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

Percentage Accurate: 79.9% → 86.3%

Time: 6.7s

Alternatives: 15

Speedup: 0.8×

• 38.0% 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: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-9}{z}, \frac{y}{c}, \frac{\frac{b}{c \cdot z} - \frac{a \cdot t}{c} \cdot 4}{-x}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.5e+99)
   (*
    (fma (/ -9.0 z) (/ y c) (/ (- (/ b (* c z)) (* (/ (* a t) c) 4.0)) (- x)))
    (- x))
   (if (<= z 7.4e+70)
     (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) a) t)) b) (* z c))
     (* (fma (/ a c) -4.0 (/ (fma (* y x) 9.0 b) (* (* t z) c))) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.5e+99) {
		tmp = fma((-9.0 / z), (y / c), (((b / (c * z)) - (((a * t) / c) * 4.0)) / -x)) * -x;
	} else if (z <= 7.4e+70) {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * a) * t)) + b) / (z * c);
	} else {
		tmp = fma((a / c), -4.0, (fma((y * x), 9.0, b) / ((t * z) * c))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.5e+99)
		tmp = Float64(fma(Float64(-9.0 / z), Float64(y / c), Float64(Float64(Float64(b / Float64(c * z)) - Float64(Float64(Float64(a * t) / c) * 4.0)) / Float64(-x))) * Float64(-x));
	elseif (z <= 7.4e+70)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * a) * t)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(y * x), 9.0, b) / Float64(Float64(t * z) * c))) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.5e+99], N[(N[(N[(-9.0 / z), $MachinePrecision] * N[(y / c), $MachinePrecision] + N[(N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / (-x)), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 7.4e+70], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000004e99

   1. Initial program 60.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   5. Applied rewrites 72.0%

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

   if -2.50000000000000004e99 < z < 7.39999999999999977e70

   1. Initial program 95.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 91.4

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

   4. Applied rewrites 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 95.0

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

   6. Applied rewrites 95.0%

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

   if 7.39999999999999977e70 < z

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 86.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-9}{z}, \frac{y}{c}, \frac{\frac{b}{c \cdot z} - \frac{a \cdot t}{c} \cdot 4}{-x}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot a\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+261}:\\ \;\;\;\;\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot \left(-x\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(t\_1, -4, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t\_1, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* (* t z) a)) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -2e+261)
     (* (* (/ (/ y c) z) -9.0) (- x))
     (if (<= t_2 -5e-29)
       (/ (/ (fma (* y x) 9.0 b) c) z)
       (if (<= t_2 2e-5)
         (/ (/ (fma t_1 -4.0 b) c) z)
         (/ (fma -4.0 t_1 (* (* y x) 9.0)) (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = (t * z) * a;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -2e+261) {
		tmp = (((y / c) / z) * -9.0) * -x;
	} else if (t_2 <= -5e-29) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else if (t_2 <= 2e-5) {
		tmp = (fma(t_1, -4.0, b) / c) / z;
	} else {
		tmp = fma(-4.0, t_1, ((y * x) * 9.0)) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(t * z) * a)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -2e+261)
		tmp = Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * Float64(-x));
	elseif (t_2 <= -5e-29)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	elseif (t_2 <= 2e-5)
		tmp = Float64(Float64(fma(t_1, -4.0, b) / c) / z);
	else
		tmp = Float64(fma(-4.0, t_1, Float64(Float64(y * x) * 9.0)) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(t * z), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+261], N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[t$95$2, -5e-29], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 2e-5], N[(N[(N[(t$95$1 * -4.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(-4.0 * t$95$1 + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e261

   1. Initial program 51.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lift-/.f64 72.8

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

   8. Applied rewrites 72.8%

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

   if -1.9999999999999999e261 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999986e-29

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -4.99999999999999986e-29 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000016e-5

   1. Initial program 81.2%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 80.4

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

   5. Applied rewrites 80.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 80.4

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

   7. Applied rewrites 80.4%

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

   if 2.00000000000000016e-5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 88.1%

