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

Percentage Accurate: 79.6% → 86.3%

Time: 8.3s

Alternatives: 15

Speedup: 0.5×

• 36.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% 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: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+24}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y, x \cdot 9, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \end{array} \end{array} \]

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 -4e+24)
     (/ (fma (* 9.0 x) y (fma (* -4.0 z) (* a t) b)) (* z c))
     (if (<= t_1 INFINITY)
       (/ (/ (fma y (* x 9.0) (fma (* t a) (* z -4.0) b)) c) z)
       (* -4.0 (* (/ t c) a))))))

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 <= -4e+24) {
		tmp = fma((9.0 * x), y, fma((-4.0 * z), (a * t), b)) / (z * c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma(y, (x * 9.0), fma((t * a), (z * -4.0), b)) / c) / z;
	} else {
		tmp = -4.0 * ((t / c) * a);
	}
	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 <= -4e+24)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(y, Float64(x * 9.0), fma(Float64(t * a), Float64(z * -4.0), b)) / c) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	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, -4e+24], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(y * N[(x * 9.0), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $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)) < -3.9999999999999999e24

   1. Initial program 86.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 92.3

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

   4. Applied rewrites 92.3%

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

   if -3.9999999999999999e24 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 85.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 86.8

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

   4. Applied rewrites 86.8%

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

   6. Applied rewrites 93.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 53.8%

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

   7. Applied rewrites 80.3%

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

Alternative 2: 85.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 86.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 88.9

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

   4. Applied rewrites 88.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 53.8%

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

   7. Applied rewrites 80.3%

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

Alternative 3: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+241}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

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))
        (t_2 (/ (fma (* -4.0 z) (* a t) (* (* y x) 9.0)) (* z c))))
   (if (<= t_1 -1000000000.0)
     t_2
     (if (<= t_1 4e-61)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (if (<= t_1 4e+241) t_2 (* (* 9.0 (/ x c)) (/ y 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 t_2 = fma((-4.0 * z), (a * t), ((y * x) * 9.0)) / (z * c);
	double tmp;
	if (t_1 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 4e-61) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else if (t_1 <= 4e+241) {
		tmp = t_2;
	} else {
		tmp = (9.0 * (x / c)) * (y / 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)
	t_2 = Float64(fma(Float64(-4.0 * z), Float64(a * t), Float64(Float64(y * x) * 9.0)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= 4e-61)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 4e+241)
		tmp = t_2;
	else
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / 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]}, Block[{t$95$2 = N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000000.0], t$95$2, If[LessEqual[t$95$1, 4e-61], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 4e+241], t$95$2, N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e9 or 4.0000000000000002e-61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.0000000000000002e241

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 74.9%

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

   if -1e9 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.0000000000000002e-61

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 89.5%

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

   if 4.0000000000000002e241 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 51.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 51.5

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 87.8%

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

Alternative 4: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

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)) (t_2 (/ (fma (* 9.0 x) y b) (* z c))))
   (if (<= t_1 -2e+124)
     t_2
     (if (<= t_1 4e-35)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (if (<= t_1 5e+117) t_2 (* (* 9.0 (/ x c)) (/ y 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 t_2 = fma((9.0 * x), y, b) / (z * c);
	double tmp;
	if (t_1 <= -2e+124) {
		tmp = t_2;
	} else if (t_1 <= 4e-35) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else if (t_1 <= 5e+117) {
		tmp = t_2;
	} else {
		tmp = (9.0 * (x / c)) * (y / 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)
	t_2 = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e+124)
		tmp = t_2;
	elseif (t_1 <= 4e-35)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 5e+117)
		tmp = t_2;
	else
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / 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]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+124], t$95$2, If[LessEqual[t$95$1, 4e-35], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+117], t$95$2, N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e124 or 4.00000000000000003e-35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999983e117

   1. Initial program 78.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 84.7

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 70.9%

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

   if -1.9999999999999999e124 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000003e-35

   1. Initial program 79.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 86.6%

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

   if 4.99999999999999983e117 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 77.5%

