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

Percentage Accurate: 91.0% → 96.6%

Time: 7.0s

Alternatives: 17

Speedup: 0.6×

• 28.1% 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: 91.0% 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: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, t \cdot \left(\frac{z}{y} \cdot -4.5\right)\right)}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - \frac{t}{a} \cdot \frac{9 \cdot z}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* (/ (fma 0.5 x (* t (* (/ z y) -4.5))) a) y)
     (if (<= t_1 1e+304)
       (/ (/ (fma (* -9.0 z) t (* y x)) a) 2.0)
       (- (* (/ y a) (/ x 2.0)) (* (/ t a) (/ (* 9.0 z) 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma(0.5, x, (t * ((z / y) * -4.5))) / a) * y;
	} else if (t_1 <= 1e+304) {
		tmp = (fma((-9.0 * z), t, (y * x)) / a) / 2.0;
	} else {
		tmp = ((y / a) * (x / 2.0)) - ((t / a) * ((9.0 * z) / 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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(0.5, x, Float64(t * Float64(Float64(z / y) * -4.5))) / a) * y);
	elseif (t_1 <= 1e+304)
		tmp = Float64(Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / a) / 2.0);
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x / 2.0)) - Float64(Float64(t / a) * Float64(Float64(9.0 * z) / 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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(0.5 * x + N[(t * N[(N[(z / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], N[(N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(N[(9.0 * z), $MachinePrecision] / 2.0), $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 72.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999994e303

   1. Initial program 98.0%

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

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.5

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 98.5

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.5

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

   4. Applied rewrites 98.5%

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

   if 9.9999999999999994e303 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 64.5%

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

      1. lift-/.f64 N/A

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

      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. lower--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. times-frac N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-/.f64 90.6

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 2: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, t \cdot \left(\frac{z}{y} \cdot -4.5\right)\right)}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+292}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, \frac{0.5}{z}, -4.5 \cdot t\right)}{a} \cdot z\\ \end{array} \end{array} \]

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 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))))
   (if (<= t_1 (- INFINITY))
     (* (/ (fma 0.5 x (* t (* (/ z y) -4.5))) a) y)
     (if (<= t_1 4e+292)
       (/ (/ (fma (* -9.0 z) t (* y x)) a) 2.0)
       (* (/ (fma (* y x) (/ 0.5 z) (* -4.5 t)) a) z)))))

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 = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma(0.5, x, (t * ((z / y) * -4.5))) / a) * y;
	} else if (t_1 <= 4e+292) {
		tmp = (fma((-9.0 * z), t, (y * x)) / a) / 2.0;
	} else {
		tmp = (fma((y * x), (0.5 / z), (-4.5 * t)) / a) * z;
	}
	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(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(0.5, x, Float64(t * Float64(Float64(z / y) * -4.5))) / a) * y);
	elseif (t_1 <= 4e+292)
		tmp = Float64(Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / a) / 2.0);
	else
		tmp = Float64(Float64(fma(Float64(y * x), Float64(0.5 / z), Float64(-4.5 * t)) / a) * z);
	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[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(0.5 * x + N[(t * N[(N[(z / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 4e+292], N[(N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * N[(0.5 / z), $MachinePrecision] + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.2%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < 4.0000000000000001e292

   1. Initial program 97.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.3

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 98.3

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.3

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

   4. Applied rewrites 98.3%

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

   if 4.0000000000000001e292 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64)))

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.6%

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

Alternative 3: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, t \cdot \left(\frac{z}{y} \cdot -4.5\right)\right)}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, y, t \cdot \left(\frac{z}{x} \cdot -4.5\right)\right)}{a} \cdot x\\ \end{array} \end{array} \]

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 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))))
   (if (<= t_1 (- INFINITY))
     (* (/ (fma 0.5 x (* t (* (/ z y) -4.5))) a) y)
     (if (<= t_1 5e+304)
       (/ (/ (fma (* -9.0 z) t (* y x)) a) 2.0)
       (* (/ (fma 0.5 y (* t (* (/ z x) -4.5))) a) x)))))

