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

Percentage Accurate: 79.9% → 91.5%

Time: 5.7s

Alternatives: 11

Speedup: 0.8×

• 37.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+36} \lor \neg \left(z \leq 5 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{x}{z}, 9, \frac{b}{z \cdot y}\right) \cdot y\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

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 -1.55e+36) (not (<= z 5e+99)))
   (/ (fma (* t a) -4.0 (* (fma (/ x z) 9.0 (/ b (* z y))) y)) 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 <= -1.55e+36) || !(z <= 5e+99)) {
		tmp = fma((t * a), -4.0, (fma((x / z), 9.0, (b / (z * y))) * y)) / 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 <= -1.55e+36) || !(z <= 5e+99))
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(fma(Float64(x / z), 9.0, Float64(b / Float64(z * y))) * y)) / 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, -1.55e+36], N[Not[LessEqual[z, 5e+99]], $MachinePrecision]], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(x / z), $MachinePrecision] * 9.0 + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $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 < -1.55e36 or 5.00000000000000008e99 < z

   1. Initial program 58.3%

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

   3. Taylor expanded in x around 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 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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-*r/ N/A

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

      8. div-add N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 84.7

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

   8. Applied rewrites 84.7%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-fma.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. *-commutative N/A

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

       8. lower-*.f64 88.7

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

   11. Applied rewrites 88.7%

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

   if -1.55e36 < z < 5.00000000000000008e99

   1. Initial program 96.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+36} \lor \neg \left(z \leq 5 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{x}{z}, 9, \frac{b}{z \cdot y}\right) \cdot y\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5000000:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+231}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* 9.0 x) c) (/ y z))))
   (if (<= t_1 -4e+170)
     t_2
     (if (<= t_1 5000000.0)
       (fma -4.0 (/ (* a t) c) (/ b (* c z)))
       (if (<= t_1 2e+231) (/ (/ (fma (* y x) 9.0 b) c) z) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -4e+170) {
		tmp = t_2;
	} else if (t_1 <= 5000000.0) {
		tmp = fma(-4.0, ((a * t) / c), (b / (c * z)));
	} else if (t_1 <= 2e+231) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z))
	tmp = 0.0
	if (t_1 <= -4e+170)
		tmp = t_2;
	elseif (t_1 <= 5000000.0)
		tmp = fma(-4.0, Float64(Float64(a * t) / c), Float64(b / Float64(c * z)));
	elseif (t_1 <= 2e+231)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+170], t$95$2, If[LessEqual[t$95$1, 5000000.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+231], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000014e170 or 2.0000000000000001e231 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 82.2

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

   5. Applied rewrites 82.2%

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

   if -4.00000000000000014e170 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e6

   1. Initial program 85.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 89.0%

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

   6. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 86.7

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

   8. Applied rewrites 86.7%

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

   if 5e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000001e231

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   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 77.9

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

   5. Applied rewrites 77.9%

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

Alternative 3: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+183}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* 9.0 x) c) (/ y z))))
   (if (<= t_1 -4e+170)
     t_2
     (if (<= t_1 5000000.0)
       (/ (fma (* (* t z) a) -4.0 b) (* z c))
       (if (<= t_1 5e+183) (/ (fma (* y x) 9.0 b) (* z c)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -4e+170) {
		tmp = t_2;
	} else if (t_1 <= 5000000.0) {
		tmp = fma(((t * z) * a), -4.0, b) / (z * c);
	} else if (t_1 <= 5e+183) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z))
	tmp = 0.0
	if (t_1 <= -4e+170)
		tmp = t_2;
	elseif (t_1 <= 5000000.0)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(z * c));
	elseif (t_1 <= 5e+183)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+170], t$95$2, If[LessEqual[t$95$1, 5000000.0], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+183], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000014e170 or 5.00000000000000009e183 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 67.5%

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

   3. Taylor expanded in x around inf

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

      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 79.7

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

   5. Applied rewrites 79.7%

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

   if -4.00000000000000014e170 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e6

   1. Initial program 85.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 86.7

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

   4. Applied rewrites 86.7%

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

   5. Taylor expanded in x around 0

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

      1. associate-+l- N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. associate-+l- N/A

