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

Percentage Accurate: 78.9% → 85.9%

Time: 10.2s

Alternatives: 19

Speedup: 0.9×

• 37.3% 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: 78.9% 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: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot z\right)\\ t_2 := t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \mathsf{fma}\left(9, \frac{x \cdot y}{t\_1}, \frac{b}{t\_1}\right)\right)\\ \mathbf{if}\;z \leq -7.3 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* c (* t z)))
        (t_2 (* t (fma -4.0 (/ a c) (fma 9.0 (/ (* x y) t_1) (/ b t_1))))))
   (if (<= z -7.3e+87)
     t_2
     (if (<= z 2.25e+86)
       (/ (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) c) z)
       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 = c * (t * z);
	double t_2 = t * fma(-4.0, (a / c), fma(9.0, ((x * y) / t_1), (b / t_1)));
	double tmp;
	if (z <= -7.3e+87) {
		tmp = t_2;
	} else if (z <= 2.25e+86) {
		tmp = (fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / c) / z;
	} 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(c * Float64(t * z))
	t_2 = Float64(t * fma(-4.0, Float64(a / c), fma(9.0, Float64(Float64(x * y) / t_1), Float64(b / t_1))))
	tmp = 0.0
	if (z <= -7.3e+87)
		tmp = t_2;
	elseif (z <= 2.25e+86)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / c) / z);
	else
		tmp = t_2;
	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[(c * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(-4.0 * N[(a / c), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.3e+87], t$95$2, If[LessEqual[z, 2.25e+86], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.29999999999999997e87 or 2.24999999999999996e86 < z

   1. Initial program 78.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 70.5

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

   4. Applied rewrites 70.5%

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

   if -7.29999999999999997e87 < z < 2.24999999999999996e86

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. lift-*.f64 N/A

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

      23. associate-*r* N/A

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

      24. lower-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

Alternative 2: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b - a \cdot \left(t \cdot \left(4 \cdot z\right)\right)\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, -4 \cdot \left(z \cdot \left(a \cdot t\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, 9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)}\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t_1 2e-153)
     (/ (/ (fma (* y x) 9.0 (- b (* a (* t (* 4.0 z))))) c) z)
     (if (<= t_1 INFINITY)
       (/ (+ (fma (* y 9.0) x (* -4.0 (* z (* a t)))) b) (* z c))
       (* t (fma -4.0 (/ a c) (* 9.0 (/ (* x y) (* c (* t z))))))))))

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);
	double tmp;
	if (t_1 <= 2e-153) {
		tmp = (fma((y * x), 9.0, (b - (a * (t * (4.0 * z))))) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma((y * 9.0), x, (-4.0 * (z * (a * t)))) + b) / (z * c);
	} else {
		tmp = t * fma(-4.0, (a / c), (9.0 * ((x * y) / (c * (t * z)))));
	}
	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))
	tmp = 0.0
	if (t_1 <= 2e-153)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, Float64(b - Float64(a * Float64(t * Float64(4.0 * z))))) / c) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(Float64(y * 9.0), x, Float64(-4.0 * Float64(z * Float64(a * t)))) + b) / Float64(z * c));
	else
		tmp = Float64(t * fma(-4.0, Float64(a / c), Float64(9.0 * Float64(Float64(x * y) / Float64(c * Float64(t * z))))));
	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]}, If[LessEqual[t$95$1, 2e-153], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(b - N[(a * N[(t * N[(4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(-4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < 2.00000000000000008e-153

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   if 2.00000000000000008e-153 < (/.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 78.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 80.1

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

   3. Applied rewrites 80.1%

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

   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 78.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 56.4

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 60.2

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

   7. Applied rewrites 60.2%

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

Alternative 3: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 3.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, -4 \cdot \left(z \cdot \left(a \cdot t\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b - a \cdot \left(t \cdot \left(4 \cdot z\right)\right)\right)}{c}}{z}\\ \end{array} \end{array} \]

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 (<= c 3.9e-81)
   (/ (+ (fma (* y 9.0) x (* -4.0 (* z (* a t)))) b) (* z c))
   (/ (/ (fma (* y x) 9.0 (- b (* a (* t (* 4.0 z))))) c) z)))