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 = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma(0.5, x, (t * ((z / y) * -4.5))) / a) * y;
	} else if (t_1 <= 5e+304) {
		tmp = (fma((-9.0 * z), t, (y * x)) / a) / 2.0;
	} else {
		tmp = (fma(0.5, y, (t * ((z / x) * -4.5))) / a) * x;
	}
	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(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(0.5, x, Float64(t * Float64(Float64(z / y) * -4.5))) / a) * y);
	elseif (t_1 <= 5e+304)
		tmp = Float64(Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / a) / 2.0);
	else
		tmp = Float64(Float64(fma(0.5, y, Float64(t * Float64(Float64(z / x) * -4.5))) / a) * x);
	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[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(0.5 * x + N[(t * N[(N[(z / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 5e+304], N[(N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(0.5 * y + N[(t * N[(N[(z / x), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.2%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < 4.9999999999999997e304

   1. Initial program 97.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.3

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 98.3

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.3

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

   4. Applied rewrites 98.3%

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

   if 4.9999999999999997e304 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64)))

   1. Initial program 69.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 83.6%

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

Alternative 4: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, t \cdot \left(\frac{z}{y} \cdot -4.5\right)\right)}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(\frac{y}{z}, 0.5, \frac{t}{x} \cdot -4.5\right)}{a} \cdot x\right) \cdot z\\ \end{array} \end{array} \]

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 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* (/ (fma 0.5 x (* t (* (/ z y) -4.5))) a) y)
     (if (<= t_1 2e+295)
       (/ (/ (fma (* -9.0 z) t (* y x)) a) 2.0)
       (* (* (/ (fma (/ y z) 0.5 (* (/ t x) -4.5)) a) x) z)))))

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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma(0.5, x, (t * ((z / y) * -4.5))) / a) * y;
	} else if (t_1 <= 2e+295) {
		tmp = (fma((-9.0 * z), t, (y * x)) / a) / 2.0;
	} else {
		tmp = ((fma((y / z), 0.5, ((t / x) * -4.5)) / a) * x) * z;
	}
	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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(0.5, x, Float64(t * Float64(Float64(z / y) * -4.5))) / a) * y);
	elseif (t_1 <= 2e+295)
		tmp = Float64(Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / a) / 2.0);
	else
		tmp = Float64(Float64(Float64(fma(Float64(y / z), 0.5, Float64(Float64(t / x) * -4.5)) / a) * x) * z);
	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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(0.5 * x + N[(t * N[(N[(z / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+295], N[(N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(N[(N[(y / z), $MachinePrecision] * 0.5 + N[(N[(t / x), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] * z), $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 72.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2e295

   1. Initial program 98.0%

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

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.5

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 98.5

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.5

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

   4. Applied rewrites 98.5%

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

   if 2e295 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 65.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 88.7%

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

Alternative 5: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;\frac{0.5 \cdot x}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \mathbf{elif}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\frac{y \cdot x}{a \cdot 2}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+196}:\\ \;\;\;\;\frac{\left(-4.5 \cdot t\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -1e+91)
     (* t (* z (/ -4.5 a)))
     (if (<= t_1 -2e+50)
       (* (/ (* 0.5 x) a) y)
       (if (<= t_1 -1e-61)
         (* (/ (* t z) a) -4.5)
         (if (<= t_1 1e-5)
           (/ (* y x) (* a 2.0))
           (if (<= t_1 2e+196)
             (/ (* (* -4.5 t) z) a)
             (* (/ t a) (* -4.5 z)))))))))

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 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= -2e+50) {
		tmp = ((0.5 * x) / a) * y;
	} else if (t_1 <= -1e-61) {
		tmp = ((t * z) / a) * -4.5;
	} else if (t_1 <= 1e-5) {
		tmp = (y * x) / (a * 2.0);
	} else if (t_1 <= 2e+196) {
		tmp = ((-4.5 * t) * z) / a;
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	return tmp;
}

