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

Percentage Accurate: 79.1% → 88.8%

Time: 17.9s

Alternatives: 19

Speedup: 0.8×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, t\_1\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c}, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ (fma (* y x) 9.0 b) z) c)))
   (if (<= z -1e+59)
     (fma a (* t (/ -4.0 c)) t_1)
     (if (<= z 2.05e+157)
       (/ (+ (fma (* y x) 9.0 (* (* (* -4.0 z) a) t)) b) (* z c))
       (fma (* -4.0 t) (/ a c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fma((y * x), 9.0, b) / z) / c;
	double tmp;
	if (z <= -1e+59) {
		tmp = fma(a, (t * (-4.0 / c)), t_1);
	} else if (z <= 2.05e+157) {
		tmp = (fma((y * x), 9.0, (((-4.0 * z) * a) * t)) + b) / (z * c);
	} else {
		tmp = fma((-4.0 * t), (a / c), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c)
	tmp = 0.0
	if (z <= -1e+59)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), t_1);
	elseif (z <= 2.05e+157)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, Float64(Float64(Float64(-4.0 * z) * a) * t)) + b) / Float64(z * c));
	else
		tmp = fma(Float64(-4.0 * t), Float64(a / c), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1e+59], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 2.05e+157], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999972e58

   1. Initial program 46.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.2%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 84.1%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   if -9.99999999999999972e58 < z < 2.05000000000000008e157

   1. Initial program 94.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right)} \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{y \cdot \left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(y \cdot \color{blue}{\left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      11. associate-*r* N/A

          \[\leadsto \frac{\left(\color{blue}{\left(y \cdot x\right) \cdot 9} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      12. associate-*r* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\left(4 \cdot t\right) \cdot a\right)}\right) + b}{z \cdot c} \]

      13. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot t\right)\right) \cdot a}\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(4 \cdot t\right)\right)\right)} \cdot a\right) + b}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      18. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

   4. Applied rewrites 94.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right)} + b}{z \cdot c} \]

   if 2.05000000000000008e157 < z

   1. Initial program 46.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 93.4%

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

Alternative 2: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := t\_1 \leq \infty\\ t_3 := \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+112}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_2 (<= t_1 INFINITY))
        (t_3 (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c)))
   (if (<= t_1 5e+112)
     t_3
     (if t_2
       (/ (fma (* 9.0 x) y (fma (* -4.0 z) (* a t) b)) (* z c))
       (if t_2 t_3 (fma a (/ (* -4.0 t) c) (/ b (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	int t_2 = t_1 <= ((double) INFINITY);
	double t_3 = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c;
	double tmp;
	if (t_1 <= 5e+112) {
		tmp = t_3;
	} else if (t_2) {
		tmp = fma((9.0 * x), y, fma((-4.0 * z), (a * t), b)) / (z * c);
	} else if (t_2) {
		tmp = t_3;
	} else {
		tmp = fma(a, ((-4.0 * t) / c), (b / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = t_1 <= Inf
	t_3 = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c)
	tmp = 0.0
	if (t_1 <= 5e+112)
		tmp = t_3;
	elseif (t_2)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c));
	elseif (t_2)
		tmp = t_3;
	else
		tmp = fma(a, Float64(Float64(-4.0 * t) / c), Float64(b / Float64(z * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = LessEqual[t$95$1, Infinity]}, Block[{t$95$3 = N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+112], t$95$3, If[t$95$2, N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[t$95$2, t$95$3, N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 5e112 or +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   if 5e112 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      5. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a + b\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a + b\right)}{z \cdot c} \]

      13. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z \cdot 4\right), t \cdot a, b\right)}\right)}{z \cdot c} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{z \cdot 4}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

      16. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{4 \cdot z}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      18. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      19. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{-4} \cdot z, t \cdot a, b\right)\right)}{z \cdot c} \]

      20. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

      21. lower-*.f64 88.8

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

   4. Applied rewrites 88.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}}{z \cdot c} \]

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 77.7%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{c \cdot z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 80.8%

