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

Percentage Accurate: 79.3% → 92.3%

Time: 8.8s

Alternatives: 15

Speedup: 0.9×

• 36.7% 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: 79.3% 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: 92.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 5 \cdot 10^{-62}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c\_m}, \frac{\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{c\_m}}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 5e-62)
    (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c_m)
    (fma (* -4.0 t) (/ a c_m) (/ (/ (fma (* y 9.0) x b) c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 5e-62) {
		tmp = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c_m;
	} else {
		tmp = fma((-4.0 * t), (a / c_m), ((fma((y * 9.0), x, b) / c_m) / z));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 5e-62)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c_m);
	else
		tmp = fma(Float64(-4.0 * t), Float64(a / c_m), Float64(Float64(fma(Float64(y * 9.0), x, b) / c_m) / z));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 5e-62], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision] + N[(N[(N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 5.0000000000000002e-62

   1. Initial program 78.2%

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

   3. Taylor expanded in 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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 87.7%

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

   if 5.0000000000000002e-62 < c

   1. Initial program 80.6%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 94.1%

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

Alternative 2: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c\_m}, \frac{b}{z \cdot c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<=
       (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))
       INFINITY)
    (/ (fma (* 9.0 x) y (fma (* -4.0 z) (* a t) b)) (* z c_m))
    (fma (* -4.0 t) (/ a c_m) (/ b (* z c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)) <= ((double) INFINITY)) {
		tmp = fma((9.0 * x), y, fma((-4.0 * z), (a * t), b)) / (z * c_m);
	} else {
		tmp = fma((-4.0 * t), (a / c_m), (b / (z * c_m)));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m)) <= Inf)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c_m));
	else
		tmp = fma(Float64(-4.0 * t), Float64(a / c_m), Float64(b / Float64(z * c_m)));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 87.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 86.3

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

   4. Applied rewrites 86.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 71.8%

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

   7. Applied rewrites 83.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 83.4%

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

Alternative 3: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{x \cdot 9}{z \cdot c\_m}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-282}:\\ \;\;\;\;\left(t \cdot \frac{a}{c\_m}\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{9 \cdot y}{z \cdot c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (*
    c_s
    (if (<= t_1 -4e+86)
      (* y (/ (* x 9.0) (* z c_m)))
      (if (<= t_1 -2e+26)
        (/ (/ b z) c_m)
        (if (<= t_1 -4e-282)
          (* (* t (/ a c_m)) -4.0)
          (if (<= t_1 0.4) (/ (/ b c_m) z) (* x (/ (* 9.0 y) (* z c_m))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+86) {
		tmp = y * ((x * 9.0) / (z * c_m));
	} else if (t_1 <= -2e+26) {
		tmp = (b / z) / c_m;
	} else if (t_1 <= -4e-282) {
		tmp = (t * (a / c_m)) * -4.0;
	} else if (t_1 <= 0.4) {
		tmp = (b / c_m) / z;
	} else {
		tmp = x * ((9.0 * y) / (z * c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m =     private
c\_s =     private
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m 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(c_s, x, y, z, t, a, b, c_m)
use fmin_fmax_functions
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    if (t_1 <= (-4d+86)) then
        tmp = y * ((x * 9.0d0) / (z * c_m))
    else if (t_1 <= (-2d+26)) then
        tmp = (b / z) / c_m
    else if (t_1 <= (-4d-282)) then
        tmp = (t * (a / c_m)) * (-4.0d0)
    else if (t_1 <= 0.4d0) then
        tmp = (b / c_m) / z
    else
        tmp = x * ((9.0d0 * y) / (z * c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+86) {
		tmp = y * ((x * 9.0) / (z * c_m));
	} else if (t_1 <= -2e+26) {
		tmp = (b / z) / c_m;
	} else if (t_1 <= -4e-282) {
		tmp = (t * (a / c_m)) * -4.0;
	} else if (t_1 <= 0.4) {
		tmp = (b / c_m) / z;
	} else {
		tmp = x * ((9.0 * y) / (z * c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -4e+86:
		tmp = y * ((x * 9.0) / (z * c_m))
	elif t_1 <= -2e+26:
		tmp = (b / z) / c_m
	elif t_1 <= -4e-282:
		tmp = (t * (a / c_m)) * -4.0
	elif t_1 <= 0.4:
		tmp = (b / c_m) / z
	else:
		tmp = x * ((9.0 * y) / (z * c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -4e+86)
		tmp = Float64(y * Float64(Float64(x * 9.0) / Float64(z * c_m)));
	elseif (t_1 <= -2e+26)
		tmp = Float64(Float64(b / z) / c_m);
	elseif (t_1 <= -4e-282)
		tmp = Float64(Float64(t * Float64(a / c_m)) * -4.0);
	elseif (t_1 <= 0.4)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = Float64(x * Float64(Float64(9.0 * y) / Float64(z * c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -4e+86)
		tmp = y * ((x * 9.0) / (z * c_m));
	elseif (t_1 <= -2e+26)
		tmp = (b / z) / c_m;
	elseif (t_1 <= -4e-282)
		tmp = (t * (a / c_m)) * -4.0;
	elseif (t_1 <= 0.4)
		tmp = (b / c_m) / z;
	else
		tmp = x * ((9.0 * y) / (z * c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -4e+86], N[(y * N[(N[(x * 9.0), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+26], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, -4e-282], N[(N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 0.4], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(9.0 * y), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000001e86