Fortran

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+91)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (t_1 <= (-2d+50)) then
        tmp = ((0.5d0 * x) / a) * y
    else if (t_1 <= (-1d-61)) then
        tmp = ((t * z) / a) * (-4.5d0)
    else if (t_1 <= 1d-5) then
        tmp = (y * x) / (a * 2.0d0)
    else if (t_1 <= 2d+196) then
        tmp = (((-4.5d0) * t) * z) / a
    else
        tmp = (t / a) * ((-4.5d0) * z)
    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 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= -2e+50) {
		tmp = ((0.5 * x) / a) * y;
	} else if (t_1 <= -1e-61) {
		tmp = ((t * z) / a) * -4.5;
	} else if (t_1 <= 1e-5) {
		tmp = (y * x) / (a * 2.0);
	} else if (t_1 <= 2e+196) {
		tmp = ((-4.5 * t) * z) / a;
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	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 <= -1e+91:
		tmp = t * (z * (-4.5 / a))
	elif t_1 <= -2e+50:
		tmp = ((0.5 * x) / a) * y
	elif t_1 <= -1e-61:
		tmp = ((t * z) / a) * -4.5
	elif t_1 <= 1e-5:
		tmp = (y * x) / (a * 2.0)
	elif t_1 <= 2e+196:
		tmp = ((-4.5 * t) * z) / a
	else:
		tmp = (t / a) * (-4.5 * z)
	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 <= -1e+91)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_1 <= -2e+50)
		tmp = Float64(Float64(Float64(0.5 * x) / a) * y);
	elseif (t_1 <= -1e-61)
		tmp = Float64(Float64(Float64(t * z) / a) * -4.5);
	elseif (t_1 <= 1e-5)
		tmp = Float64(Float64(y * x) / Float64(a * 2.0));
	elseif (t_1 <= 2e+196)
		tmp = Float64(Float64(Float64(-4.5 * t) * z) / a);
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 <= -1e+91)
		tmp = t * (z * (-4.5 / a));
	elseif (t_1 <= -2e+50)
		tmp = ((0.5 * x) / a) * y;
	elseif (t_1 <= -1e-61)
		tmp = ((t * z) / a) * -4.5;
	elseif (t_1 <= 1e-5)
		tmp = (y * x) / (a * 2.0);
	elseif (t_1 <= 2e+196)
		tmp = ((-4.5 * t) * z) / a;
	else
		tmp = (t / a) * (-4.5 * z);
	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, -1e+91], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+50], N[(N[(N[(0.5 * x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -1e-61], N[(N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[t$95$1, 1e-5], N[(N[(y * x), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+196], N[(N[(N[(-4.5 * t), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91

   1. Initial program 85.3%

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 85.0%

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

   9. Applied rewrites 85.2%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000002e50

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 87.8%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1e-61

   1. Initial program 93.9%

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

   5. Applied rewrites 75.8%

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

   if -1e-61 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.00000000000000008e-5

   1. Initial program 94.2%

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

   5. Applied rewrites 80.5%

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

   if 1.00000000000000008e-5 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.9999999999999999e196

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 76.2%

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

   7. Applied rewrites 63.7%

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

   9. Applied rewrites 76.4%

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

   11. Applied rewrites 76.2%

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

   if 1.9999999999999999e196 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 77.6%

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

   5. Applied rewrites 81.0%

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

   7. Applied rewrites 96.6%

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

   9. Applied rewrites 96.7%

      \[\leadsto \frac{t}{a} \cdot \color{blue}{\left(-4.5 \cdot z\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5 \cdot x}{a} \cdot y\\ t_2 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \mathbf{elif}\;t\_2 \leq 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

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 (* (/ (* 0.5 x) a) y)) (t_2 (* (* z 9.0) t)))
   (if (<= t_2 -1e+91)
     (* t (* z (/ -4.5 a)))
     (if (<= t_2 -2e+50)
       t_1
       (if (<= t_2 -1e-61)
         (* (/ (* t z) a) -4.5)
         (if (<= t_2 1e-58)
           t_1
           (if (<= t_2 2e+132)
             (* (* t z) (/ -4.5 a))
             (* (/ t a) (* -4.5 z)))))))))

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 = ((0.5 * x) / a) * y;
	double t_2 = (z * 9.0) * t;
	double tmp;
	if (t_2 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_2 <= -2e+50) {
		tmp = t_1;
	} else if (t_2 <= -1e-61) {
		tmp = ((t * z) / a) * -4.5;
	} else if (t_2 <= 1e-58) {
		tmp = t_1;
	} else if (t_2 <= 2e+132) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	return tmp;
}