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

Alternative 3: 79.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(y \cdot x\right) \cdot 9\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, t\_1\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_2 \leq 10^{+273}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{t\_1}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* y x) 9.0)) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 (- INFINITY))
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_2 -2e+18)
       (/ (fma (* -4.0 z) (* a t) t_1) (* z c))
       (if (<= t_2 -1e-203)
         (fma a (* t (/ -4.0 c)) (/ b (* z c)))
         (if (<= t_2 2e+51)
           (/ (fma (* -4.0 t) a (/ b z)) c)
           (if (<= t_2 1e+273)
             (/ (fma (* -4.0 t) a (/ t_1 z)) c)
             (* (/ (* y 9.0) z) (/ x c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (y * x) * 9.0;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_2 <= -2e+18) {
		tmp = fma((-4.0 * z), (a * t), t_1) / (z * c);
	} else if (t_2 <= -1e-203) {
		tmp = fma(a, (t * (-4.0 / c)), (b / (z * c)));
	} else if (t_2 <= 2e+51) {
		tmp = fma((-4.0 * t), a, (b / z)) / c;
	} else if (t_2 <= 1e+273) {
		tmp = fma((-4.0 * t), a, (t_1 / z)) / c;
	} else {
		tmp = ((y * 9.0) / z) * (x / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(y * x) * 9.0)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_2 <= -2e+18)
		tmp = Float64(fma(Float64(-4.0 * z), Float64(a * t), t_1) / Float64(z * c));
	elseif (t_2 <= -1e-203)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), Float64(b / Float64(z * c)));
	elseif (t_2 <= 2e+51)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c);
	elseif (t_2 <= 1e+273)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(t_1 / z)) / c);
	else
		tmp = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+18], N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-203], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+51], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 1e+273], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 54.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18

   1. Initial program 85.9%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 77.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4 \cdot z, a \cdot t, \left(y \cdot x\right) \cdot 9\right)}}{z \cdot c} \]

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.1%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 85.0%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{c \cdot z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 92.2%

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right) \]

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e51

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.0%

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]

   if 2e51 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999945e272

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 82.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\left(y \cdot x\right) \cdot 9}{z}\right)}{c} \]

   if 9.99999999999999945e272 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 67.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.6%

      \[\leadsto \frac{y \cdot 9}{z} \cdot \color{blue}{\frac{x}{c}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 4: 78.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, t\_2\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (/ b (* z c))))
   (if (<= t_1 (- INFINITY))
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_1 -2e+18)
       (/ (fma (* -4.0 z) (* a t) (* (* y x) 9.0)) (* z c))
       (if (<= t_1 -1e-203)
         (fma a (* t (/ -4.0 c)) t_2)
         (if (<= t_1 1e+50)
           (/ (fma (* -4.0 t) a (/ b z)) c)
           (if (<= t_1 1e+156)
             (fma a (/ (* -4.0 t) c) t_2)
             (* (/ (* y 9.0) z) (/ x c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = b / (z * c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_1 <= -2e+18) {
		tmp = fma((-4.0 * z), (a * t), ((y * x) * 9.0)) / (z * c);
	} else if (t_1 <= -1e-203) {
		tmp = fma(a, (t * (-4.0 / c)), t_2);
	} else if (t_1 <= 1e+50) {
		tmp = fma((-4.0 * t), a, (b / z)) / c;
	} else if (t_1 <= 1e+156) {
		tmp = fma(a, ((-4.0 * t) / c), t_2);
	} else {
		tmp = ((y * 9.0) / z) * (x / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_1 <= -2e+18)
		tmp = Float64(fma(Float64(-4.0 * z), Float64(a * t), Float64(Float64(y * x) * 9.0)) / Float64(z * c));
	elseif (t_1 <= -1e-203)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), t_2);
	elseif (t_1 <= 1e+50)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c);
	elseif (t_1 <= 1e+156)
		tmp = fma(a, Float64(Float64(-4.0 * t) / c), t_2);
	else
		tmp = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+18], N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-203], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 1e+50], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+156], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 54.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18

   1. Initial program 85.9%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 77.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4 \cdot z, a \cdot t, \left(y \cdot x\right) \cdot 9\right)}}{z \cdot c} \]

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.1%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 85.0%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{c \cdot z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 92.2%

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right) \]