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

   3. Taylor expanded in b around 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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -2 \cdot 10^{+261}:\\ \;\;\;\;\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot \left(-x\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{y}{c \cdot z}, 9, \frac{b}{\left(z \cdot x\right) \cdot c}\right) - \frac{\frac{a \cdot t}{c}}{x} \cdot 4\right) \cdot x\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.5e+99)
   (*
    (- (fma (/ y (* c z)) 9.0 (/ b (* (* z x) c))) (* (/ (/ (* a t) c) x) 4.0))
    x)
   (if (<= z 7.4e+70)
     (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) a) t)) b) (* z c))
     (* (fma (/ a c) -4.0 (/ (fma (* y x) 9.0 b) (* (* t z) c))) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.5e+99) {
		tmp = (fma((y / (c * z)), 9.0, (b / ((z * x) * c))) - ((((a * t) / c) / x) * 4.0)) * x;
	} else if (z <= 7.4e+70) {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * a) * t)) + b) / (z * c);
	} else {
		tmp = fma((a / c), -4.0, (fma((y * x), 9.0, b) / ((t * z) * c))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.5e+99)
		tmp = Float64(Float64(fma(Float64(y / Float64(c * z)), 9.0, Float64(b / Float64(Float64(z * x) * c))) - Float64(Float64(Float64(Float64(a * t) / c) / x) * 4.0)) * x);
	elseif (z <= 7.4e+70)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * a) * t)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(y * x), 9.0, b) / Float64(Float64(t * z) * c))) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.5e+99], N[(N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0 + N[(b / N[(N[(z * x), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] / x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 7.4e+70], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000004e99

   1. Initial program 60.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.4%

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

   if -2.50000000000000004e99 < z < 7.39999999999999977e70

   1. Initial program 95.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 91.4

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

   4. Applied rewrites 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 95.0

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

   6. Applied rewrites 95.0%

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

   if 7.39999999999999977e70 < z

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 86.9%

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

Alternative 4: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{t \cdot a}{c}}{y}, -4, \mathsf{fma}\left(\frac{x}{c \cdot z}, 9, \frac{b}{\left(z \cdot y\right) \cdot c}\right)\right) \cdot y\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -8e+185)
   (*
    (fma (/ (/ (* t a) c) y) -4.0 (fma (/ x (* c z)) 9.0 (/ b (* (* z y) c))))
    y)
   (if (<= z 7.4e+70)
     (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) a) t)) b) (* z c))
     (* (fma (/ a c) -4.0 (/ (fma (* y x) 9.0 b) (* (* t z) c))) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -8e+185) {
		tmp = fma((((t * a) / c) / y), -4.0, fma((x / (c * z)), 9.0, (b / ((z * y) * c)))) * y;
	} else if (z <= 7.4e+70) {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * a) * t)) + b) / (z * c);
	} else {
		tmp = fma((a / c), -4.0, (fma((y * x), 9.0, b) / ((t * z) * c))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -8e+185)
		tmp = Float64(fma(Float64(Float64(Float64(t * a) / c) / y), -4.0, fma(Float64(x / Float64(c * z)), 9.0, Float64(b / Float64(Float64(z * y) * c)))) * y);
	elseif (z <= 7.4e+70)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * a) * t)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(y * x), 9.0, b) / Float64(Float64(t * z) * c))) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -8e+185], N[(N[(N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] / y), $MachinePrecision] * -4.0 + N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0 + N[(b / N[(N[(z * y), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 7.4e+70], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999998e185

   1. Initial program 42.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 50.1

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

   4. Applied rewrites 50.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 45.9

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

   6. Applied rewrites 45.9%

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

   7. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   9. Applied rewrites 78.2%

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

   if -7.9999999999999998e185 < z < 7.39999999999999977e70

   1. Initial program 93.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 91.3

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

   4. Applied rewrites 91.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 93.5

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

   6. Applied rewrites 93.5%

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

   if 7.39999999999999977e70 < z

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 86.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{t \cdot a}{c}}{y}, -4, \mathsf{fma}\left(\frac{x}{c \cdot z}, 9, \frac{b}{\left(z \cdot y\right) \cdot c}\right)\right) \cdot y\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+261}:\\ \;\;\;\;\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot \left(-x\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{t\_2}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* y x) 9.0 b)))
   (if (<= t_1 -2e+261)
     (* (* (/ (/ y c) z) -9.0) (- x))
     (if (<= t_1 -5e-29)
       (/ (/ t_2 c) z)
       (if (<= t_1 5e-37)
         (/ (/ (fma (* (* t z) a) -4.0 b) c) z)
         (/ t_2 (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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((y * x), 9.0, b);
	double tmp;
	if (t_1 <= -2e+261) {
		tmp = (((y / c) / z) * -9.0) * -x;
	} else if (t_1 <= -5e-29) {
		tmp = (t_2 / c) / z;
	} else if (t_1 <= 5e-37) {
		tmp = (fma(((t * z) * a), -4.0, b) / c) / z;
	} else {
		tmp = t_2 / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (t_1 <= -2e+261)
		tmp = Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * Float64(-x));
	elseif (t_1 <= -5e-29)
		tmp = Float64(Float64(t_2 / c) / z);
	elseif (t_1 <= 5e-37)
		tmp = Float64(Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / c) / z);
	else
		tmp = Float64(t_2 / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+261], N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[t$95$1, -5e-29], N[(N[(t$95$2 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e-37], N[(N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(t$95$2 / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e261

