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

Percentage Accurate: 91.5% → 91.8%

Time: 7.5s

Alternatives: 8

Speedup: 1.1×

• 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 91.5% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 91.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+174}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5 \cdot y, x, \left(-4.5 \cdot t\right) \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-9 \cdot t}{a}, \frac{z}{2}, \frac{x}{2 \cdot a} \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 3.2e+174)
   (/ (fma (* 0.5 y) x (* (* -4.5 t) z)) a)
   (fma (/ (* -9.0 t) a) (/ z 2.0) (* (/ x (* 2.0 a)) y))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.2e+174) {
		tmp = fma((0.5 * y), x, ((-4.5 * t) * z)) / a;
	} else {
		tmp = fma(((-9.0 * t) / a), (z / 2.0), ((x / (2.0 * a)) * y));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3.2e+174)
		tmp = Float64(fma(Float64(0.5 * y), x, Float64(Float64(-4.5 * t) * z)) / a);
	else
		tmp = fma(Float64(Float64(-9.0 * t) / a), Float64(z / 2.0), Float64(Float64(x / Float64(2.0 * a)) * y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3.2e+174], N[(N[(N[(0.5 * y), $MachinePrecision] * x + N[(N[(-4.5 * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(-9.0 * t), $MachinePrecision] / a), $MachinePrecision] * N[(z / 2.0), $MachinePrecision] + N[(N[(x / N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2e174

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 95.8

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

   5. Applied rewrites 95.8%

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

   if 3.2e174 < y

   1. Initial program 73.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. div-add N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. associate-*r* N/A

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

      19. *-commutative N/A

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

      20. lower-/.f64 N/A

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

   4. Applied rewrites 81.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. metadata-eval N/A

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

      12. times-frac N/A

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

      13. *-commutative N/A

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

      14. associate-*r* N/A

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

      15. times-frac N/A

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

      16. associate-*r/ N/A

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

      17. *-commutative N/A

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

      18. associate-/l/ N/A

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

      19. lower-fma.f64 N/A

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

   6. Applied rewrites 99.8%

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

Alternative 2: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+283}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, -4.5 \cdot t, \frac{x}{2 \cdot a} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5 \cdot y, x, \left(-4.5 \cdot t\right) \cdot z\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) -5e+283)
   (fma (/ z a) (* -4.5 t) (* (/ x (* 2.0 a)) y))
   (/ (fma (* 0.5 y) x (* (* -4.5 t) z)) a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= -5e+283) {
		tmp = fma((z / a), (-4.5 * t), ((x / (2.0 * a)) * y));
	} else {
		tmp = fma((0.5 * y), x, ((-4.5 * t) * z)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= -5e+283)
		tmp = fma(Float64(z / a), Float64(-4.5 * t), Float64(Float64(x / Float64(2.0 * a)) * y));
	else
		tmp = Float64(fma(Float64(0.5 * y), x, Float64(Float64(-4.5 * t) * z)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], -5e+283], N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision] + N[(N[(x / N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.5 * y), $MachinePrecision] * x + N[(N[(-4.5 * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5.0000000000000004e283

   1. Initial program 76.1%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 76.1

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

   4. Applied rewrites 76.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. div-add N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. times-frac N/A

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

      11. metadata-eval N/A

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

      12. *-commutative N/A

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

      13. associate-*r/ N/A

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

      14. associate-*r/ N/A

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

      15. *-commutative N/A

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

   6. Applied rewrites 91.3%

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

   if -5.0000000000000004e283 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 96.8