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e50

   1. Initial program 78.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.9%

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]

   if 1.0000000000000001e50 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 75.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.1%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{c \cdot z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 79.7%

       \[\leadsto \mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{z \cdot c}\right) \]

   if 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 66.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.9%

      \[\leadsto \frac{y \cdot 9}{z} \cdot \color{blue}{\frac{x}{c}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 5: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := \frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+126}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, t\_2\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ b (* z c)))
        (t_3 (* (/ (* y 9.0) z) (/ x c))))
   (if (<= t_1 -1e+126)
     t_3
     (if (<= t_1 -1e-203)
       (fma a (* t (/ -4.0 c)) t_2)
       (if (<= t_1 1e+50)
         (/ (fma (* -4.0 t) a (/ b z)) c)
         (if (<= t_1 1e+156) (fma a (/ (* -4.0 t) c) t_2) t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = b / (z * c);
	double t_3 = ((y * 9.0) / z) * (x / c);
	double tmp;
	if (t_1 <= -1e+126) {
		tmp = t_3;
	} else if (t_1 <= -1e-203) {
		tmp = fma(a, (t * (-4.0 / c)), t_2);
	} else if (t_1 <= 1e+50) {
		tmp = fma((-4.0 * t), a, (b / z)) / c;
	} else if (t_1 <= 1e+156) {
		tmp = fma(a, ((-4.0 * t) / c), t_2);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(b / Float64(z * c))
	t_3 = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c))
	tmp = 0.0
	if (t_1 <= -1e+126)
		tmp = t_3;
	elseif (t_1 <= -1e-203)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), t_2);
	elseif (t_1 <= 1e+50)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c);
	elseif (t_1 <= 1e+156)
		tmp = fma(a, Float64(Float64(-4.0 * t) / c), t_2);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+126], t$95$3, If[LessEqual[t$95$1, -1e-203], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 1e+50], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+156], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999925e125 or 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.5%

      \[\leadsto \frac{y \cdot 9}{z} \cdot \color{blue}{\frac{x}{c}} \]

   if -9.99999999999999925e125 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203

   1. Initial program 83.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 83.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.7%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 87.6%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{c \cdot z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 82.1%

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right) \]

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e50

   1. Initial program 78.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.9%

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]

   if 1.0000000000000001e50 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 75.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.1%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{c \cdot z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 79.7%

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

Alternative 6: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := \frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+126}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_2 \leq 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma a (* t (/ -4.0 c)) (/ b (* z c))))
        (t_2 (* (* x 9.0) y))
        (t_3 (* (/ (* y 9.0) z) (/ x c))))
   (if (<= t_2 -1e+126)
     t_3
     (if (<= t_2 -1e-203)
       t_1
       (if (<= t_2 1e+50)
         (/ (fma (* -4.0 t) a (/ b z)) c)
         (if (<= t_2 1e+156) t_1 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(a, (t * (-4.0 / c)), (b / (z * c)));
	double t_2 = (x * 9.0) * y;
	double t_3 = ((y * 9.0) / z) * (x / c);
	double tmp;
	if (t_2 <= -1e+126) {
		tmp = t_3;
	} else if (t_2 <= -1e-203) {
		tmp = t_1;
	} else if (t_2 <= 1e+50) {
		tmp = fma((-4.0 * t), a, (b / z)) / c;
	} else if (t_2 <= 1e+156) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(a, Float64(t * Float64(-4.0 / c)), Float64(b / Float64(z * c)))
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c))
	tmp = 0.0
	if (t_2 <= -1e+126)
		tmp = t_3;
	elseif (t_2 <= -1e-203)
		tmp = t_1;
	elseif (t_2 <= 1e+50)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c);
	elseif (t_2 <= 1e+156)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+126], t$95$3, If[LessEqual[t$95$2, -1e-203], t$95$1, If[LessEqual[t$95$2, 1e+50], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 1e+156], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999925e125 or 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.5%

      \[\leadsto \frac{y \cdot 9}{z} \cdot \color{blue}{\frac{x}{c}} \]

   if -9.99999999999999925e125 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203 or 1.0000000000000001e50 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.0%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 86.9%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{c \cdot z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 81.5%

       \[\leadsto \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right) \]

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e50

   1. Initial program 78.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.9%

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

Alternative 7: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) INFINITY)
   (/ (fma (* 9.0 x) y (fma (* -4.0 z) (* a t) b)) (* z c))
   (fma a (/ (* -4.0 t) c) (/ b (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)) <= ((double) INFINITY)) {
		tmp = fma((9.0 * x), y, fma((-4.0 * z), (a * t), b)) / (z * c);
	} else {
		tmp = fma(a, ((-4.0 * t) / c), (b / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c)) <= Inf)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c));
	else
		tmp = fma(a, Float64(Float64(-4.0 * t) / c), Float64(b / Float64(z * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      5. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a + b\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a + b\right)}{z \cdot c} \]