   1. Initial program 51.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lift-/.f64 72.8

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

   8. Applied rewrites 72.8%

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

   if -1.9999999999999999e261 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999986e-29

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -4.99999999999999986e-29 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e-37

   1. Initial program 82.4%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 81.5

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

   5. Applied rewrites 81.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 81.5

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

   7. Applied rewrites 81.5%

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

   if 4.9999999999999997e-37 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -2 \cdot 10^{+261}:\\ \;\;\;\;\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot \left(-x\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-11} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+271)
     (/ (* (* 9.0 x) (/ y z)) c)
     (if (or (<= t_1 -1e-11) (not (<= t_1 5e-37)))
       (/ (fma (* y x) 9.0 b) (* z c))
       (/ (fma (* (* t z) a) -4.0 b) (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -2e+271) {
		tmp = ((9.0 * x) * (y / z)) / c;
	} else if ((t_1 <= -1e-11) || !(t_1 <= 5e-37)) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = fma(((t * z) * a), -4.0, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -2e+271)
		tmp = Float64(Float64(Float64(9.0 * x) * Float64(y / z)) / c);
	elseif ((t_1 <= -1e-11) || !(t_1 <= 5e-37))
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+271], N[(N[(N[(9.0 * x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-11], N[Not[LessEqual[t$95$1, 5e-37]], $MachinePrecision]], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999991e271

   1. Initial program 41.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.0

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

   5. Applied rewrites 80.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-/.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -1.99999999999999991e271 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-12 or 4.9999999999999997e-37 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.2

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

   5. Applied rewrites 72.2%

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

   if -9.99999999999999939e-12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e-37

   1. Initial program 82.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 86.2

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

   4. Applied rewrites 86.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 85.3

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

   6. Applied rewrites 85.3%

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

   7. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 80.4

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

   9. Applied rewrites 80.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -2 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -1 \cdot 10^{-11} \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+261}:\\ \;\;\;\;\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot \left(-x\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{t\_2}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* y x) 9.0 b)))
   (if (<= t_1 -2e+261)
     (* (* (/ (/ y c) z) -9.0) (- x))
     (if (<= t_1 -1e-11)
       (/ (/ t_2 c) z)
       (if (<= t_1 5e-37)
         (/ (fma (* (* t z) a) -4.0 b) (* z c))
         (/ t_2 (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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((y * x), 9.0, b);
	double tmp;
	if (t_1 <= -2e+261) {
		tmp = (((y / c) / z) * -9.0) * -x;
	} else if (t_1 <= -1e-11) {
		tmp = (t_2 / c) / z;
	} else if (t_1 <= 5e-37) {
		tmp = fma(((t * z) * a), -4.0, b) / (z * c);
	} else {
		tmp = t_2 / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (t_1 <= -2e+261)
		tmp = Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * Float64(-x));
	elseif (t_1 <= -1e-11)
		tmp = Float64(Float64(t_2 / c) / z);
	elseif (t_1 <= 5e-37)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(z * c));
	else
		tmp = Float64(t_2 / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+261], N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[t$95$1, -1e-11], N[(N[(t$95$2 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e-37], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$2 / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e261

   1. Initial program 51.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lift-/.f64 72.8

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

   8. Applied rewrites 72.8%

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

   if -1.9999999999999999e261 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-12

   1. Initial program 83.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.9

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

   5. Applied rewrites 74.9%

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

   if -9.99999999999999939e-12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e-37