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

Alternative 5: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

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)) (t_2 (/ (fma (* 9.0 x) y b) (* z c))))
   (if (<= t_1 -4e-20)
     t_2
     (if (<= t_1 4e-35)
       (/ (fma -4.0 (* (* t z) a) b) (* z c))
       (if (<= t_1 5e+117) t_2 (* (* 9.0 (/ x c)) (/ y 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 t_2 = fma((9.0 * x), y, b) / (z * c);
	double tmp;
	if (t_1 <= -4e-20) {
		tmp = t_2;
	} else if (t_1 <= 4e-35) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else if (t_1 <= 5e+117) {
		tmp = t_2;
	} else {
		tmp = (9.0 * (x / c)) * (y / 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)
	t_2 = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-20)
		tmp = t_2;
	elseif (t_1 <= 4e-35)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	elseif (t_1 <= 5e+117)
		tmp = t_2;
	else
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / 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]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-20], t$95$2, If[LessEqual[t$95$1, 4e-35], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+117], t$95$2, N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999978e-20 or 4.00000000000000003e-35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999983e117

   1. Initial program 77.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 71.3%

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

   if -3.99999999999999978e-20 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000003e-35

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 77.7%

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

   if 4.99999999999999983e117 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 77.5%

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

Alternative 6: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, z \cdot a, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

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)) (t_2 (/ (fma (* 9.0 x) y b) (* z c))))
   (if (<= t_1 -4e-20)
     t_2
     (if (<= t_1 4e-35)
       (/ (fma (* -4.0 t) (* z a) b) (* c z))
       (if (<= t_1 5e+117) t_2 (* (* 9.0 (/ x c)) (/ y 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 t_2 = fma((9.0 * x), y, b) / (z * c);
	double tmp;
	if (t_1 <= -4e-20) {
		tmp = t_2;
	} else if (t_1 <= 4e-35) {
		tmp = fma((-4.0 * t), (z * a), b) / (c * z);
	} else if (t_1 <= 5e+117) {
		tmp = t_2;
	} else {
		tmp = (9.0 * (x / c)) * (y / 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)
	t_2 = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-20)
		tmp = t_2;
	elseif (t_1 <= 4e-35)
		tmp = Float64(fma(Float64(-4.0 * t), Float64(z * a), b) / Float64(c * z));
	elseif (t_1 <= 5e+117)
		tmp = t_2;
	else
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / 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]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-20], t$95$2, If[LessEqual[t$95$1, 4e-35], N[(N[(N[(-4.0 * t), $MachinePrecision] * N[(z * a), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+117], t$95$2, N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999978e-20 or 4.00000000000000003e-35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999983e117

   1. Initial program 77.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 71.3%

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

   if -3.99999999999999978e-20 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000003e-35

   1. Initial program 80.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 81.7

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

   4. Applied rewrites 81.7%

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

   6. Applied rewrites 88.6%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 77.6%

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

   if 4.99999999999999983e117 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 77.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -4 \cdot 10^{-20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, z \cdot a, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1000000000 \lor \neg \left(t\_1 \leq 4 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{z} \cdot 9, y, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (or (<= t_1 -1000000000.0) (not (<= t_1 4e-61)))
     (/ (fma (* (/ x z) 9.0) y (* (* a t) -4.0)) c)
     (/ (fma (* t a) -4.0 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -1000000000.0) || !(t_1 <= 4e-61)) {
		tmp = fma(((x / z) * 9.0), y, ((a * t) * -4.0)) / c;
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if ((t_1 <= -1000000000.0) || !(t_1 <= 4e-61))
		tmp = Float64(fma(Float64(Float64(x / z) * 9.0), y, Float64(Float64(a * t) * -4.0)) / c);
	else
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1000000000.0], N[Not[LessEqual[t$95$1, 4e-61]], $MachinePrecision]], N[(N[(N[(N[(x / z), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e9 or 4.0000000000000002e-61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.2%

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

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. associate-+l+ N/A

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

      7. div-add N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-/l* N/A

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

      12. lower-fma.f64 N/A

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

   4. Applied rewrites 76.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 64.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 79.1%

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

   if -1e9 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.0000000000000002e-61