Fortran

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) :: t_2
    real(8) :: tmp
    t_1 = ((0.5d0 * x) / a) * y
    t_2 = (z * 9.0d0) * t
    if (t_2 <= (-1d+91)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (t_2 <= (-2d+50)) then
        tmp = t_1
    else if (t_2 <= (-1d-61)) then
        tmp = ((t * z) / a) * (-4.5d0)
    else if (t_2 <= 1d-58) then
        tmp = t_1
    else if (t_2 <= 2d+132) then
        tmp = (t * z) * ((-4.5d0) / a)
    else
        tmp = (t / a) * ((-4.5d0) * z)
    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 = ((0.5 * x) / a) * y;
	double t_2 = (z * 9.0) * t;
	double tmp;
	if (t_2 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_2 <= -2e+50) {
		tmp = t_1;
	} else if (t_2 <= -1e-61) {
		tmp = ((t * z) / a) * -4.5;
	} else if (t_2 <= 1e-58) {
		tmp = t_1;
	} else if (t_2 <= 2e+132) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = ((0.5 * x) / a) * y
	t_2 = (z * 9.0) * t
	tmp = 0
	if t_2 <= -1e+91:
		tmp = t * (z * (-4.5 / a))
	elif t_2 <= -2e+50:
		tmp = t_1
	elif t_2 <= -1e-61:
		tmp = ((t * z) / a) * -4.5
	elif t_2 <= 1e-58:
		tmp = t_1
	elif t_2 <= 2e+132:
		tmp = (t * z) * (-4.5 / a)
	else:
		tmp = (t / a) * (-4.5 * z)
	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(Float64(0.5 * x) / a) * y)
	t_2 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_2 <= -1e+91)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_2 <= -2e+50)
		tmp = t_1;
	elseif (t_2 <= -1e-61)
		tmp = Float64(Float64(Float64(t * z) / a) * -4.5);
	elseif (t_2 <= 1e-58)
		tmp = t_1;
	elseif (t_2 <= 2e+132)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 = ((0.5 * x) / a) * y;
	t_2 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_2 <= -1e+91)
		tmp = t * (z * (-4.5 / a));
	elseif (t_2 <= -2e+50)
		tmp = t_1;
	elseif (t_2 <= -1e-61)
		tmp = ((t * z) / a) * -4.5;
	elseif (t_2 <= 1e-58)
		tmp = t_1;
	elseif (t_2 <= 2e+132)
		tmp = (t * z) * (-4.5 / a);
	else
		tmp = (t / a) * (-4.5 * z);
	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[(N[(0.5 * x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+91], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+50], t$95$1, If[LessEqual[t$95$2, -1e-61], N[(N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[t$95$2, 1e-58], t$95$1, If[LessEqual[t$95$2, 2e+132], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91

   1. Initial program 85.3%

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 85.0%

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

   9. Applied rewrites 85.2%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000002e50 or -1e-61 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e-58

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 79.4%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1e-61

   1. Initial program 93.9%

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

   5. Applied rewrites 75.8%

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

   if 1e-58 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999998e132

   1. Initial program 92.2%

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

   5. Applied rewrites 65.9%

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

   7. Applied rewrites 65.9%

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

   if 1.99999999999999998e132 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.6%

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

   5. Applied rewrites 81.4%

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

   7. Applied rewrites 92.7%

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

   9. Applied rewrites 93.0%

      \[\leadsto \frac{t}{a} \cdot \color{blue}{\left(-4.5 \cdot z\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5 \cdot x}{a} \cdot y\\ t_2 := \left(z \cdot 9\right) \cdot t\\ t_3 := \left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+132}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

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 (* (/ (* 0.5 x) a) y))
        (t_2 (* (* z 9.0) t))
        (t_3 (* (* t z) (/ -4.5 a))))
   (if (<= t_2 -1e+91)
     (* t (* z (/ -4.5 a)))
     (if (<= t_2 -2e+50)
       t_1
       (if (<= t_2 -1e-61)
         t_3
         (if (<= t_2 1e-58)
           t_1
           (if (<= t_2 2e+132) t_3 (* (/ t a) (* -4.5 z)))))))))

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 = ((0.5 * x) / a) * y;
	double t_2 = (z * 9.0) * t;
	double t_3 = (t * z) * (-4.5 / a);
	double tmp;
	if (t_2 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_2 <= -2e+50) {
		tmp = t_1;
	} else if (t_2 <= -1e-61) {
		tmp = t_3;
	} else if (t_2 <= 1e-58) {
		tmp = t_1;
	} else if (t_2 <= 2e+132) {
		tmp = t_3;
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	return tmp;
}