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

   5. Applied rewrites 96.8%

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

Alternative 3: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-92} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+27}\right):\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a + a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (or (<= t_1 -1e-92) (not (<= t_1 2e+27)))
     (* (* t (/ z a)) -4.5)
     (/ (* x y) (+ a a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -1e-92) || !(t_1 <= 2e+27)) {
		tmp = (t * (z / a)) * -4.5;
	} else {
		tmp = (x * y) / (a + a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-1d-92)) .or. (.not. (t_1 <= 2d+27))) then
        tmp = (t * (z / a)) * (-4.5d0)
    else
        tmp = (x * y) / (a + a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -1e-92) || !(t_1 <= 2e+27)) {
		tmp = (t * (z / a)) * -4.5;
	} else {
		tmp = (x * y) / (a + a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if (t_1 <= -1e-92) or not (t_1 <= 2e+27):
		tmp = (t * (z / a)) * -4.5
	else:
		tmp = (x * y) / (a + a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if ((t_1 <= -1e-92) || !(t_1 <= 2e+27))
		tmp = Float64(Float64(t * Float64(z / a)) * -4.5);
	else
		tmp = Float64(Float64(x * y) / Float64(a + a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if ((t_1 <= -1e-92) || ~((t_1 <= 2e+27)))
		tmp = (t * (z / a)) * -4.5;
	else
		tmp = (x * y) / (a + a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-92], N[Not[LessEqual[t$95$1, 2e+27]], $MachinePrecision]], N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(a + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -9.99999999999999988e-93 or 2e27 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 93.2%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 70.4

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

   5. Applied rewrites 70.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 69.9

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

   7. Applied rewrites 69.9%

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

   if -9.99999999999999988e-93 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2e27

   1. Initial program 94.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 94.0

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

   4. Applied rewrites 94.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 94.0

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

   6. Applied rewrites 94.0%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 77.3

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

   9. Applied rewrites 77.3%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{-92} \lor \neg \left(\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+27}\right):\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a + a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot y}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -1e-92)
     (* (* (/ z a) -4.5) t)
     (if (<= t_1 2e+27) (/ (* x y) (+ a a)) (* (* t (/ z a)) -4.5)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e-92) {
		tmp = ((z / a) * -4.5) * t;
	} else if (t_1 <= 2e+27) {
		tmp = (x * y) / (a + a);
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-1d-92)) then
        tmp = ((z / a) * (-4.5d0)) * t
    else if (t_1 <= 2d+27) then
        tmp = (x * y) / (a + a)
    else
        tmp = (t * (z / a)) * (-4.5d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e-92) {
		tmp = ((z / a) * -4.5) * t;
	} else if (t_1 <= 2e+27) {
		tmp = (x * y) / (a + a);
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -1e-92:
		tmp = ((z / a) * -4.5) * t
	elif t_1 <= 2e+27:
		tmp = (x * y) / (a + a)
	else:
		tmp = (t * (z / a)) * -4.5
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -1e-92)
		tmp = Float64(Float64(Float64(z / a) * -4.5) * t);
	elseif (t_1 <= 2e+27)
		tmp = Float64(Float64(x * y) / Float64(a + a));
	else
		tmp = Float64(Float64(t * Float64(z / a)) * -4.5);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -1e-92)
		tmp = ((z / a) * -4.5) * t;
	elseif (t_1 <= 2e+27)
		tmp = (x * y) / (a + a);
	else
		tmp = (t * (z / a)) * -4.5;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-92], N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+27], N[(N[(x * y), $MachinePrecision] / N[(a + a), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -9.99999999999999988e-93

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 69.0

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

   5. Applied rewrites 69.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 67.9

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

   7. Applied rewrites 67.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 68.0

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

   9. Applied rewrites 68.0%

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

   if -9.99999999999999988e-93 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2e27

   1. Initial program 94.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 94.0

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

   4. Applied rewrites 94.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 94.0

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

   6. Applied rewrites 94.0%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 77.3

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

   9. Applied rewrites 77.3%

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

   if 2e27 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 93.4%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 72.8