      13. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z \cdot 4\right), t \cdot a, b\right)}\right)}{z \cdot c} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{z \cdot 4}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

      16. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{4 \cdot z}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      18. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      19. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{-4} \cdot z, t \cdot a, b\right)\right)}{z \cdot c} \]

      20. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

      21. lower-*.f64 87.0

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

   4. Applied rewrites 87.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}}{z \cdot c} \]

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 77.7%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, \frac{b}{c \cdot z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 80.8%

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

Alternative 8: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+156}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -1e+215)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_1 -5e-17)
       (/ (fma (* 9.0 x) y b) (* z c))
       (if (<= t_1 1e+156)
         (/ (fma -4.0 (* (* t z) a) b) (* z c))
         (* (/ (* y 9.0) z) (/ x c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -1e+215) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_1 <= -5e-17) {
		tmp = fma((9.0 * x), y, b) / (z * c);
	} else if (t_1 <= 1e+156) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else {
		tmp = ((y * 9.0) / z) * (x / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -1e+215)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_1 <= -5e-17)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	elseif (t_1 <= 1e+156)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+215], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-17], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+156], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999907e214

   1. Initial program 69.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]

   if -9.99999999999999907e214 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-17

   1. Initial program 83.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      5. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a + b\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a + b\right)}{z \cdot c} \]

      13. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z \cdot 4\right), t \cdot a, b\right)}\right)}{z \cdot c} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{z \cdot 4}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

      16. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{4 \cdot z}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      18. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      19. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{-4} \cdot z, t \cdot a, b\right)\right)}{z \cdot c} \]

      20. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

      21. lower-*.f64 84.1

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

   4. Applied rewrites 84.1%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}}{z \cdot c} \]

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 69.3%

      \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{b}\right)}{z \cdot c} \]

   if -4.9999999999999999e-17 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 74.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}}{z \cdot c} \]

   if 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 66.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.9%

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

Alternative 9: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(9 \cdot x\right) \cdot \frac{y}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+156}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* 9.0 x) (/ y (* c z)))))
   (if (<= t_1 -2e+18)
     t_2
     (if (<= t_1 2e-306)
       (/ b (* z c))
       (if (<= t_1 1e+156) (* -4.0 (/ (* a t) c)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (9.0 * x) * (y / (c * z));
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 2e-306) {
		tmp = b / (z * c);
	} else if (t_1 <= 1e+156) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = (9.0d0 * x) * (y / (c * z))
    if (t_1 <= (-2d+18)) then
        tmp = t_2
    else if (t_1 <= 2d-306) then
        tmp = b / (z * c)
    else if (t_1 <= 1d+156) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (9.0 * x) * (y / (c * z));
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 2e-306) {
		tmp = b / (z * c);
	} else if (t_1 <= 1e+156) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = (9.0 * x) * (y / (c * z))
	tmp = 0
	if t_1 <= -2e+18:
		tmp = t_2
	elif t_1 <= 2e-306:
		tmp = b / (z * c)
	elif t_1 <= 1e+156:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(9.0 * x) * Float64(y / Float64(c * z)))
	tmp = 0.0
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 2e-306)
		tmp = Float64(b / Float64(z * c));
	elseif (t_1 <= 1e+156)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = (9.0 * x) * (y / (c * z));
	tmp = 0.0;
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 2e-306)
		tmp = b / (z * c);
	elseif (t_1 <= 1e+156)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * x), $MachinePrecision] * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+18], t$95$2, If[LessEqual[t$95$1, 2e-306], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+156], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18 or 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 70.2%

      \[\leadsto \left(9 \cdot x\right) \cdot \color{blue}{\frac{y}{c \cdot z}} \]