Fortran

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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((0.5d0 * x) / a) * y
    t_2 = (z * 9.0d0) * t
    t_3 = (t * z) * ((-4.5d0) / a)
    if (t_2 <= (-1d+91)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (t_2 <= (-2d+50)) then
        tmp = t_1
    else if (t_2 <= (-1d-61)) then
        tmp = t_3
    else if (t_2 <= 1d-58) then
        tmp = t_1
    else if (t_2 <= 2d+132) then
        tmp = t_3
    else
        tmp = (t / a) * ((-4.5d0) * z)
    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 = ((0.5 * x) / a) * y;
	double t_2 = (z * 9.0) * t;
	double t_3 = (t * z) * (-4.5 / a);
	double tmp;
	if (t_2 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_2 <= -2e+50) {
		tmp = t_1;
	} else if (t_2 <= -1e-61) {
		tmp = t_3;
	} else if (t_2 <= 1e-58) {
		tmp = t_1;
	} else if (t_2 <= 2e+132) {
		tmp = t_3;
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = ((0.5 * x) / a) * y
	t_2 = (z * 9.0) * t
	t_3 = (t * z) * (-4.5 / a)
	tmp = 0
	if t_2 <= -1e+91:
		tmp = t * (z * (-4.5 / a))
	elif t_2 <= -2e+50:
		tmp = t_1
	elif t_2 <= -1e-61:
		tmp = t_3
	elif t_2 <= 1e-58:
		tmp = t_1
	elif t_2 <= 2e+132:
		tmp = t_3
	else:
		tmp = (t / a) * (-4.5 * z)
	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(Float64(0.5 * x) / a) * y)
	t_2 = Float64(Float64(z * 9.0) * t)
	t_3 = Float64(Float64(t * z) * Float64(-4.5 / a))
	tmp = 0.0
	if (t_2 <= -1e+91)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_2 <= -2e+50)
		tmp = t_1;
	elseif (t_2 <= -1e-61)
		tmp = t_3;
	elseif (t_2 <= 1e-58)
		tmp = t_1;
	elseif (t_2 <= 2e+132)
		tmp = t_3;
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 = ((0.5 * x) / a) * y;
	t_2 = (z * 9.0) * t;
	t_3 = (t * z) * (-4.5 / a);
	tmp = 0.0;
	if (t_2 <= -1e+91)
		tmp = t * (z * (-4.5 / a));
	elseif (t_2 <= -2e+50)
		tmp = t_1;
	elseif (t_2 <= -1e-61)
		tmp = t_3;
	elseif (t_2 <= 1e-58)
		tmp = t_1;
	elseif (t_2 <= 2e+132)
		tmp = t_3;
	else
		tmp = (t / a) * (-4.5 * z);
	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[(N[(0.5 * x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+91], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+50], t$95$1, If[LessEqual[t$95$2, -1e-61], t$95$3, If[LessEqual[t$95$2, 1e-58], t$95$1, If[LessEqual[t$95$2, 2e+132], t$95$3, N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91

   1. Initial program 85.3%

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 85.0%

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

   9. Applied rewrites 85.2%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000002e50 or -1e-61 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e-58

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 79.4%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1e-61 or 1e-58 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999998e132

   1. Initial program 92.7%

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

   5. Applied rewrites 68.8%

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

   7. Applied rewrites 68.7%

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

   if 1.99999999999999998e132 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.6%

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

   5. Applied rewrites 81.4%

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

   7. Applied rewrites 92.7%

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

   9. Applied rewrites 93.0%

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

Alternative 8: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, t \cdot \left(\frac{z}{y} \cdot -4.5\right)\right)}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* (/ (fma 0.5 x (* t (* (/ z y) -4.5))) a) y)
     (if (<= t_1 1e+304)
       (/ (/ (fma (* -9.0 z) t (* y x)) a) 2.0)
       (* (* -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) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma(0.5, x, (t * ((z / y) * -4.5))) / a) * y;
	} else if (t_1 <= 1e+304) {
		tmp = (fma((-9.0 * z), t, (y * x)) / a) / 2.0;
	} else {
		tmp = (-4.5 * t) * (z / 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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(0.5, x, Float64(t * Float64(Float64(z / y) * -4.5))) / a) * y);
	elseif (t_1 <= 1e+304)
		tmp = Float64(Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / a) / 2.0);
	else
		tmp = Float64(Float64(-4.5 * t) * Float64(z / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(0.5 * x + N[(t * N[(N[(z / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], N[(N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $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 72.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999994e303

   1. Initial program 98.0%

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

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.5

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 98.5

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 98.5

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

   4. Applied rewrites 98.5%

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

   if 9.9999999999999994e303 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 64.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 61.6%

