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

Percentage Accurate: 79.2% → 91.1%

Time: 6.4s

Alternatives: 14

Speedup: 0.8×

• 37.4% 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: 79.2% 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: 91.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+54} \lor \neg \left(z \leq 1.9 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y \cdot 9, \left(\left(4 \cdot z\right) \cdot \left(-t\right)\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

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 -5.9e+54) (not (<= z 1.9e-90)))
   (/ (fma (* a t) -4.0 (/ (fma (* y x) 9.0 b) z)) c)
   (/ (+ (fma x (* y 9.0) (* (* (* 4.0 z) (- 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 <= -5.9e+54) || !(z <= 1.9e-90)) {
		tmp = fma((a * t), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = (fma(x, (y * 9.0), (((4.0 * z) * -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 <= -5.9e+54) || !(z <= 1.9e-90))
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), Float64(Float64(Float64(4.0 * z) * Float64(-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, -5.9e+54], N[Not[LessEqual[z, 1.9e-90]], $MachinePrecision]], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + N[(N[(N[(4.0 * z), $MachinePrecision] * (-t)), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8999999999999997e54 or 1.9e-90 < z

   1. Initial program 63.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 92.2

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

   8. Applied rewrites 92.2%

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

   if -5.8999999999999997e54 < z < 1.9e-90

   1. Initial program 92.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 92.9

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

   4. Applied rewrites 92.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+54} \lor \neg \left(z \leq 1.9 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y \cdot 9, \left(\left(4 \cdot z\right) \cdot \left(-t\right)\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+58}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\left(y \cdot x\right) \cdot 9}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+201}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{x}{c} \cdot 9\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+58)
     (/ (fma (* a t) -4.0 (/ (* (* y x) 9.0) z)) c)
     (if (<= t_1 1e+201)
       (/ (fma (* a t) -4.0 (/ b z)) c)
       (* (/ y z) (* (/ x c) 9.0))))))

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+58) {
		tmp = fma((a * t), -4.0, (((y * x) * 9.0) / z)) / c;
	} else if (t_1 <= 1e+201) {
		tmp = fma((a * t), -4.0, (b / z)) / c;
	} else {
		tmp = (y / z) * ((x / c) * 9.0);
	}
	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+58)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(Float64(Float64(y * x) * 9.0) / z)) / c);
	elseif (t_1 <= 1e+201)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(x / c) * 9.0));
	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+58], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+201], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999989e58

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 87.5

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

   8. Applied rewrites 87.5%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 80.8

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

   11. Applied rewrites 80.8%

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

   if -1.99999999999999989e58 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000004e201

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 83.9%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 90.3

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

   8. Applied rewrites 90.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 83.5%

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

   if 1.00000000000000004e201 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.0%

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

   3. Taylor expanded in x around inf

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

      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 95.6

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

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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. associate-*r/ N/A

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

      5. lift-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 95.6

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

   7. Applied rewrites 95.6%

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

Alternative 3: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2.6 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+201}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{x}{c} \cdot 9\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2.6e+61)
     (/ (/ (fma (* 9.0 x) y b) c) z)
     (if (<= t_1 1e+201)
       (/ (fma (* a t) -4.0 (/ b z)) c)
       (* (/ y z) (* (/ x c) 9.0))))))

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 <= -2.6e+61) {
		tmp = (fma((9.0 * x), y, b) / c) / z;
	} else if (t_1 <= 1e+201) {
		tmp = fma((a * t), -4.0, (b / z)) / c;
	} else {
		tmp = (y / z) * ((x / c) * 9.0);
	}
	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 <= -2.6e+61)
		tmp = Float64(Float64(fma(Float64(9.0 * x), y, b) / c) / z);
	elseif (t_1 <= 1e+201)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(x / c) * 9.0));
	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, -2.6e+61], N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+201], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.59999999999999973e61

   1. Initial program 75.5%

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

   3. Taylor expanded in z around 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 74.2

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

   5. Applied rewrites 74.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 74.2

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

   7. Applied rewrites 74.2%

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

   if -2.59999999999999973e61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000004e201

   1. Initial program 77.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 90.4

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

   8. Applied rewrites 90.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 83.2%

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

   if 1.00000000000000004e201 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.0%

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

   3. Taylor expanded in x around inf

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

      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 95.6

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

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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. associate-*r/ N/A