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

      6. metadata-eval N/A

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

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

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 79.7

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

   7. Applied rewrites 79.7%

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

   if 5e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000009e183

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 75.5

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

   5. Applied rewrites 75.5%

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

Alternative 4: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+36} \lor \neg \left(z \leq 9.4 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

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 -1.32e+36) (not (<= z 9.4e-122)))
   (/ (fma (* t a) -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 <= -1.32e+36) || !(z <= 9.4e-122)) {
		tmp = fma((t * a), -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 <= -1.32e+36) || !(z <= 9.4e-122))
		tmp = Float64(fma(Float64(t * a), -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, -1.32e+36], N[Not[LessEqual[z, 9.4e-122]], $MachinePrecision]], N[(N[(N[(t * a), $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 < -1.3200000000000001e36 or 9.3999999999999999e-122 < z

   1. Initial program 69.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 81.4%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-*r/ N/A

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

      8. div-add N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 88.2

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

   8. Applied rewrites 88.2%

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

   if -1.3200000000000001e36 < z < 9.3999999999999999e-122

   1. Initial program 98.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+36} \lor \neg \left(z \leq 9.4 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+179}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(c \cdot z\right) \cdot a}\right) \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-139}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \left(a \cdot t\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.5e+179)
   (* (fma (/ t c) -4.0 (/ b (* (* c z) a))) a)
   (if (<= z 3e-139)
     (/ (+ (- (* (* x 9.0) y) (* (* 4.0 z) (* a t))) b) (* z c))
     (/ (fma (* t a) -4.0 (/ (fma (* y x) 9.0 b) z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.5e+179) {
		tmp = fma((t / c), -4.0, (b / ((c * z) * a))) * a;
	} else if (z <= 3e-139) {
		tmp = ((((x * 9.0) * y) - ((4.0 * z) * (a * t))) + b) / (z * c);
	} else {
		tmp = fma((t * a), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.5e+179)
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(c * z) * a))) * a);
	elseif (z <= 3e-139)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(4.0 * z) * Float64(a * t))) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.5e+179], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(c * z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 3e-139], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000015e179

   1. Initial program 58.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 55.9

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 86.6

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

   8. Applied rewrites 86.6%

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

   if -3.50000000000000015e179 < z < 2.9999999999999999e-139

   1. Initial program 93.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 89.3

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

   4. Applied rewrites 89.3%

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

   if 2.9999999999999999e-139 < z

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 83.6%

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

   6. Taylor expanded in 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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-*r/ N/A

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

      8. div-add N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 88.4

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

   8. Applied rewrites 88.4%

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

Alternative 6: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-88} \lor \neg \left(z \leq 6.8 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{t\_1}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (* y x) 9.0 b)))
   (if (or (<= z -5.8e-88) (not (<= z 6.8e-125)))
     (/ (fma (* t a) -4.0 (/ t_1 z)) c)
     (/ t_1 (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((y * x), 9.0, b);
	double tmp;
	if ((z <= -5.8e-88) || !(z <= 6.8e-125)) {
		tmp = fma((t * a), -4.0, (t_1 / z)) / c;
	} else {
		tmp = t_1 / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if ((z <= -5.8e-88) || !(z <= 6.8e-125))
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(t_1 / z)) / c);
	else
		tmp = Float64(t_1 / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[Or[LessEqual[z, -5.8e-88], N[Not[LessEqual[z, 6.8e-125]], $MachinePrecision]], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000003e-88 or 6.7999999999999995e-125 < z

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 83.1%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-*r/ N/A

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

      8. div-add N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 88.9

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

   8. Applied rewrites 88.9%

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

   if -5.8000000000000003e-88 < z < 6.7999999999999995e-125

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 87.7

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

   5. Applied rewrites 87.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-88} \lor \neg \left(z \leq 6.8 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+147} \lor \neg \left(z \leq 7.3 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.85e+147) (not (<= z 7.3e-37)))
   (/ (fma (* t a) -4.0 (/ b z)) c)
   (/ (fma (* y x) 9.0 b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.85e+147) || !(z <= 7.3e-37)) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.85e+147) || !(z <= 7.3e-37))
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.85e+147], N[Not[LessEqual[z, 7.3e-37]], $MachinePrecision]], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e147 or 7.2999999999999997e-37 < z

   1. Initial program 64.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.3%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-*r/ N/A