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 (c <= 3.9e-81) {
		tmp = (fma((y * 9.0), x, (-4.0 * (z * (a * t)))) + b) / (z * c);
	} else {
		tmp = (fma((y * x), 9.0, (b - (a * (t * (4.0 * z))))) / c) / z;
	}
	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 (c <= 3.9e-81)
		tmp = Float64(Float64(fma(Float64(y * 9.0), x, Float64(-4.0 * Float64(z * Float64(a * t)))) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, Float64(b - Float64(a * Float64(t * Float64(4.0 * z))))) / c) / z);
	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[c, 3.9e-81], N[(N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(-4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(b - N[(a * N[(t * N[(4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 3.89999999999999985e-81

   1. Initial program 78.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 80.1

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

   3. Applied rewrites 80.1%

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

   if 3.89999999999999985e-81 < c

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

Alternative 4: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, -4 \cdot \left(z \cdot \left(a \cdot t\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

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) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 5e-168)
     (/ (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) c) z)
     (if (<= t_1 INFINITY)
       (/ (+ (fma (* y 9.0) x (* -4.0 (* z (* a t)))) b) (* z c))
       (* -4.0 (/ (* a t) 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);
	double tmp;
	if (t_1 <= 5e-168) {
		tmp = (fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma((y * 9.0), x, (-4.0 * (z * (a * t)))) + b) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / 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))
	tmp = 0.0
	if (t_1 <= 5e-168)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / c) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(Float64(y * 9.0), x, Float64(-4.0 * Float64(z * Float64(a * t)))) + b) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / 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]}, If[LessEqual[t$95$1, 5e-168], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(-4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $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)) < 5.00000000000000001e-168

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. lift-*.f64 N/A

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

      23. associate-*r* N/A

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

      24. lower-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

   if 5.00000000000000001e-168 < (/.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 78.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 80.1

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

   3. Applied rewrites 80.1%

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

   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 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

Alternative 5: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, b - a \cdot \left(t \cdot \left(4 \cdot z\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

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) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 5e-168)
     (/ (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) c) z)
     (if (<= t_1 INFINITY)
       (/ (fma (* y 9.0) x (- b (* a (* t (* 4.0 z))))) (* z c))
       (* -4.0 (/ (* a t) 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);
	double tmp;
	if (t_1 <= 5e-168) {
		tmp = (fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((y * 9.0), x, (b - (a * (t * (4.0 * z))))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / 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))
	tmp = 0.0
	if (t_1 <= 5e-168)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / c) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(y * 9.0), x, Float64(b - Float64(a * Float64(t * Float64(4.0 * z))))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / 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]}, If[LessEqual[t$95$1, 5e-168], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(b - N[(a * N[(t * N[(4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $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)) < 5.00000000000000001e-168

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. lift-*.f64 N/A

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

      23. associate-*r* N/A

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

      24. lower-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

   if 5.00000000000000001e-168 < (/.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 78.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. associate-+l- N/A

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

      4. sub-flip N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 79.2

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 79.2

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 79.2

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 79.2

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

   3. Applied rewrites 79.2%

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

   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 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

Alternative 6: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b - a \cdot \left(t \cdot \left(4 \cdot z\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

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) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 5e-168)
     (/ (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) c) z)
     (if (<= t_1 INFINITY)
       (/ (fma (* 9.0 x) y (- b (* a (* t (* 4.0 z))))) (* z c))
       (* -4.0 (/ (* a t) 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);
	double tmp;
	if (t_1 <= 5e-168) {
		tmp = (fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((9.0 * x), y, (b - (a * (t * (4.0 * z))))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / 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))
	tmp = 0.0
	if (t_1 <= 5e-168)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / c) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(9.0 * x), y, Float64(b - Float64(a * Float64(t * Float64(4.0 * z))))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / 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]}, If[LessEqual[t$95$1, 5e-168], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(b - N[(a * N[(t * N[(4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $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)) < 5.00000000000000001e-168

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. lift-*.f64 N/A

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

      23. associate-*r* N/A

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

      24. lower-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

   if 5.00000000000000001e-168 < (/.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 78.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. associate-+l- N/A

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

      4. sub-flip N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower--.f64 79.2

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.2

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 79.2

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 79.2

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

   3. Applied rewrites 79.2%

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

   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 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

Alternative 7: 80.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+223}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c}}{z}\\ \end{array} \end{array} \]