   1. Initial program 82.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 86.2

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

   4. Applied rewrites 86.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 85.3

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

   6. Applied rewrites 85.3%

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

   7. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 80.4

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

   9. Applied rewrites 80.4%

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

   if 4.9999999999999997e-37 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -2 \cdot 10^{+261}:\\ \;\;\;\;\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot \left(-x\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-179}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (/ (* (* y x) 9.0) (* z c))))
   (if (<= t_1 -1e-11)
     t_2
     (if (<= t_1 -5e-179)
       (* -4.0 (* a (/ t c)))
       (if (<= t_1 2e-5) (/ (/ b c) z) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = ((y * x) * 9.0) / (z * c);
	double tmp;
	if (t_1 <= -1e-11) {
		tmp = t_2;
	} else if (t_1 <= -5e-179) {
		tmp = -4.0 * (a * (t / c));
	} else if (t_1 <= 2e-5) {
		tmp = (b / c) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = ((y * x) * 9.0d0) / (z * c)
    if (t_1 <= (-1d-11)) then
        tmp = t_2
    else if (t_1 <= (-5d-179)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (t_1 <= 2d-5) then
        tmp = (b / c) / z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = ((y * x) * 9.0) / (z * c);
	double tmp;
	if (t_1 <= -1e-11) {
		tmp = t_2;
	} else if (t_1 <= -5e-179) {
		tmp = -4.0 * (a * (t / c));
	} else if (t_1 <= 2e-5) {
		tmp = (b / c) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = ((y * x) * 9.0) / (z * c)
	tmp = 0
	if t_1 <= -1e-11:
		tmp = t_2
	elif t_1 <= -5e-179:
		tmp = -4.0 * (a * (t / c))
	elif t_1 <= 2e-5:
		tmp = (b / c) / z
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(y * x) * 9.0) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-11)
		tmp = t_2;
	elseif (t_1 <= -5e-179)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (t_1 <= 2e-5)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = ((y * x) * 9.0) / (z * c);
	tmp = 0.0;
	if (t_1 <= -1e-11)
		tmp = t_2;
	elseif (t_1 <= -5e-179)
		tmp = -4.0 * (a * (t / c));
	elseif (t_1 <= 2e-5)
		tmp = (b / c) / z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-11], t$95$2, If[LessEqual[t$95$1, -5e-179], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-5], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-12 or 2.00000000000000016e-5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 81.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 54.9

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

   5. Applied rewrites 54.9%

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

   if -9.99999999999999939e-12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e-179

   1. Initial program 73.2%

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 62.1

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

   7. Applied rewrites 62.1%

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

   if -4.9999999999999998e-179 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000016e-5

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.5%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -5 \cdot 10^{-179}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot c\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{t\_1}\right) \cdot t\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{t\_1}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* (* t z) c)))
   (if (<= z -1.12e+201)
     (* (fma (/ a c) -4.0 (/ b t_1)) t)
     (if (<= z 7.4e+70)
       (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) a) t)) b) (* z c))
       (* (fma (/ a c) -4.0 (/ (fma (* y x) 9.0 b) t_1)) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = (t * z) * c;
	double tmp;
	if (z <= -1.12e+201) {
		tmp = fma((a / c), -4.0, (b / t_1)) * t;
	} else if (z <= 7.4e+70) {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * a) * t)) + b) / (z * c);
	} else {
		tmp = fma((a / c), -4.0, (fma((y * x), 9.0, b) / t_1)) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(t * z) * c)
	tmp = 0.0
	if (z <= -1.12e+201)
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(b / t_1)) * t);
	elseif (z <= 7.4e+70)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * a) * t)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(y * x), 9.0, b) / t_1)) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(t * z), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[z, -1.12e+201], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 7.4e+70], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.11999999999999994e201

   1. Initial program 35.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 32.4

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

   5. Applied rewrites 32.4%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 63.7

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

   8. Applied rewrites 63.7%

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

   if -1.11999999999999994e201 < z < 7.39999999999999977e70

   1. Initial program 93.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 91.5

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

   4. Applied rewrites 91.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 93.1

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

   6. Applied rewrites 93.1%

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

   if 7.39999999999999977e70 < z

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 86.9%

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

Alternative 10: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+201} \lor \neg \left(z \leq 2.4 \cdot 10^{+127}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.12e+201) (not (<= z 2.4e+127)))
   (* (fma (/ a c) -4.0 (/ b (* (* t z) c))) t)
   (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) a) t)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -1.12e+201) || !(z <= 2.4e+127)) {
		tmp = fma((a / c), -4.0, (b / ((t * z) * c))) * t;
	} else {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * a) * t)) + b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -1.12e+201) || !(z <= 2.4e+127))
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(b / Float64(Float64(t * z) * c))) * t);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * a) * t)) + b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.12e+201], N[Not[LessEqual[z, 2.4e+127]], $MachinePrecision]], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.11999999999999994e201 or 2.4000000000000002e127 < z