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 89.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -1000000000 \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 4 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{z} \cdot 9, y, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(9 \cdot x\right) \cdot y}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-61}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-35}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (/ (* (* 9.0 x) y) (* z c))))
   (if (<= t_1 -1000000000.0)
     t_2
     (if (<= t_1 -5e-61)
       (/ b (* z c))
       (if (<= t_1 4e-35) (* -4.0 (* (/ t c) a)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((9.0 * x) * y) / (z * c);
	double tmp;
	if (t_1 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= -5e-61) {
		tmp = b / (z * c);
	} else if (t_1 <= 4e-35) {
		tmp = -4.0 * ((t / c) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = ((9.0d0 * x) * y) / (z * c)
    if (t_1 <= (-1000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= (-5d-61)) then
        tmp = b / (z * c)
    else if (t_1 <= 4d-35) then
        tmp = (-4.0d0) * ((t / c) * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((9.0 * x) * y) / (z * c);
	double tmp;
	if (t_1 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= -5e-61) {
		tmp = b / (z * c);
	} else if (t_1 <= 4e-35) {
		tmp = -4.0 * ((t / c) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = ((9.0 * x) * y) / (z * c)
	tmp = 0
	if t_1 <= -1000000000.0:
		tmp = t_2
	elif t_1 <= -5e-61:
		tmp = b / (z * c)
	elif t_1 <= 4e-35:
		tmp = -4.0 * ((t / c) * a)
	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(Float64(9.0 * x) * y) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= -5e-61)
		tmp = Float64(b / Float64(z * c));
	elseif (t_1 <= 4e-35)
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = ((9.0 * x) * y) / (z * c);
	tmp = 0.0;
	if (t_1 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= -5e-61)
		tmp = b / (z * c);
	elseif (t_1 <= 4e-35)
		tmp = -4.0 * ((t / c) * a);
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000000.0], t$95$2, If[LessEqual[t$95$1, -5e-61], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-35], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e9 or 4.00000000000000003e-35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 57.9%

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

   7. Applied rewrites 58.0%

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

   if -1e9 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-61

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 67.5%

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

   if -4.9999999999999999e-61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000003e-35

   1. Initial program 78.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 61.9%

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

Alternative 9: 68.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+107}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -9.6e+107)
   (* -4.0 (* (/ t c) a))
   (if (<= z 2.5e+58) (/ (fma (* 9.0 y) x b) (* z c)) (* (* a t) (/ -4.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -9.6e+107) {
		tmp = -4.0 * ((t / c) * a);
	} else if (z <= 2.5e+58) {
		tmp = fma((9.0 * y), x, b) / (z * c);
	} else {
		tmp = (a * t) * (-4.0 / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -9.6e+107)
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	elseif (z <= 2.5e+58)
		tmp = Float64(fma(Float64(9.0 * y), x, b) / Float64(z * c));
	else
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -9.6e+107], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+58], N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6000000000000002e107

   1. Initial program 42.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 64.4%

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

   7. Applied rewrites 71.5%

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

   if -9.6000000000000002e107 < z < 2.49999999999999993e58

   1. Initial program 93.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.6

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 72.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 72.2

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 72.2

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

   9. Applied rewrites 72.2%

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

   if 2.49999999999999993e58 < z

   1. Initial program 54.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 64.0%

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

   7. Applied rewrites 60.5%

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

   9. Applied rewrites 64.1%

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

Alternative 10: 68.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+107}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -9.6e+107)
   (* -4.0 (* (/ t c) a))
   (if (<= z 2.5e+58) (/ (fma (* 9.0 x) y b) (* z c)) (* (* a t) (/ -4.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -9.6e+107) {
		tmp = -4.0 * ((t / c) * a);
	} else if (z <= 2.5e+58) {
		tmp = fma((9.0 * x), y, b) / (z * c);
	} else {
		tmp = (a * t) * (-4.0 / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -9.6e+107)
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	elseif (z <= 2.5e+58)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	else
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -9.6e+107], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+58], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6000000000000002e107

   1. Initial program 42.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 64.4%

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

   7. Applied rewrites 71.5%

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

   if -9.6000000000000002e107 < z < 2.49999999999999993e58

   1. Initial program 93.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.6

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 72.1%

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

   if 2.49999999999999993e58 < z

   1. Initial program 54.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 64.0%

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

   7. Applied rewrites 60.5%

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

   9. Applied rewrites 64.1%

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

Alternative 11: 68.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+107}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -9.6e+107)
   (* -4.0 (* (/ t c) a))
   (if (<= z 2.5e+58) (/ (fma (* y x) 9.0 b) (* z c)) (* (* a t) (/ -4.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -9.6e+107) {
		tmp = -4.0 * ((t / c) * a);
	} else if (z <= 2.5e+58) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = (a * t) * (-4.0 / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -9.6e+107)
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	elseif (z <= 2.5e+58)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -9.6e+107], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+58], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6000000000000002e107