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000006e-306

   1. Initial program 83.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 60.5%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]

   if 2.00000000000000006e-306 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := x \cdot \frac{y \cdot 9}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+156}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* x (/ (* y 9.0) (* c z)))))
   (if (<= t_1 -2e+18)
     t_2
     (if (<= t_1 2e-306)
       (/ b (* z c))
       (if (<= t_1 1e+156) (* -4.0 (/ (* a t) c)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = x * ((y * 9.0) / (c * z));
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 2e-306) {
		tmp = b / (z * c);
	} else if (t_1 <= 1e+156) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = x * ((y * 9.0d0) / (c * z))
    if (t_1 <= (-2d+18)) then
        tmp = t_2
    else if (t_1 <= 2d-306) then
        tmp = b / (z * c)
    else if (t_1 <= 1d+156) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = x * ((y * 9.0) / (c * z));
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 2e-306) {
		tmp = b / (z * c);
	} else if (t_1 <= 1e+156) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = x * ((y * 9.0) / (c * z))
	tmp = 0
	if t_1 <= -2e+18:
		tmp = t_2
	elif t_1 <= 2e-306:
		tmp = b / (z * c)
	elif t_1 <= 1e+156:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(x * Float64(Float64(y * 9.0) / Float64(c * z)))
	tmp = 0.0
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 2e-306)
		tmp = Float64(b / Float64(z * c));
	elseif (t_1 <= 1e+156)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = x * ((y * 9.0) / (c * z));
	tmp = 0.0;
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 2e-306)
		tmp = b / (z * c);
	elseif (t_1 <= 1e+156)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * 9.0), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+18], t$95$2, If[LessEqual[t$95$1, 2e-306], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+156], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18 or 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 70.0%

      \[\leadsto x \cdot \color{blue}{\frac{y \cdot 9}{c \cdot z}} \]

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000006e-306

   1. Initial program 83.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 60.5%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]

   if 2.00000000000000006e-306 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* 9.0 (/ (* x y) (* z c)))))
   (if (<= t_1 -2e+18)
     t_2
     (if (<= t_1 2e-306)
       (/ b (* z c))
       (if (<= t_1 1.05e+38) (* -4.0 (/ (* a t) c)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = 9.0 * ((x * y) / (z * c));
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 2e-306) {
		tmp = b / (z * c);
	} else if (t_1 <= 1.05e+38) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = 9.0d0 * ((x * y) / (z * c))
    if (t_1 <= (-2d+18)) then
        tmp = t_2
    else if (t_1 <= 2d-306) then
        tmp = b / (z * c)
    else if (t_1 <= 1.05d+38) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = 9.0 * ((x * y) / (z * c));
	double tmp;
	if (t_1 <= -2e+18) {
		tmp = t_2;
	} else if (t_1 <= 2e-306) {
		tmp = b / (z * c);
	} else if (t_1 <= 1.05e+38) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = 9.0 * ((x * y) / (z * c))
	tmp = 0
	if t_1 <= -2e+18:
		tmp = t_2
	elif t_1 <= 2e-306:
		tmp = b / (z * c)
	elif t_1 <= 1.05e+38:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))
	tmp = 0.0
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 2e-306)
		tmp = Float64(b / Float64(z * c));
	elseif (t_1 <= 1.05e+38)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = 9.0 * ((x * y) / (z * c));
	tmp = 0.0;
	if (t_1 <= -2e+18)
		tmp = t_2;
	elseif (t_1 <= 2e-306)
		tmp = b / (z * c);
	elseif (t_1 <= 1.05e+38)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+18], t$95$2, If[LessEqual[t$95$1, 2e-306], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.05e+38], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18 or 1.05e38 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 74.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 61.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 56.0%

      \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{\frac{9}{c \cdot z}} \]
   8. Step-by-step derivation

   9. Applied rewrites 56.0%

      \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]
   10. Step-by-step derivation

   11. Applied rewrites 56.0%

       \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot y}{z \cdot c}} \]

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000006e-306

   1. Initial program 83.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 60.5%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]

   if 2.00000000000000006e-306 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.05e38

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 56.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+59} \lor \neg \left(z \leq 4 \cdot 10^{+85}\right):\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1e+59) (not (<= z 4e+85)))
   (fma a (* t (/ -4.0 c)) (/ (/ (fma (* y x) 9.0 b) z) c))
   (/ (+ (fma (* y x) 9.0 (* (* (* -4.0 z) a) t)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e+59) || !(z <= 4e+85)) {
		tmp = fma(a, (t * (-4.0 / c)), ((fma((y * x), 9.0, b) / z) / c));
	} else {
		tmp = (fma((y * x), 9.0, (((-4.0 * z) * a) * t)) + b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1e+59) || !(z <= 4e+85))
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c));
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, Float64(Float64(Float64(-4.0 * z) * a) * t)) + b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1e+59], N[Not[LessEqual[z, 4e+85]], $MachinePrecision]], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999972e58 or 4.0000000000000001e85 < z