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

   7. Applied rewrites 72.8%

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

Alternative 5: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 10^{+23}\right):\\ \;\;\;\;\frac{x \cdot y}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+62) (not (<= (* x y) 1e+23)))
   (/ (* x y) (+ a a))
   (* (/ (* t z) a) -4.5)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+62) || !((x * y) <= 1e+23)) {
		tmp = (x * y) / (a + a);
	} else {
		tmp = ((t * z) / a) * -4.5;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-2d+62)) .or. (.not. ((x * y) <= 1d+23))) then
        tmp = (x * y) / (a + a)
    else
        tmp = ((t * z) / a) * (-4.5d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+62) || !((x * y) <= 1e+23)) {
		tmp = (x * y) / (a + a);
	} else {
		tmp = ((t * z) / a) * -4.5;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+62) or not ((x * y) <= 1e+23):
		tmp = (x * y) / (a + a)
	else:
		tmp = ((t * z) / a) * -4.5
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+62) || !(Float64(x * y) <= 1e+23))
		tmp = Float64(Float64(x * y) / Float64(a + a));
	else
		tmp = Float64(Float64(Float64(t * z) / a) * -4.5);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+62) || ~(((x * y) <= 1e+23)))
		tmp = (x * y) / (a + a);
	else
		tmp = ((t * z) / a) * -4.5;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+62], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+23]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / N[(a + a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision] * -4.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000007e62 or 9.9999999999999992e22 < (*.f64 x y)

   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. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 91.6

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

   4. Applied rewrites 91.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 91.6

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

   6. Applied rewrites 91.6%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 74.2

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

   9. Applied rewrites 74.2%

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

   if -2.00000000000000007e62 < (*.f64 x y) < 9.9999999999999992e22

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 10^{+23}\right):\\ \;\;\;\;\frac{x \cdot y}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \frac{\mathsf{fma}\left(0.5 \cdot y, x, \left(-4.5 \cdot t\right) \cdot z\right)}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (/ (fma (* 0.5 y) x (* (* -4.5 t) z)) a))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return fma((0.5 * y), x, ((-4.5 * t) * z)) / a;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(fma(Float64(0.5 * y), x, Float64(Float64(-4.5 * t) * z)) / a)
end

Wolfram

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

Derivation

1. Initial program 93.5%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate-*r/ N/A

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

   3. associate-*r/ N/A

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

   4. div-add-rev N/A

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

   5. lower-/.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-*r* N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-*.f64 N/A

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

   10. associate-*r* N/A

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

   11. lower-*.f64 N/A

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

   12. lower-*.f64 94.0

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

5. Applied rewrites 94.0%

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

Alternative 7: 92.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \frac{\mathsf{fma}\left(y, x, \left(t \cdot z\right) \cdot -9\right)}{a + a} \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return fma(y, x, ((t * z) * -9.0)) / (a + a);
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(fma(y, x, Float64(Float64(t * z) * -9.0)) / Float64(a + a))
end

Wolfram

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

Derivation

1. Initial program 93.5%

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

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

   3. lift-*.f64 N/A

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

   4. fp-cancel-sub-sign-inv N/A

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

   5. +-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

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

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

   9. metadata-eval N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 93.5

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

4. Applied rewrites 93.5%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. count-2-rev N/A

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

   4. lower-+.f64 93.5

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

6. Applied rewrites 93.5%

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

   1. lift-*.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-*.f64 93.9

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

8. Applied rewrites 93.9%

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

Alternative 8: 51.0% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (/ (* x y) (+ a a)))

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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) / (a + a)
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return (x * y) / (a + a);
}

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (x * y) / (a + a);
end

Wolfram

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

Derivation

1. Initial program 93.5%

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

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

   3. lift-*.f64 N/A

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

   4. fp-cancel-sub-sign-inv N/A

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

   5. +-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

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

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

   9. metadata-eval N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 93.5

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

4. Applied rewrites 93.5%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. count-2-rev N/A

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

   4. lower-+.f64 93.5

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

6. Applied rewrites 93.5%

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

7. Taylor expanded in x around inf

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

   1. lower-*.f64 50.0

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

9. Applied rewrites 50.0%

   \[\leadsto \frac{\color{blue}{x \cdot y}}{a + a} \]
10. Add Preprocessing

Developer Target 1: 93.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 2025084 
(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)))