   1. Initial program 42.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 37.5

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

   5. Applied rewrites 37.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 71.0

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

   8. Applied rewrites 71.0%

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

   if -1.11999999999999994e201 < z < 2.4000000000000002e127

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 91.5

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

   4. Applied rewrites 91.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 93.0

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

   6. Applied rewrites 93.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+201} \lor \neg \left(z \leq 2.4 \cdot 10^{+127}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+201} \lor \neg \left(z \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot \left(y \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.4e+201) (not (<= z 2.4e+126)))
   (* (fma (/ a c) -4.0 (/ b (* (* t z) c))) t)
   (/ (+ (- (* x (* y 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -1.4e+201) || !(z <= 2.4e+126)) {
		tmp = fma((a / c), -4.0, (b / ((t * z) * c))) * t;
	} else {
		tmp = (((x * (y * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -1.4e+201) || !(z <= 2.4e+126))
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(b / Float64(Float64(t * z) * c))) * t);
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.4e+201], N[Not[LessEqual[z, 2.4e+126]], $MachinePrecision]], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000003e201 or 2.40000000000000012e126 < z

   1. Initial program 42.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 37.5

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

   5. Applied rewrites 37.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 71.0

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

   8. Applied rewrites 71.0%

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

   if -1.40000000000000003e201 < z < 2.40000000000000012e126

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.5

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

   4. Applied rewrites 93.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+201} \lor \neg \left(z \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot \left(y \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+128} \lor \neg \left(z \leq 1.28 \cdot 10^{+144}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.2e+128) (not (<= z 1.28e+144)))
   (* -4.0 (/ (* a t) c))
   (/ (fma (* y x) 9.0 b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.2e+128) || !(z <= 1.28e+144)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.2e+128) || !(z <= 1.28e+144))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.2e+128], N[Not[LessEqual[z, 1.28e+144]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000017e128 or 1.28000000000000007e144 < z

   1. Initial program 49.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

   if -2.20000000000000017e128 < z < 1.28000000000000007e144

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+128} \lor \neg \left(z \leq 1.28 \cdot 10^{+144}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+106} \lor \neg \left(b \leq 4.8 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -1.6e+106) (not (<= b 4.8e-82)))
   (/ b (* z c))
   (* -4.0 (/ (* a t) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 ((b <= -1.6e+106) || !(b <= 4.8e-82)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 ((b <= (-1.6d+106)) .or. (.not. (b <= 4.8d-82))) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 ((b <= -1.6e+106) || !(b <= 4.8e-82)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 (b <= -1.6e+106) or not (b <= 4.8e-82):
		tmp = b / (z * c)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 ((b <= -1.6e+106) || !(b <= 4.8e-82))
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 ((b <= -1.6e+106) || ~((b <= 4.8e-82)))
		tmp = b / (z * c);
	else
		tmp = -4.0 * ((a * t) / 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.
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[b, -1.6e+106], N[Not[LessEqual[b, 4.8e-82]], $MachinePrecision]], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5999999999999999e106 or 4.80000000000000017e-82 < b

   1. Initial program 78.3%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 63.7%

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

   if -1.5999999999999999e106 < b < 4.80000000000000017e-82

   1. Initial program 84.2%

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 45.2

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

   5. Applied rewrites 45.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+106} \lor \neg \left(b \leq 4.8 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+106} \lor \neg \left(b \leq 8.5 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -1.6e+106) (not (<= b 8.5e-49)))
   (/ b (* z c))
   (* -4.0 (* a (/ t c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 ((b <= -1.6e+106) || !(b <= 8.5e-49)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 ((b <= (-1.6d+106)) .or. (.not. (b <= 8.5d-49))) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 ((b <= -1.6e+106) || !(b <= 8.5e-49)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 (b <= -1.6e+106) or not (b <= 8.5e-49):
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 ((b <= -1.6e+106) || !(b <= 8.5e-49))
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 ((b <= -1.6e+106) || ~((b <= 8.5e-49)))
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / 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.
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[b, -1.6e+106], N[Not[LessEqual[b, 8.5e-49]], $MachinePrecision]], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5999999999999999e106 or 8.50000000000000069e-49 < b

   1. Initial program 77.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 65.8%

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

   if -1.5999999999999999e106 < b < 8.50000000000000069e-49

   1. Initial program 84.2%

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 44.0

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

   5. Applied rewrites 44.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 44.1

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

   7. Applied rewrites 44.1%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+106} \lor \neg \left(b \leq 8.5 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.4% accurate, 2.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 81.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 38.9%

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

6. Final simplification 38.9%

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

Developer Target 1: 81.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025064 
(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)))