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 (<= z -2.6e+223)
   (* -4.0 (/ (* a t) c))
   (/ (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) c) z)))

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 <= -2.6e+223) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = (fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / c) / z;
	}
	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 <= -2.6e+223)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / c) / z);
	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[z, -2.6e+223], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e223

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

   if -2.6000000000000002e223 < z

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. lift-*.f64 N/A

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

      23. associate-*r* N/A

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

      24. lower-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

Alternative 8: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9 \cdot x, y, \left(\left(t \cdot a\right) \cdot z\right) \cdot -4\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{9 \cdot x}{c}, \frac{y}{z}, \frac{b}{c \cdot z}\right)\\ \end{array} \end{array} \]

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)))
   (if (<= t_1 -5e-43)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= t_1 2e-36)
       (/ (/ (- b (* 4.0 (* a (* t z)))) c) z)
       (if (<= t_1 2e+225)
         (/ (/ (fma (* 9.0 x) y (* (* (* t a) z) -4.0)) c) z)
         (fma (/ (* 9.0 x) c) (/ y z) (/ b (* c z))))))))

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 <= -5e-43) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t_1 <= 2e-36) {
		tmp = ((b - (4.0 * (a * (t * z)))) / c) / z;
	} else if (t_1 <= 2e+225) {
		tmp = (fma((9.0 * x), y, (((t * a) * z) * -4.0)) / c) / z;
	} else {
		tmp = fma(((9.0 * x) / c), (y / z), (b / (c * z)));
	}
	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 <= -5e-43)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (t_1 <= 2e-36)
		tmp = Float64(Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / c) / z);
	elseif (t_1 <= 2e+225)
		tmp = Float64(Float64(fma(Float64(9.0 * x), y, Float64(Float64(Float64(t * a) * z) * -4.0)) / c) / z);
	else
		tmp = fma(Float64(Float64(9.0 * x) / c), Float64(y / z), Float64(b / Float64(c * z)));
	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, -5e-43], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-36], N[(N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+225], N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(N[(t * a), $MachinePrecision] * z), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000019e-43

   1. Initial program 78.9%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.7

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

   4. Applied rewrites 59.7%

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

   if -5.00000000000000019e-43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e-36

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 55.9

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

   6. Applied rewrites 55.9%

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

   if 1.9999999999999999e-36 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999986e225

   1. Initial program 78.9%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 56.4

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

   4. Applied rewrites 56.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

   6. Applied rewrites 57.7%

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

   if 1.99999999999999986e225 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 78.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 57.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. div-add N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. times-frac N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-/.f64 N/A

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

   8. Applied rewrites 54.4%

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

Alternative 9: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \end{array} \]

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 -5e-43)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= t_1 5e-57)
       (/ (/ (- b (* 4.0 (* a (* t z)))) c) z)
       (/ (/ (fma (* y x) 9.0 b) c) z)))))

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 <= -5e-43) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t_1 <= 5e-57) {
		tmp = ((b - (4.0 * (a * (t * z)))) / c) / z;
	} else {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	}
	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 <= -5e-43)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (t_1 <= 5e-57)
		tmp = Float64(Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / c) / z);
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	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, -5e-43], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-57], N[(N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000019e-43

   1. Initial program 78.9%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.7

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

   4. Applied rewrites 59.7%

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

   if -5.00000000000000019e-43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000002e-57

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 55.9

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

   6. Applied rewrites 55.9%

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

   if 5.0000000000000002e-57 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 60.5%

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

Alternative 10: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \end{array} \]

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 -5e-43)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= t_1 5e-57)
       (/ (- b (* 4.0 (* a (* t z)))) (* z c))
       (/ (/ (fma (* y x) 9.0 b) c) z)))))

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 <= -5e-43) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t_1 <= 5e-57) {
		tmp = (b - (4.0 * (a * (t * z)))) / (z * c);
	} else {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	}
	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 <= -5e-43)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (t_1 <= 5e-57)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / Float64(z * c));
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	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, -5e-43], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-57], N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000019e-43

   1. Initial program 78.9%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.7

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

   4. Applied rewrites 59.7%

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

   if -5.00000000000000019e-43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000002e-57

   1. Initial program 78.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 55.6

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

   4. Applied rewrites 55.6%

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

   if 5.0000000000000002e-57 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 60.5%