   1. Initial program 49.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 86.8%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 86.7%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   if -9.99999999999999972e58 < z < 4.0000000000000001e85

   1. Initial program 95.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right)} \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{y \cdot \left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(y \cdot \color{blue}{\left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      11. associate-*r* N/A

          \[\leadsto \frac{\left(\color{blue}{\left(y \cdot x\right) \cdot 9} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      12. associate-*r* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\left(4 \cdot t\right) \cdot a\right)}\right) + b}{z \cdot c} \]

      13. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot t\right)\right) \cdot a}\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(4 \cdot t\right)\right)\right)} \cdot a\right) + b}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      18. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

   4. Applied rewrites 95.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+59} \lor \neg \left(z \leq 4 \cdot 10^{+85}\right):\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, t\_1\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-4 \cdot t}{c}, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ (fma (* y x) 9.0 b) z) c)))
   (if (<= z -1e+59)
     (fma a (* t (/ -4.0 c)) t_1)
     (if (<= z 4e+85)
       (/ (+ (fma (* y x) 9.0 (* (* (* -4.0 z) a) t)) b) (* z c))
       (fma a (/ (* -4.0 t) c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fma((y * x), 9.0, b) / z) / c;
	double tmp;
	if (z <= -1e+59) {
		tmp = fma(a, (t * (-4.0 / c)), t_1);
	} else if (z <= 4e+85) {
		tmp = (fma((y * x), 9.0, (((-4.0 * z) * a) * t)) + b) / (z * c);
	} else {
		tmp = fma(a, ((-4.0 * t) / c), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c)
	tmp = 0.0
	if (z <= -1e+59)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), t_1);
	elseif (z <= 4e+85)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, Float64(Float64(Float64(-4.0 * z) * a) * t)) + b) / Float64(z * c));
	else
		tmp = fma(a, Float64(Float64(-4.0 * t) / c), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1e+59], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 4e+85], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999972e58

   1. Initial program 46.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.2%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\frac{-4 \cdot t}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 84.1%

      \[\leadsto \mathsf{fma}\left(a, t \cdot \color{blue}{\frac{-4}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\right) \]

   if -9.99999999999999972e58 < z < 4.0000000000000001e85

   1. Initial program 95.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right)} \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{y \cdot \left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(y \cdot \color{blue}{\left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      11. associate-*r* N/A

          \[\leadsto \frac{\left(\color{blue}{\left(y \cdot x\right) \cdot 9} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      12. associate-*r* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\left(4 \cdot t\right) \cdot a\right)}\right) + b}{z \cdot c} \]

      13. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot t\right)\right) \cdot a}\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(4 \cdot t\right)\right)\right)} \cdot a\right) + b}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      18. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

   4. Applied rewrites 95.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right)} + b}{z \cdot c} \]

   if 4.0000000000000001e85 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 83.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 89.5%

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

Alternative 14: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+126} \lor \neg \left(t\_1 \leq 10^{+156}\right):\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (or (<= t_1 -1e+126) (not (<= t_1 1e+156)))
     (* (/ (* y 9.0) z) (/ x c))
     (/ (fma (* -4.0 t) a (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -1e+126) || !(t_1 <= 1e+156)) {
		tmp = ((y * 9.0) / z) * (x / c);
	} else {
		tmp = fma((-4.0 * t), a, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if ((t_1 <= -1e+126) || !(t_1 <= 1e+156))
		tmp = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c));
	else
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+126], N[Not[LessEqual[t$95$1, 1e+156]], $MachinePrecision]], N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999925e125 or 9.9999999999999998e155 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.5%

      \[\leadsto \frac{y \cdot 9}{z} \cdot \color{blue}{\frac{x}{c}} \]

   if -9.99999999999999925e125 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e155

   1. Initial program 80.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.4%

      \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -1 \cdot 10^{+126} \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 10^{+156}\right):\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+58} \lor \neg \left(z \leq 4.5 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5.5e+58) (not (<= z 4.5e+78)))
   (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c)
   (/ (+ (fma (* y x) 9.0 (* (* (* -4.0 z) a) t)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.5e+58) || !(z <= 4.5e+78)) {
		tmp = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = (fma((y * x), 9.0, (((-4.0 * z) * a) * t)) + b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5.5e+58) || !(z <= 4.5e+78))
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, Float64(Float64(Float64(-4.0 * z) * a) * t)) + b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5.5e+58], N[Not[LessEqual[z, 4.5e+78]], $MachinePrecision]], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999999e58 or 4.4999999999999999e78 < z