   1. Initial program 42.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 64.4%

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

   7. Applied rewrites 71.5%

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

   if -9.6000000000000002e107 < z < 2.49999999999999993e58

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 72.1%

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

   if 2.49999999999999993e58 < z

   1. Initial program 54.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 64.0%

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

   7. Applied rewrites 60.5%

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

   9. Applied rewrites 64.1%

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

Alternative 12: 51.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{-182}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1.62e-182)
   (* -4.0 (* (/ t c) a))
   (if (<= a 2.2e-5) (/ (/ b c) z) (* -4.0 (* t (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.62e-182) {
		tmp = -4.0 * ((t / c) * a);
	} else if (a <= 2.2e-5) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1.62d-182)) then
        tmp = (-4.0d0) * ((t / c) * a)
    else if (a <= 2.2d-5) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.62e-182) {
		tmp = -4.0 * ((t / c) * a);
	} else if (a <= 2.2e-5) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.62e-182:
		tmp = -4.0 * ((t / c) * a)
	elif a <= 2.2e-5:
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.62e-182)
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	elseif (a <= 2.2e-5)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.62e-182)
		tmp = -4.0 * ((t / c) * a);
	elseif (a <= 2.2e-5)
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1.62e-182], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-5], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.62000000000000013e-182

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 52.2%

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

   7. Applied rewrites 50.5%

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

   if -1.62000000000000013e-182 < a < 2.1999999999999999e-5

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 42.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 46.5

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

   7. Applied rewrites 46.5%

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

   if 2.1999999999999999e-5 < 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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 59.6%

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

   7. Applied rewrites 66.8%

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

Alternative 13: 51.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-98} \lor \neg \left(a \leq 2.2 \cdot 10^{-5}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -4.5e-98) (not (<= a 2.2e-5)))
   (* -4.0 (* t (/ a c)))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.5e-98) || !(a <= 2.2e-5)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-4.5d-98)) .or. (.not. (a <= 2.2d-5))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.5e-98) || !(a <= 2.2e-5)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -4.5e-98) or not (a <= 2.2e-5):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -4.5e-98) || !(a <= 2.2e-5))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -4.5e-98) || ~((a <= 2.2e-5)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -4.5e-98], N[Not[LessEqual[a, 2.2e-5]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999997e-98 or 2.1999999999999999e-5 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 57.3%

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

   7. Applied rewrites 59.5%

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

   if -4.49999999999999997e-98 < a < 2.1999999999999999e-5

   1. Initial program 77.2%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 40.7%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-98} \lor \neg \left(a \leq 2.2 \cdot 10^{-5}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{-182}:\\ \;\;\;\;-4 \cdot \left(\frac{t}{c} \cdot a\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1.62e-182)
   (* -4.0 (* (/ t c) a))
   (if (<= a 2.2e-5) (/ b (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.62e-182) {
		tmp = -4.0 * ((t / c) * a);
	} else if (a <= 2.2e-5) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1.62d-182)) then
        tmp = (-4.0d0) * ((t / c) * a)
    else if (a <= 2.2d-5) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.62e-182) {
		tmp = -4.0 * ((t / c) * a);
	} else if (a <= 2.2e-5) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.62e-182:
		tmp = -4.0 * ((t / c) * a)
	elif a <= 2.2e-5:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.62e-182)
		tmp = Float64(-4.0 * Float64(Float64(t / c) * a));
	elseif (a <= 2.2e-5)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.62e-182)
		tmp = -4.0 * ((t / c) * a);
	elseif (a <= 2.2e-5)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1.62e-182], N[(-4.0 * N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-5], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.62000000000000013e-182

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 52.2%

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

   7. Applied rewrites 50.5%

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

   if -1.62000000000000013e-182 < a < 2.1999999999999999e-5

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 42.9%

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

   if 2.1999999999999999e-5 < 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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 59.6%

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

   7. Applied rewrites 66.8%

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

Alternative 15: 35.2% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.6%

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

3. Taylor expanded in b around inf

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

5. Applied rewrites 30.2%

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

Developer Target 1: 80.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025022 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

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

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