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

Alternative 11: 66.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (/ (* a t) c))))
   (if (<= a -6.5e-78)
     t_1
     (if (<= a 4e+179) (/ (/ (fma (* y x) 9.0 b) c) z) 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 = -4.0 * ((a * t) / c);
	double tmp;
	if (a <= -6.5e-78) {
		tmp = t_1;
	} else if (a <= 4e+179) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else {
		tmp = 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(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (a <= -6.5e-78)
		tmp = t_1;
	elseif (a <= 4e+179)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	else
		tmp = 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[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-78], t$95$1, If[LessEqual[a, 4e+179], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000003e-78 or 3.99999999999999992e179 < a

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

   if -6.5000000000000003e-78 < a < 3.99999999999999992e179

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 60.5%

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

Alternative 12: 66.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+179}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (/ (* a t) c))))
   (if (<= a -6.5e-78)
     t_1
     (if (<= a 4e+179) (/ (fma 9.0 (* x y) b) (* c z)) 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 = -4.0 * ((a * t) / c);
	double tmp;
	if (a <= -6.5e-78) {
		tmp = t_1;
	} else if (a <= 4e+179) {
		tmp = fma(9.0, (x * y), b) / (c * z);
	} else {
		tmp = 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(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (a <= -6.5e-78)
		tmp = t_1;
	elseif (a <= 4e+179)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c * z));
	else
		tmp = 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[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-78], t$95$1, If[LessEqual[a, 4e+179], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000003e-78 or 3.99999999999999992e179 < a

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

   if -6.5000000000000003e-78 < a < 3.99999999999999992e179

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 78.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 57.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lower-/.f64 59.7

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

      7. lift-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 59.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 59.7

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

   8. Applied rewrites 59.7%

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

Alternative 13: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot \frac{x \cdot y}{c}}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{-32}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -5e-43)
     t_2
     (if (<= t_1 -5e-314)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 1e-32) (/ (/ b c) z) 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 <= -5e-43) {
		tmp = t_2;
	} else if (t_1 <= -5e-314) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 1e-32) {
		tmp = (b / c) / z;
	} 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 <= (-5d-43)) then
        tmp = t_2
    else if (t_1 <= (-5d-314)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 1d-32) then
        tmp = (b / c) / z
    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 <= -5e-43) {
		tmp = t_2;
	} else if (t_1 <= -5e-314) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 1e-32) {
		tmp = (b / c) / z;
	} 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 <= -5e-43:
		tmp = t_2
	elif t_1 <= -5e-314:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 1e-32:
		tmp = (b / c) / z
	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 * Float64(Float64(x * y) / c)) / z)
	tmp = 0.0
	if (t_1 <= -5e-43)
		tmp = t_2;
	elseif (t_1 <= -5e-314)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 1e-32)
		tmp = Float64(Float64(b / c) / z);
	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 <= -5e-43)
		tmp = t_2;
	elseif (t_1 <= -5e-314)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 1e-32)
		tmp = (b / c) / z;
	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 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-43], t$95$2, If[LessEqual[t$95$1, -5e-314], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-32], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000019e-43 or 1.00000000000000006e-32 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 35.5

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

   6. Applied rewrites 35.5%

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

   if -5.00000000000000019e-43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999982e-314

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

   if -4.99999999982e-314 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000006e-32

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in b around inf

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

      1. lower-/.f64 34.3

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

   6. Applied rewrites 34.3%

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

Alternative 14: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \end{array} \end{array} \]

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 -5e-43)
     (/ (* 9.0 (* x y)) (* c z))
     (if (<= t_1 -5e-314)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 100000.0) (/ (/ b c) z) (* 9.0 (/ (* x y) (* c z))))))))