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

      5. lift-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 95.6

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

   7. Applied rewrites 95.6%

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

Alternative 4: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+77}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+201}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{x}{c} \cdot 9\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+77)
     (/ (* (* 9.0 x) (/ y z)) c)
     (if (<= t_1 1e+201)
       (/ (fma (* a t) -4.0 (/ b z)) c)
       (* (/ y z) (* (/ x c) 9.0))))))

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+77) {
		tmp = ((9.0 * x) * (y / z)) / c;
	} else if (t_1 <= 1e+201) {
		tmp = fma((a * t), -4.0, (b / z)) / c;
	} else {
		tmp = (y / z) * ((x / c) * 9.0);
	}
	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+77)
		tmp = Float64(Float64(Float64(9.0 * x) * Float64(y / z)) / c);
	elseif (t_1 <= 1e+201)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(x / c) * 9.0));
	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+77], N[(N[(N[(9.0 * x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+201], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999997e77

   1. Initial program 74.0%

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

   3. Taylor expanded in x around inf

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

      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 65.1

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

   5. Applied rewrites 65.1%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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 69.0

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

   7. Applied rewrites 69.0%

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

   if -1.99999999999999997e77 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000004e201

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 90.0

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

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 82.4%

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

   if 1.00000000000000004e201 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.0%

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

   3. Taylor expanded in x around inf

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

      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 95.6

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

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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. associate-*r/ N/A

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

      5. lift-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 95.6

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

   7. Applied rewrites 95.6%

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

Alternative 5: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;c \leq 55000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{t\_1}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\frac{t\_1}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (* y x) 9.0 b)))
   (if (<= c 55000000000.0)
     (/ (fma (* a t) -4.0 (/ t_1 z)) c)
     (fma -4.0 (/ (* a t) c) (/ (/ t_1 c) z)))))

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 = fma((y * x), 9.0, b);
	double tmp;
	if (c <= 55000000000.0) {
		tmp = fma((a * t), -4.0, (t_1 / z)) / c;
	} else {
		tmp = fma(-4.0, ((a * t) / c), ((t_1 / c) / z));
	}
	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 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (c <= 55000000000.0)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(t_1 / z)) / c);
	else
		tmp = fma(-4.0, Float64(Float64(a * t) / c), Float64(Float64(t_1 / c) / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[c, 55000000000.0], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] + N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < 5.5e10

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 91.0

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

   8. Applied rewrites 91.0%

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

   if 5.5e10 < c

   1. Initial program 65.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 90.1%

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

Alternative 6: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq 2 \cdot 10^{+245}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{x}{c} \cdot 9\right)\\ \end{array} \end{array} \]

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 (<= (* (* x 9.0) y) 2e+245)
   (/ (fma (* a t) -4.0 (/ (fma (* y x) 9.0 b) z)) c)
   (* (/ y z) (* (/ x c) 9.0))))

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 (((x * 9.0) * y) <= 2e+245) {
		tmp = fma((a * t), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = (y / z) * ((x / c) * 9.0);
	}
	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 (Float64(Float64(x * 9.0) * y) <= 2e+245)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(x / c) * 9.0));
	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[N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision], 2e+245], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000009e245

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 89.3

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

   8. Applied rewrites 89.3%

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

   if 2.00000000000000009e245 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 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 98.4

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

   5. Applied rewrites 98.4%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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. associate-*r/ N/A

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

      5. lift-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 98.4

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

   7. Applied rewrites 98.4%

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

Alternative 7: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-30} \lor \neg \left(z \leq 1.9 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

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-30) (not (<= z 1.9e-90)))
   (/ (fma (* a t) -4.0 (/ (fma (* y x) 9.0 b) z)) c)
   (/ (+ (- (* (* x 9.0) y) (* (* (* 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-30) || !(z <= 1.9e-90)) {
		tmp = fma((a * t), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = ((((x * 9.0) * y) - (((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-30) || !(z <= 1.9e-90))
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - 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-30], N[Not[LessEqual[z, 1.9e-90]], $MachinePrecision]], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999994e-30 or 1.9e-90 < z