   1. Initial program 49.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   if -5.4999999999999999e58 < z < 4.4999999999999999e78

   1. Initial program 95.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right)} \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{y \cdot \left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(y \cdot \color{blue}{\left(x \cdot 9\right)} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      11. associate-*r* N/A

          \[\leadsto \frac{\left(\color{blue}{\left(y \cdot x\right) \cdot 9} + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z \cdot c} \]

      12. associate-*r* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\left(4 \cdot t\right) \cdot a\right)}\right) + b}{z \cdot c} \]

      13. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(4 \cdot t\right)\right) \cdot a}\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(4 \cdot t\right)\right)\right)} \cdot a\right) + b}{z \cdot c} \]

      15. associate-*l* N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

      18. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right) + b}{z \cdot c} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a\right) + b}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

   4. Applied rewrites 95.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+58} \lor \neg \left(z \leq 4.5 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58} \lor \neg \left(z \leq 3.6 \cdot 10^{+125}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5e+58) (not (<= z 3.6e+125)))
   (* -4.0 (/ (* a t) c))
   (/ (fma (* 9.0 x) y b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e+58) || !(z <= 3.6e+125)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = fma((9.0 * x), y, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e+58) || !(z <= 3.6e+125))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5e+58], N[Not[LessEqual[z, 3.6e+125]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999986e58 or 3.6000000000000003e125 < z

   1. Initial program 48.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 63.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -4.99999999999999986e58 < z < 3.6000000000000003e125

   1. Initial program 94.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      5. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{x \cdot 9}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{9 \cdot x}, y, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a + b\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a + b\right)}{z \cdot c} \]

      13. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z \cdot 4\right), t \cdot a, b\right)}\right)}{z \cdot c} \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{z \cdot 4}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

      16. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{4 \cdot z}\right), t \cdot a, b\right)\right)}{z \cdot c} \]

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

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      18. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot z}, t \cdot a, b\right)\right)}{z \cdot c} \]

      19. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\color{blue}{-4} \cdot z, t \cdot a, b\right)\right)}{z \cdot c} \]

      20. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

      21. lower-*.f64 93.0

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, \color{blue}{a \cdot t}, b\right)\right)}{z \cdot c} \]

   4. Applied rewrites 93.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}}{z \cdot c} \]

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 79.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58} \lor \neg \left(z \leq 3.6 \cdot 10^{+125}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58} \lor \neg \left(z \leq 3.6 \cdot 10^{+125}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5e+58) (not (<= z 3.6e+125)))
   (* -4.0 (/ (* a t) c))
   (/ (fma (* y x) 9.0 b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e+58) || !(z <= 3.6e+125)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e+58) || !(z <= 3.6e+125))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5e+58], N[Not[LessEqual[z, 3.6e+125]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999986e58 or 3.6000000000000003e125 < z

   1. Initial program 48.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 63.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -4.99999999999999986e58 < z < 3.6000000000000003e125

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 79.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58} \lor \neg \left(z \leq 3.6 \cdot 10^{+125}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+26} \lor \neg \left(t \leq 4 \cdot 10^{-92}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.8e+26) (not (<= t 4e-92)))
   (* -4.0 (/ (* a t) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.8e+26) || !(t <= 4e-92)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-3.8d+26)) .or. (.not. (t <= 4d-92))) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.8e+26) || !(t <= 4e-92)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.8e+26) or not (t <= 4e-92):
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.8e+26) || !(t <= 4e-92))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3.8e+26) || ~((t <= 4e-92)))
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.8e+26], N[Not[LessEqual[t, 4e-92]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000002e26 or 3.99999999999999995e-92 < t

   1. Initial program 70.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -3.8000000000000002e26 < t < 3.99999999999999995e-92

   1. Initial program 87.4%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 49.8%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+26} \lor \neg \left(t \leq 4 \cdot 10^{-92}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.3% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, b, and c 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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.4%

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

3. Taylor expanded in b around inf

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
4. Step-by-step derivation

5. Applied rewrites 36.2%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
6. Add Preprocessing

Developer Target 1: 80.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	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, b, c)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2025020 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))