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

      8. div-add N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 87.3

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

   8. Applied rewrites 87.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 83.2%

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

   if -1.85e147 < z < 7.2999999999999997e-37

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.9

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

   5. Applied rewrites 80.9%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+147} \lor \neg \left(z \leq 7.3 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+147} \lor \neg \left(z \leq 10^{+48}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9e+147) (not (<= z 1e+48)))
   (* -4.0 (* a (/ t c)))
   (/ (fma (* y x) 9.0 b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9e+147) || !(z <= 1e+48)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9e+147) || !(z <= 1e+48))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9e+147], N[Not[LessEqual[z, 1e+48]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000016e147 or 1.00000000000000004e48 < z

   1. Initial program 58.0%

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

   3. Taylor expanded in z around inf

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

      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 71.8

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

   5. Applied rewrites 71.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 71.1

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

   7. Applied rewrites 71.1%

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

   if -9.00000000000000016e147 < z < 1.00000000000000004e48

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+147} \lor \neg \left(z \leq 10^{+48}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-246}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a (/ t c)))))
   (if (<= z -1.4e-72)
     t_1
     (if (<= z 6.6e-246)
       (/ (* (* y x) 9.0) (* z c))
       (if (<= z 8.2e+47) (/ b (* z c)) t_1)))))

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 = -4.0 * (a * (t / c));
	double tmp;
	if (z <= -1.4e-72) {
		tmp = t_1;
	} else if (z <= 6.6e-246) {
		tmp = ((y * x) * 9.0) / (z * c);
	} else if (z <= 8.2e+47) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * (t / c))
    if (z <= (-1.4d-72)) then
        tmp = t_1
    else if (z <= 6.6d-246) then
        tmp = ((y * x) * 9.0d0) / (z * c)
    else if (z <= 8.2d+47) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * (t / c));
	double tmp;
	if (z <= -1.4e-72) {
		tmp = t_1;
	} else if (z <= 6.6e-246) {
		tmp = ((y * x) * 9.0) / (z * c);
	} else if (z <= 8.2e+47) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * (t / c))
	tmp = 0
	if z <= -1.4e-72:
		tmp = t_1
	elif z <= 6.6e-246:
		tmp = ((y * x) * 9.0) / (z * c)
	elif z <= 8.2e+47:
		tmp = b / (z * c)
	else:
		tmp = t_1
	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(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (z <= -1.4e-72)
		tmp = t_1;
	elseif (z <= 6.6e-246)
		tmp = Float64(Float64(Float64(y * x) * 9.0) / Float64(z * c));
	elseif (z <= 8.2e+47)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (z <= -1.4e-72)
		tmp = t_1;
	elseif (z <= 6.6e-246)
		tmp = ((y * x) * 9.0) / (z * c);
	elseif (z <= 8.2e+47)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-72], t$95$1, If[LessEqual[z, 6.6e-246], N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+47], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999e-72 or 8.2000000000000002e47 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf

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

      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 58.6

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

   5. Applied rewrites 58.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if -1.3999999999999999e-72 < z < 6.6000000000000002e-246

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   if 6.6000000000000002e-246 < z < 8.2000000000000002e47

   1. Initial program 98.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 59.8%

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

Alternative 10: 49.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-88} \lor \neg \left(z \leq 8.2 \cdot 10^{+47}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -7e-88) (not (<= z 8.2e+47)))
   (* -4.0 (* a (/ t c)))
   (/ 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 <= -7e-88) || !(z <= 8.2e+47)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 ((z <= (-7d-88)) .or. (.not. (z <= 8.2d+47))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 ((z <= -7e-88) || !(z <= 8.2e+47)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 (z <= -7e-88) or not (z <= 8.2e+47):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -7e-88) || !(z <= 8.2e+47))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 ((z <= -7e-88) || ~((z <= 8.2e+47)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -7e-88], N[Not[LessEqual[z, 8.2e+47]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000002e-88 or 8.2000000000000002e47 < z

   1. Initial program 67.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 58.8

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

   5. Applied rewrites 58.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 60.4

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

   7. Applied rewrites 60.4%

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

   if -7.0000000000000002e-88 < z < 8.2000000000000002e47

   1. Initial program 98.2%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 54.6%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-88} \lor \neg \left(z \leq 8.2 \cdot 10^{+47}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.0% 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 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 39.8%

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

Developer Target 1: 80.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025082 
(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)))