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

   7. Applied rewrites 84.5%

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

Alternative 9: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* (* z (/ t a)) -4.5)
     (if (<= t_1 2e+286)
       (/ (/ (fma (* -9.0 z) t (* y x)) a) 2.0)
       (* (/ t a) (* -4.5 z))))))

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 <= -((double) INFINITY)) {
		tmp = (z * (t / a)) * -4.5;
	} else if (t_1 <= 2e+286) {
		tmp = (fma((-9.0 * z), t, (y * x)) / a) / 2.0;
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(t / a)) * -4.5);
	elseif (t_1 <= 2e+286)
		tmp = Float64(Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / a) / 2.0);
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], N[(N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.0%

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 95.8%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2.00000000000000007e286

   1. Initial program 94.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 95.1

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 95.1

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 95.1

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

   4. Applied rewrites 95.1%

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

   if 2.00000000000000007e286 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 69.6%

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

   5. Applied rewrites 78.7%

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

   7. Applied rewrites 99.9%

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

   9. Applied rewrites 100.0%

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

Alternative 10: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-58}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -1e+91)
     (* t (* z (/ -4.5 a)))
     (if (<= t_1 1e-58)
       (* (* 0.5 x) (/ y a))
       (if (<= t_1 2e+132) (* (* t z) (/ -4.5 a)) (* (/ t a) (* -4.5 z)))))))

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 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 1e-58) {
		tmp = (0.5 * x) * (y / a);
	} else if (t_1 <= 2e+132) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	return tmp;
}

Fortran

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+91)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (t_1 <= 1d-58) then
        tmp = (0.5d0 * x) * (y / a)
    else if (t_1 <= 2d+132) then
        tmp = (t * z) * ((-4.5d0) / a)
    else
        tmp = (t / a) * ((-4.5d0) * z)
    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 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 1e-58) {
		tmp = (0.5 * x) * (y / a);
	} else if (t_1 <= 2e+132) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	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 <= -1e+91:
		tmp = t * (z * (-4.5 / a))
	elif t_1 <= 1e-58:
		tmp = (0.5 * x) * (y / a)
	elif t_1 <= 2e+132:
		tmp = (t * z) * (-4.5 / a)
	else:
		tmp = (t / a) * (-4.5 * z)
	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 <= -1e+91)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_1 <= 1e-58)
		tmp = Float64(Float64(0.5 * x) * Float64(y / a));
	elseif (t_1 <= 2e+132)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 <= -1e+91)
		tmp = t * (z * (-4.5 / a));
	elseif (t_1 <= 1e-58)
		tmp = (0.5 * x) * (y / a);
	elseif (t_1 <= 2e+132)
		tmp = (t * z) * (-4.5 / a);
	else
		tmp = (t / a) * (-4.5 * z);
	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, -1e+91], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-58], N[(N[(0.5 * x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+132], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91

   1. Initial program 85.3%

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 85.0%

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

   9. Applied rewrites 85.2%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e-58

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.8%

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

   10. Applied rewrites 73.2%

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

   if 1e-58 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999998e132

   1. Initial program 92.2%

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

   5. Applied rewrites 65.9%

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

   7. Applied rewrites 65.9%

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

   if 1.99999999999999998e132 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.6%

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

   5. Applied rewrites 81.4%

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

   7. Applied rewrites 92.7%

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

   9. Applied rewrites 93.0%

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

Alternative 11: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-58}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+117}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 -1e+91)
     (* t (* z (/ -4.5 a)))
     (if (<= t_1 1e-58)
       (* (* 0.5 x) (/ y a))
       (if (<= t_1 1e+117) (* (* t z) (/ -4.5 a)) (* (* -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) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 1e-58) {
		tmp = (0.5 * x) * (y / a);
	} else if (t_1 <= 1e+117) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (-4.5 * t) * (z / a);
	}
	return tmp;
}