   1. Initial program 66.4%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 91.9

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

   8. Applied rewrites 91.9%

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

   if -1.39999999999999994e-30 < z < 1.9e-90

   1. Initial program 93.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-30} \lor \neg \left(z \leq 1.9 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-9}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -8.7e+142)
   (/ (/ b c) z)
   (if (<= b -1.26e-9)
     (* (* a (/ t c)) -4.0)
     (if (<= b -2.15e-88)
       (* (/ (* 9.0 x) c) (/ y z))
       (if (<= b 9.2e+158) (* (* (/ a c) -4.0) 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 (b <= -8.7e+142) {
		tmp = (b / c) / z;
	} else if (b <= -1.26e-9) {
		tmp = (a * (t / c)) * -4.0;
	} else if (b <= -2.15e-88) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-8.7d+142)) then
        tmp = (b / c) / z
    else if (b <= (-1.26d-9)) then
        tmp = (a * (t / c)) * (-4.0d0)
    else if (b <= (-2.15d-88)) then
        tmp = ((9.0d0 * x) / c) * (y / z)
    else if (b <= 9.2d+158) then
        tmp = ((a / c) * (-4.0d0)) * t
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -8.7e+142) {
		tmp = (b / c) / z;
	} else if (b <= -1.26e-9) {
		tmp = (a * (t / c)) * -4.0;
	} else if (b <= -2.15e-88) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * 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 <= -8.7e+142:
		tmp = (b / c) / z
	elif b <= -1.26e-9:
		tmp = (a * (t / c)) * -4.0
	elif b <= -2.15e-88:
		tmp = ((9.0 * x) / c) * (y / z)
	elif b <= 9.2e+158:
		tmp = ((a / c) * -4.0) * t
	else:
		tmp = 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 (b <= -8.7e+142)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -1.26e-9)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	elseif (b <= -2.15e-88)
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (b <= 9.2e+158)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -8.7e+142)
		tmp = (b / c) / z;
	elseif (b <= -1.26e-9)
		tmp = (a * (t / c)) * -4.0;
	elseif (b <= -2.15e-88)
		tmp = ((9.0 * x) / c) * (y / z);
	elseif (b <= 9.2e+158)
		tmp = ((a / c) * -4.0) * t;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[b, -8.7e+142], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -1.26e-9], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, -2.15e-88], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+158], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.6999999999999999e142

   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 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 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.7%

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

   if -8.6999999999999999e142 < b < -1.25999999999999999e-9

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 53.3

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

   8. Applied rewrites 53.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 58.9

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

   10. Applied rewrites 58.9%

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

   if -1.25999999999999999e-9 < b < -2.1499999999999999e-88

   1. Initial program 77.1%

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

   3. Taylor expanded in x around inf

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

      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 67.7

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

   5. Applied rewrites 67.7%

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

   if -2.1499999999999999e-88 < b < 9.19999999999999942e158

   1. Initial program 77.7%

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

   3. 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 85.4%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 59.6

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

   8. Applied rewrites 59.6%

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

   if 9.19999999999999942e158 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 75.8%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 49.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-9}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{x}{c} \cdot 9\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -8.7e+142)
   (/ (/ b c) z)
   (if (<= b -1.26e-9)
     (* (* a (/ t c)) -4.0)
     (if (<= b -2.15e-88)
       (* (/ y z) (* (/ x c) 9.0))
       (if (<= b 9.2e+158) (* (* (/ a c) -4.0) 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 (b <= -8.7e+142) {
		tmp = (b / c) / z;
	} else if (b <= -1.26e-9) {
		tmp = (a * (t / c)) * -4.0;
	} else if (b <= -2.15e-88) {
		tmp = (y / z) * ((x / c) * 9.0);
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-8.7d+142)) then
        tmp = (b / c) / z
    else if (b <= (-1.26d-9)) then
        tmp = (a * (t / c)) * (-4.0d0)
    else if (b <= (-2.15d-88)) then
        tmp = (y / z) * ((x / c) * 9.0d0)
    else if (b <= 9.2d+158) then
        tmp = ((a / c) * (-4.0d0)) * t
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -8.7e+142) {
		tmp = (b / c) / z;
	} else if (b <= -1.26e-9) {
		tmp = (a * (t / c)) * -4.0;
	} else if (b <= -2.15e-88) {
		tmp = (y / z) * ((x / c) * 9.0);
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * 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 <= -8.7e+142:
		tmp = (b / c) / z
	elif b <= -1.26e-9:
		tmp = (a * (t / c)) * -4.0
	elif b <= -2.15e-88:
		tmp = (y / z) * ((x / c) * 9.0)
	elif b <= 9.2e+158:
		tmp = ((a / c) * -4.0) * t
	else:
		tmp = 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 (b <= -8.7e+142)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -1.26e-9)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	elseif (b <= -2.15e-88)
		tmp = Float64(Float64(y / z) * Float64(Float64(x / c) * 9.0));
	elseif (b <= 9.2e+158)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -8.7e+142)
		tmp = (b / c) / z;
	elseif (b <= -1.26e-9)
		tmp = (a * (t / c)) * -4.0;
	elseif (b <= -2.15e-88)
		tmp = (y / z) * ((x / c) * 9.0);
	elseif (b <= 9.2e+158)
		tmp = ((a / c) * -4.0) * t;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[b, -8.7e+142], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -1.26e-9], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, -2.15e-88], N[(N[(y / z), $MachinePrecision] * N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+158], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.6999999999999999e142

