Applied rewrites 92.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 92.0

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

   6. Applied rewrites 92.0%

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

   if 5.0000000000000002e268 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 57.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 89.7

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

   5. Applied rewrites 89.7%

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

   7. Applied rewrites 89.7%

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

   9. Applied rewrites 89.8%

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

   11. Applied rewrites 89.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{0.5}{a} \cdot \mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{0.5}{a} \cdot \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* (* z 9.0) t) 5e+268)
   (* (/ 0.5 a) (fma z (* t -9.0) (* x y)))
   (* 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 tmp;
	if (((z * 9.0) * t) <= 5e+268) {
		tmp = (0.5 / a) * fma(z, (t * -9.0), (x * y));
	} 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)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 5e+268)
		tmp = Float64(Float64(0.5 / a) * fma(z, Float64(t * -9.0), Float64(x * y)));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / 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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 5e+268], N[(N[(0.5 / a), $MachinePrecision] * N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.0000000000000002e268

   1. Initial program 92.0%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 92.0

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

   4. Applied rewrites 92.0%

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

   if 5.0000000000000002e268 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 57.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 89.7

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

   5. Applied rewrites 89.7%

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

   7. Applied rewrites 89.7%

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

   9. Applied rewrites 89.8%

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

   11. Applied rewrites 89.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{0.5}{a} \cdot \mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 1.6× speedup

Math

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

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 a) (* z -4.5)))

C

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

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 / a) * (z * (-4.5d0))
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 / a) * (z * -4.5);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 47.8

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

5. Applied rewrites 47.8%

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

7. Applied rewrites 47.8%

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

9. Applied rewrites 48.5%

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

11. Applied rewrites 48.5%

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

12. Final simplification 48.5%

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

Alternative 13: 51.8% accurate, 1.6× speedup

Math

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

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 (* z (/ t a))))

C

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

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * (z * (t / 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(z * Float64(t / 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 * (z * (t / 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[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 47.8

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

5. Applied rewrites 47.8%

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

7. Applied rewrites 48.4%

   \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\left(\frac{1}{a} \cdot t\right)}\right) \]
8. Step-by-step derivation

9. Applied rewrites 48.4%

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

10. Final simplification 48.4%

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

Alternative 14: 51.7% 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 89.3%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 47.8

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

5. Applied rewrites 47.8%

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

Developer Target 1: 93.2% 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 2024234 
(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)))