Fortran

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+91)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (t_1 <= 1d-58) then
        tmp = (0.5d0 * x) * (y / a)
    else if (t_1 <= 1d+117) then
        tmp = (t * z) * ((-4.5d0) / a)
    else
        tmp = ((-4.5d0) * t) * (z / 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 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 1e-58) {
		tmp = (0.5 * x) * (y / a);
	} else if (t_1 <= 1e+117) {
		tmp = (t * z) * (-4.5 / a);
	} else {
		tmp = (-4.5 * t) * (z / 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 <= -1e+91:
		tmp = t * (z * (-4.5 / a))
	elif t_1 <= 1e-58:
		tmp = (0.5 * x) * (y / a)
	elif t_1 <= 1e+117:
		tmp = (t * z) * (-4.5 / a)
	else:
		tmp = (-4.5 * t) * (z / 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 <= -1e+91)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_1 <= 1e-58)
		tmp = Float64(Float64(0.5 * x) * Float64(y / a));
	elseif (t_1 <= 1e+117)
		tmp = Float64(Float64(t * z) * Float64(-4.5 / a));
	else
		tmp = Float64(Float64(-4.5 * t) * Float64(z / 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 <= -1e+91)
		tmp = t * (z * (-4.5 / a));
	elseif (t_1 <= 1e-58)
		tmp = (0.5 * x) * (y / a);
	elseif (t_1 <= 1e+117)
		tmp = (t * z) * (-4.5 / a);
	else
		tmp = (-4.5 * t) * (z / 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, -1e+91], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-58], N[(N[(0.5 * x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+117], N[(N[(t * z), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91

   1. Initial program 85.3%

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 85.0%

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

   9. Applied rewrites 85.2%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e-58

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.8%

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

   10. Applied rewrites 73.2%

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

   if 1e-58 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.00000000000000005e117

   1. Initial program 92.0%

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

   5. Applied rewrites 65.0%

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

   7. Applied rewrites 65.0%

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

   if 1.00000000000000005e117 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 84.0%

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 90.7%

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

Alternative 12: 95.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* (* z (/ t a)) -4.5)
     (if (<= t_1 2e+286)
       (* (fma (* -9.0 z) t (* y x)) (/ 0.5 a))
       (* (/ t a) (* -4.5 z))))))

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 <= -((double) INFINITY)) {
		tmp = (z * (t / a)) * -4.5;
	} else if (t_1 <= 2e+286) {
		tmp = fma((-9.0 * z), t, (y * x)) * (0.5 / a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(t / a)) * -4.5);
	elseif (t_1 <= 2e+286)
		tmp = Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.0%

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 95.8%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2.00000000000000007e286

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.9%

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

   if 2.00000000000000007e286 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 69.6%

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

   5. Applied rewrites 78.7%

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

   7. Applied rewrites 99.9%

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

   9. Applied rewrites 100.0%

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

Alternative 13: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot t, z, x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* (* z (/ t a)) -4.5)
     (if (<= t_1 2e+286)
       (* (fma (* -9.0 t) z (* x y)) (/ 0.5 a))
       (* (/ t a) (* -4.5 z))))))

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 <= -((double) INFINITY)) {
		tmp = (z * (t / a)) * -4.5;
	} else if (t_1 <= 2e+286) {
		tmp = fma((-9.0 * t), z, (x * y)) * (0.5 / a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(t / a)) * -4.5);
	elseif (t_1 <= 2e+286)
		tmp = Float64(fma(Float64(-9.0 * t), z, Float64(x * y)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], N[(N[(N[(-9.0 * t), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.0%

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 95.8%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2.00000000000000007e286

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.9%

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

   7. Applied rewrites 94.9%

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

   if 2.00000000000000007e286 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 69.6%

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

   5. Applied rewrites 78.7%

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

   7. Applied rewrites 99.9%

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

   9. Applied rewrites 100.0%

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

Alternative 14: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z \cdot \frac{t}{a}\right) \cdot -4.5\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot z, -9, x \cdot y\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* (* z (/ t a)) -4.5)
     (if (<= t_1 2e+286)
       (/ (fma (* t z) -9.0 (* x y)) (+ a a))
       (* (/ t a) (* -4.5 z))))))

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 <= -((double) INFINITY)) {
		tmp = (z * (t / a)) * -4.5;
	} else if (t_1 <= 2e+286) {
		tmp = fma((t * z), -9.0, (x * y)) / (a + a);
	} else {
		tmp = (t / a) * (-4.5 * z);
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(t / a)) * -4.5);
	elseif (t_1 <= 2e+286)
		tmp = Float64(fma(Float64(t * z), -9.0, Float64(x * y)) / Float64(a + a));
	else
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	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 * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], N[(N[(N[(t * z), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a + a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.0%

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 95.8%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2.00000000000000007e286

   1. Initial program 94.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 94.6

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

   4. Applied rewrites 94.6%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-neg.f64 N/A

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

      5. fp-cancel-sub-sign N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift-*.f64 N/A