   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 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 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.7%

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

   if -8.6999999999999999e142 < b < -1.25999999999999999e-9

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 53.3

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

   8. Applied rewrites 53.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 58.9

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

   10. Applied rewrites 58.9%

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

   if -1.25999999999999999e-9 < b < -2.1499999999999999e-88

   1. Initial program 77.1%

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

   3. Taylor expanded in x around inf

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

      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 67.7

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

   5. Applied rewrites 67.7%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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. associate-*r/ N/A

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

      5. lift-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 67.6

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

   7. Applied rewrites 67.6%

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

   if -2.1499999999999999e-88 < b < 9.19999999999999942e158

   1. Initial program 77.7%

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

   3. 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 85.4%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 59.6

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

   8. Applied rewrites 59.6%

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

   if 9.19999999999999942e158 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 75.8%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-88}:\\ \;\;\;\;\left(9 \cdot x\right) \cdot \frac{y}{c \cdot z}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -8.7e+142)
   (/ (/ b c) z)
   (if (<= b -9.5e-20)
     (* (* a (/ t c)) -4.0)
     (if (<= b -2.15e-88)
       (* (* 9.0 x) (/ y (* c z)))
       (if (<= b 9.2e+158) (* (* (/ a c) -4.0) 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 (b <= -8.7e+142) {
		tmp = (b / c) / z;
	} else if (b <= -9.5e-20) {
		tmp = (a * (t / c)) * -4.0;
	} else if (b <= -2.15e-88) {
		tmp = (9.0 * x) * (y / (c * z));
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-8.7d+142)) then
        tmp = (b / c) / z
    else if (b <= (-9.5d-20)) then
        tmp = (a * (t / c)) * (-4.0d0)
    else if (b <= (-2.15d-88)) then
        tmp = (9.0d0 * x) * (y / (c * z))
    else if (b <= 9.2d+158) then
        tmp = ((a / c) * (-4.0d0)) * t
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -8.7e+142) {
		tmp = (b / c) / z;
	} else if (b <= -9.5e-20) {
		tmp = (a * (t / c)) * -4.0;
	} else if (b <= -2.15e-88) {
		tmp = (9.0 * x) * (y / (c * z));
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * 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 <= -8.7e+142:
		tmp = (b / c) / z
	elif b <= -9.5e-20:
		tmp = (a * (t / c)) * -4.0
	elif b <= -2.15e-88:
		tmp = (9.0 * x) * (y / (c * z))
	elif b <= 9.2e+158:
		tmp = ((a / c) * -4.0) * t
	else:
		tmp = 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 (b <= -8.7e+142)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -9.5e-20)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	elseif (b <= -2.15e-88)
		tmp = Float64(Float64(9.0 * x) * Float64(y / Float64(c * z)));
	elseif (b <= 9.2e+158)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -8.7e+142)
		tmp = (b / c) / z;
	elseif (b <= -9.5e-20)
		tmp = (a * (t / c)) * -4.0;
	elseif (b <= -2.15e-88)
		tmp = (9.0 * x) * (y / (c * z));
	elseif (b <= 9.2e+158)
		tmp = ((a / c) * -4.0) * t;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[b, -8.7e+142], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -9.5e-20], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, -2.15e-88], N[(N[(9.0 * x), $MachinePrecision] * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+158], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.6999999999999999e142

   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 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 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.7%

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

   if -8.6999999999999999e142 < b < -9.5e-20

   1. Initial program 59.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 52.0

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

   8. Applied rewrites 52.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 57.4

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

   10. Applied rewrites 57.4%

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

   if -9.5e-20 < b < -2.1499999999999999e-88

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 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 66.1

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

   5. Applied rewrites 66.1%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{c} \cdot \frac{y}{z}} \]
   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. frac-2neg N/A

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

      6. frac-times N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 52.4

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

   7. Applied rewrites 52.4%

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

      1. lift-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. associate-/l* N/A

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

      9. frac-2neg N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 61.8

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

   9. Applied rewrites 61.8%

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

   if -2.1499999999999999e-88 < b < 9.19999999999999942e158

   1. Initial program 77.7%

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

   3. 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 85.4%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 59.6