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 <= -5e-43) {
		tmp = (9.0 * (x * y)) / (c * z);
	} else if (t_1 <= -5e-314) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 100000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = 9.0 * ((x * y) / (c * z));
	}
	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) :: tmp
    t_1 = (x * 9.0d0) * y
    if (t_1 <= (-5d-43)) then
        tmp = (9.0d0 * (x * y)) / (c * z)
    else if (t_1 <= (-5d-314)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 100000.0d0) then
        tmp = (b / c) / z
    else
        tmp = 9.0d0 * ((x * y) / (c * z))
    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 tmp;
	if (t_1 <= -5e-43) {
		tmp = (9.0 * (x * y)) / (c * z);
	} else if (t_1 <= -5e-314) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 100000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = 9.0 * ((x * y) / (c * z));
	}
	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
	tmp = 0
	if t_1 <= -5e-43:
		tmp = (9.0 * (x * y)) / (c * z)
	elif t_1 <= -5e-314:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 100000.0:
		tmp = (b / c) / z
	else:
		tmp = 9.0 * ((x * y) / (c * z))
	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 <= -5e-43)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(c * z));
	elseif (t_1 <= -5e-314)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 100000.0)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	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;
	tmp = 0.0;
	if (t_1 <= -5e-43)
		tmp = (9.0 * (x * y)) / (c * z);
	elseif (t_1 <= -5e-314)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 100000.0)
		tmp = (b / c) / z;
	else
		tmp = 9.0 * ((x * y) / (c * z));
	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]}, If[LessEqual[t$95$1, -5e-43], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-314], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000019e-43

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 78.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 57.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lower-/.f64 59.7

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

      7. lift-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 59.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 59.7

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

   8. Applied rewrites 59.7%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 35.8

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

   11. Applied rewrites 35.8%

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

   if -5.00000000000000019e-43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999982e-314

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

   if -4.99999999982e-314 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e5

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in b around inf

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

      1. lower-/.f64 34.3

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

   6. Applied rewrites 34.3%

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

   if 1e5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.8

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

   4. Applied rewrites 35.8%

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

Alternative 15: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -5e-43)
     t_2
     (if (<= t_1 -5e-314)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 100000.0) (/ (/ b c) z) 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 <= -5e-43) {
		tmp = t_2;
	} else if (t_1 <= -5e-314) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 100000.0) {
		tmp = (b / c) / z;
	} 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 <= (-5d-43)) then
        tmp = t_2
    else if (t_1 <= (-5d-314)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 100000.0d0) then
        tmp = (b / c) / z
    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 <= -5e-43) {
		tmp = t_2;
	} else if (t_1 <= -5e-314) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 100000.0) {
		tmp = (b / c) / z;
	} 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 <= -5e-43:
		tmp = t_2
	elif t_1 <= -5e-314:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 100000.0:
		tmp = (b / c) / z
	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(c * z)))
	tmp = 0.0
	if (t_1 <= -5e-43)
		tmp = t_2;
	elseif (t_1 <= -5e-314)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 100000.0)
		tmp = Float64(Float64(b / c) / z);
	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 <= -5e-43)
		tmp = t_2;
	elseif (t_1 <= -5e-314)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 100000.0)
		tmp = (b / c) / z;
	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[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-43], t$95$2, If[LessEqual[t$95$1, -5e-314], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000019e-43 or 1e5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.8

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

   4. Applied rewrites 35.8%

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

   if -5.00000000000000019e-43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999982e-314

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

   if -4.99999999982e-314 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e5

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in b around inf

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

      1. lower-/.f64 34.3

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

   6. Applied rewrites 34.3%

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

Alternative 16: 49.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+48}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (/ b c) z)))
   (if (<= b -2.2e-50) t_1 (if (<= b 3.5e+48) (* -4.0 (/ (* a 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 = (b / c) / z;
	double tmp;
	if (b <= -2.2e-50) {
		tmp = t_1;
	} else if (b <= 3.5e+48) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (b / c) / z
    if (b <= (-2.2d-50)) then
        tmp = t_1
    else if (b <= 3.5d+48) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = t_1
    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 = (b / c) / z;
	double tmp;
	if (b <= -2.2e-50) {
		tmp = t_1;
	} else if (b <= 3.5e+48) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_1;
	}
	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 = (b / c) / z
	tmp = 0
	if b <= -2.2e-50:
		tmp = t_1
	elif b <= 3.5e+48:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = 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(b / c) / z)
	tmp = 0.0
	if (b <= -2.2e-50)
		tmp = t_1;
	elseif (b <= 3.5e+48)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = t_1;
	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 = (b / c) / z;
	tmp = 0.0;
	if (b <= -2.2e-50)
		tmp = t_1;
	elseif (b <= 3.5e+48)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = t_1;
	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[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.2e-50], t$95$1, If[LessEqual[b, 3.5e+48], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1999999999999999e-50 or 3.4999999999999997e48 < b