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

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

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 94.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 94.7

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

   6. Applied rewrites 94.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 94.7

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

   8. Applied rewrites 94.7%

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

   if 2.00000000000000007e286 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 69.6%

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

   5. Applied rewrites 78.7%

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

   7. Applied rewrites 99.9%

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

   9. Applied rewrites 100.0%

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

Alternative 15: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+91} \lor \neg \left(t\_1 \leq 10^{+90}\right):\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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 (or (<= t_1 -1e+91) (not (<= t_1 1e+90)))
     (* t (* z (/ -4.5 a)))
     (* (* 0.5 x) (/ y 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 <= -1e+91) || !(t_1 <= 1e+90)) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (0.5 * x) * (y / a);
	}
	return tmp;
}

Fortran

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+91)) .or. (.not. (t_1 <= 1d+90))) then
        tmp = t * (z * ((-4.5d0) / a))
    else
        tmp = (0.5d0 * x) * (y / 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 <= -1e+91) || !(t_1 <= 1e+90)) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = (0.5 * x) * (y / 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 <= -1e+91) or not (t_1 <= 1e+90):
		tmp = t * (z * (-4.5 / a))
	else:
		tmp = (0.5 * x) * (y / 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 <= -1e+91) || !(t_1 <= 1e+90))
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	else
		tmp = Float64(Float64(0.5 * x) * Float64(y / 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 <= -1e+91) || ~((t_1 <= 1e+90)))
		tmp = t * (z * (-4.5 / a));
	else
		tmp = (0.5 * x) * (y / 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[Or[LessEqual[t$95$1, -1e+91], N[Not[LessEqual[t$95$1, 1e+90]], $MachinePrecision]], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91 or 9.99999999999999966e89 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 85.7%

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

   5. Applied rewrites 81.7%

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

   7. Applied rewrites 87.3%

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

   9. Applied rewrites 87.4%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 9.99999999999999966e89

   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 y around inf

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.6%

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

   10. Applied rewrites 67.1%

       \[\leadsto \color{blue}{\left(0.5 \cdot x\right) \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+91} \lor \neg \left(\left(z \cdot 9\right) \cdot t \leq 10^{+90}\right):\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+90}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 -1e+91)
     (* t (* z (/ -4.5 a)))
     (if (<= t_1 1e+90) (* (* 0.5 x) (/ y a)) (* (* -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) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 1e+90) {
		tmp = (0.5 * x) * (y / a);
	} else {
		tmp = (-4.5 * t) * (z / a);
	}
	return tmp;
}

Fortran

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+91)) then
        tmp = t * (z * ((-4.5d0) / a))
    else if (t_1 <= 1d+90) then
        tmp = (0.5d0 * x) * (y / a)
    else
        tmp = ((-4.5d0) * t) * (z / 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 <= -1e+91) {
		tmp = t * (z * (-4.5 / a));
	} else if (t_1 <= 1e+90) {
		tmp = (0.5 * x) * (y / a);
	} else {
		tmp = (-4.5 * t) * (z / 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 <= -1e+91:
		tmp = t * (z * (-4.5 / a))
	elif t_1 <= 1e+90:
		tmp = (0.5 * x) * (y / a)
	else:
		tmp = (-4.5 * t) * (z / 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 <= -1e+91)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	elseif (t_1 <= 1e+90)
		tmp = Float64(Float64(0.5 * x) * Float64(y / a));
	else
		tmp = Float64(Float64(-4.5 * t) * Float64(z / 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 <= -1e+91)
		tmp = t * (z * (-4.5 / a));
	elseif (t_1 <= 1e+90)
		tmp = (0.5 * x) * (y / a);
	else
		tmp = (-4.5 * t) * (z / 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, -1e+91], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+90], N[(N[(0.5 * x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -1.00000000000000008e91

   1. Initial program 85.3%

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 85.0%

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

   9. Applied rewrites 85.2%

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

   if -1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 9.99999999999999966e89

   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 y around inf

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.6%

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

   10. Applied rewrites 67.1%

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

   if 9.99999999999999966e89 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 86.3%

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

   5. Applied rewrites 84.4%

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

   7. Applied rewrites 90.1%

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

Alternative 17: 51.2% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = t * (z * ((-4.5d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.1%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 55.8%

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

7. Applied rewrites 56.2%

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

9. Applied rewrites 56.3%

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

Developer Target 1: 93.3% 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 2025019 
(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)))