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

   8. Applied rewrites 59.6%

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

   if 9.19999999999999942e158 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 75.8%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 49.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+143} \lor \neg \left(b \leq 9.2 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

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 (or (<= b -1.22e+143) (not (<= b 9.2e+158)))
   (/ b (* z c))
   (* (* (/ a c) -4.0) 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 ((b <= -1.22e+143) || !(b <= 9.2e+158)) {
		tmp = b / (z * c);
	} else {
		tmp = ((a / c) * -4.0) * t;
	}
	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 <= (-1.22d+143)) .or. (.not. (b <= 9.2d+158))) then
        tmp = b / (z * c)
    else
        tmp = ((a / c) * (-4.0d0)) * t
    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 <= -1.22e+143) || !(b <= 9.2e+158)) {
		tmp = b / (z * c);
	} else {
		tmp = ((a / c) * -4.0) * t;
	}
	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 <= -1.22e+143) or not (b <= 9.2e+158):
		tmp = b / (z * c)
	else:
		tmp = ((a / c) * -4.0) * 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 ((b <= -1.22e+143) || !(b <= 9.2e+158))
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	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 <= -1.22e+143) || ~((b <= 9.2e+158)))
		tmp = b / (z * c);
	else
		tmp = ((a / c) * -4.0) * t;
	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, -1.22e+143], N[Not[LessEqual[b, 9.2e+158]], $MachinePrecision]], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.22000000000000004e143 or 9.19999999999999942e158 < b

   1. Initial program 81.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 73.4%

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

   if -1.22000000000000004e143 < b < 9.19999999999999942e158

   1. Initial program 74.8%

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

   3. Taylor expanded in 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 80.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 55.1

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

   8. Applied rewrites 55.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+143} \lor \neg \left(b \leq 9.2 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+142} \lor \neg \left(b \leq 1.12 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

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 -3.7e+142) (not (<= b 1.12e+164)))
   (/ 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 <= -3.7e+142) || !(b <= 1.12e+164)) {
		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 <= (-3.7d+142)) .or. (.not. (b <= 1.12d+164))) 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 <= -3.7e+142) || !(b <= 1.12e+164)) {
		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 <= -3.7e+142) or not (b <= 1.12e+164):
		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 <= -3.7e+142) || !(b <= 1.12e+164))
		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 <= -3.7e+142) || ~((b <= 1.12e+164)))
		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, -3.7e+142], N[Not[LessEqual[b, 1.12e+164]], $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 < -3.6999999999999997e142 or 1.12000000000000006e164 < b

   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 b around inf

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

   5. Applied rewrites 75.1%

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

   if -3.6999999999999997e142 < b < 1.12000000000000006e164

   1. Initial program 74.7%

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

   3. Taylor expanded in 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 52.8

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

   5. Applied rewrites 52.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+142} \lor \neg \left(b \leq 1.12 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+143}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -1.22e+143)
   (/ (/ b c) z)
   (if (<= b 9.2e+158) (* (* (/ a c) -4.0) 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 (b <= -1.22e+143) {
		tmp = (b / c) / z;
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-1.22d+143)) then
        tmp = (b / c) / z
    else if (b <= 9.2d+158) then
        tmp = ((a / c) * (-4.0d0)) * t
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -1.22e+143) {
		tmp = (b / c) / z;
	} else if (b <= 9.2e+158) {
		tmp = ((a / c) * -4.0) * t;
	} else {
		tmp = b / (z * 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 <= -1.22e+143:
		tmp = (b / c) / z
	elif b <= 9.2e+158:
		tmp = ((a / c) * -4.0) * t
	else:
		tmp = 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 (b <= -1.22e+143)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 9.2e+158)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -1.22e+143)
		tmp = (b / c) / z;
	elseif (b <= 9.2e+158)
		tmp = ((a / c) * -4.0) * t;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[b, -1.22e+143], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 9.2e+158], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.22000000000000004e143

   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 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 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.7%

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

   if -1.22000000000000004e143 < b < 9.19999999999999942e158

   1. Initial program 74.8%

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

   3. Taylor expanded in 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 80.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 55.1

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

   8. Applied rewrites 55.1%

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

   if 9.19999999999999942e158 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 75.8%

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

Alternative 14: 35.2% accurate, 2.8× speedup

Math

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

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 76.7%

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

3. Taylor expanded in b around inf

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

5. Applied rewrites 34.1%

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

Developer Target 1: 80.0% 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 2025037 
(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)))