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in b around inf

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

      1. lower-/.f64 34.3

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

   6. Applied rewrites 34.3%

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

   if -2.1999999999999999e-50 < b < 3.4999999999999997e48

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.8

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

   4. Applied rewrites 38.8%

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

Alternative 17: 37.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{-192}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{b}{c \cdot z}\right|\\ \end{array} \end{array} \]

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)) 2e-192)
   (/ (/ b c) z)
   (fabs (/ b (* c z)))))

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)) <= 2e-192) {
		tmp = (b / c) / z;
	} else {
		tmp = fabs((b / (c * z)));
	}
	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 ((((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)) <= 2d-192) then
        tmp = (b / c) / z
    else
        tmp = abs((b / (c * z)))
    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 ((((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)) <= 2e-192) {
		tmp = (b / c) / z;
	} else {
		tmp = Math.abs((b / (c * z)));
	}
	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 (((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)) <= 2e-192:
		tmp = (b / c) / z
	else:
		tmp = math.fabs((b / (c * z)))
	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)) <= 2e-192)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = abs(Float64(b / Float64(c * z)));
	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 ((((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)) <= 2e-192)
		tmp = (b / c) / z;
	else
		tmp = abs((b / (c * z)));
	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[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], 2e-192], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[Abs[N[(b / N[(c * z), $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)) < 2.0000000000000002e-192

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in b around inf

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

      1. lower-/.f64 34.3

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

   6. Applied rewrites 34.3%

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

   if 2.0000000000000002e-192 < (/.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 78.9%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 34.6

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

   4. Applied rewrites 34.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]

      4. lower-/.f64 34.6

         \[\leadsto \frac{1}{\frac{c \cdot z}{\color{blue}{b}}} \]

   6. Applied rewrites 34.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]

      2. inv-pow N/A

         \[\leadsto {\left(\frac{c \cdot z}{b}\right)}^{\color{blue}{-1}} \]

      3. pow-to-exp N/A

         \[\leadsto e^{\log \left(\frac{c \cdot z}{b}\right) \cdot -1} \]

      4. exp-fabs N/A

         \[\leadsto \left|e^{\log \left(\frac{c \cdot z}{b}\right) \cdot -1}\right| \]

      5. pow-to-exp N/A

         \[\leadsto \left|{\left(\frac{c \cdot z}{b}\right)}^{-1}\right| \]

      6. inv-pow N/A

         \[\leadsto \left|\frac{1}{\frac{c \cdot z}{b}}\right| \]

      7. lift-/.f64 N/A

         \[\leadsto \left|\frac{1}{\frac{c \cdot z}{b}}\right| \]

      8. lower-fabs.f64 22.1

         \[\leadsto \left|\frac{1}{\frac{c \cdot z}{b}}\right| \]

      9. lift-/.f64 N/A

         \[\leadsto \left|\frac{1}{\frac{c \cdot z}{b}}\right| \]

      10. lift-/.f64 N/A

          \[\leadsto \left|\frac{1}{\frac{c \cdot z}{b}}\right| \]

      11. div-flip-rev N/A

          \[\leadsto \left|\frac{b}{c \cdot z}\right| \]

      12. lower-/.f64 22.2

          \[\leadsto \left|\frac{b}{c \cdot z}\right| \]

   8. Applied rewrites 22.2%

      \[\leadsto \left|\frac{b}{c \cdot z}\right| \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 34.6% accurate, 3.6× speedup

Math

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

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 c) z))

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 / c) / z;
}

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 / c) / z
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 / c) / z;
}

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 / c) / z

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(Float64(b / c) / z)
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 / c) / z;
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[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 78.9%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

3. Applied rewrites 79.6%

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

4. Taylor expanded in b around inf

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

   1. lower-/.f64 34.3

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

6. Applied rewrites 34.3%

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

Alternative 19: 34.3% accurate, 3.8× speedup

Math

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

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 (* c z)))

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 / (c * z);
}

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 / (c * z)
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 / (c * z);
}

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 / (c * z)

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(c * z))
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 / (c * z);
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[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.9%

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

2. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 34.6

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

4. Applied rewrites 34.6%

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

Reproduce

herbie shell --seed 2025142 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64
  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))