   1. Initial program 76.1%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 75.1

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

   5. Applied rewrites 75.1%

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

   7. Applied rewrites 67.6%

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

   if -4.0000000000000001e86 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.0000000000000001e26

   1. Initial program 75.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 67.6

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

   5. Applied rewrites 67.6%

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

   7. Applied rewrites 75.8%

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

   if -2.0000000000000001e26 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000001e-282

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.2

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

   8. Applied rewrites 58.2%

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

   if -4.0000000000000001e-282 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.40000000000000002

   1. Initial program 81.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 54.4

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

   5. Applied rewrites 54.4%

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

   7. Applied rewrites 59.9%

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

   if 0.40000000000000002 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 87.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 50.4

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

   5. Applied rewrites 50.4%

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

   7. Applied rewrites 59.0%

      \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{z \cdot c}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{9 \cdot y}{z \cdot c\_m}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-282}:\\ \;\;\;\;\left(t \cdot \frac{a}{c\_m}\right) \cdot -4\\ \mathbf{elif}\;t\_2 \leq 0.4:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* x (/ (* 9.0 y) (* z c_m)))) (t_2 (* (* x 9.0) y)))
   (*
    c_s
    (if (<= t_2 -4e+86)
      t_1
      (if (<= t_2 -2e+26)
        (/ (/ b z) c_m)
        (if (<= t_2 -4e-282)
          (* (* t (/ a c_m)) -4.0)
          (if (<= t_2 0.4) (/ (/ b c_m) z) t_1)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = x * ((9.0 * y) / (z * c_m));
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -4e+86) {
		tmp = t_1;
	} else if (t_2 <= -2e+26) {
		tmp = (b / z) / c_m;
	} else if (t_2 <= -4e-282) {
		tmp = (t * (a / c_m)) * -4.0;
	} else if (t_2 <= 0.4) {
		tmp = (b / c_m) / z;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m =     private
c\_s =     private
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m 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(c_s, x, y, z, t, a, b, c_m)
use fmin_fmax_functions
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((9.0d0 * y) / (z * c_m))
    t_2 = (x * 9.0d0) * y
    if (t_2 <= (-4d+86)) then
        tmp = t_1
    else if (t_2 <= (-2d+26)) then
        tmp = (b / z) / c_m
    else if (t_2 <= (-4d-282)) then
        tmp = (t * (a / c_m)) * (-4.0d0)
    else if (t_2 <= 0.4d0) then
        tmp = (b / c_m) / z
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = x * ((9.0 * y) / (z * c_m));
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -4e+86) {
		tmp = t_1;
	} else if (t_2 <= -2e+26) {
		tmp = (b / z) / c_m;
	} else if (t_2 <= -4e-282) {
		tmp = (t * (a / c_m)) * -4.0;
	} else if (t_2 <= 0.4) {
		tmp = (b / c_m) / z;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = x * ((9.0 * y) / (z * c_m))
	t_2 = (x * 9.0) * y
	tmp = 0
	if t_2 <= -4e+86:
		tmp = t_1
	elif t_2 <= -2e+26:
		tmp = (b / z) / c_m
	elif t_2 <= -4e-282:
		tmp = (t * (a / c_m)) * -4.0
	elif t_2 <= 0.4:
		tmp = (b / c_m) / z
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(x * Float64(Float64(9.0 * y) / Float64(z * c_m)))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -4e+86)
		tmp = t_1;
	elseif (t_2 <= -2e+26)
		tmp = Float64(Float64(b / z) / c_m);
	elseif (t_2 <= -4e-282)
		tmp = Float64(Float64(t * Float64(a / c_m)) * -4.0);
	elseif (t_2 <= 0.4)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = x * ((9.0 * y) / (z * c_m));
	t_2 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_2 <= -4e+86)
		tmp = t_1;
	elseif (t_2 <= -2e+26)
		tmp = (b / z) / c_m;
	elseif (t_2 <= -4e-282)
		tmp = (t * (a / c_m)) * -4.0;
	elseif (t_2 <= 0.4)
		tmp = (b / c_m) / z;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(x * N[(N[(9.0 * y), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -4e+86], t$95$1, If[LessEqual[t$95$2, -2e+26], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$2, -4e-282], N[(N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$2, 0.4], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000001e86 or 0.40000000000000002 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 62.0

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

   5. Applied rewrites 62.0%

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

   7. Applied rewrites 63.9%

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

   if -4.0000000000000001e86 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.0000000000000001e26

   1. Initial program 75.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 67.6

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

   5. Applied rewrites 67.6%

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

   7. Applied rewrites 75.8%

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

   if -2.0000000000000001e26 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000001e-282

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.2

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

   8. Applied rewrites 58.2%

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

   if -4.0000000000000001e-282 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.40000000000000002

   1. Initial program 81.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 54.4

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

   5. Applied rewrites 54.4%

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

   7. Applied rewrites 59.9%

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

Alternative 5: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+211}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{z} \cdot 9, y, -4 \cdot \left(a \cdot t\right)\right)}{c\_m}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{t\_1}{c\_m}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c\_m}, \frac{b}{z \cdot c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{z \cdot c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (fma (* y x) 9.0 b)) (t_2 (* (* x 9.0) y)))
   (*
    c_s
    (if (<= t_2 -5e+211)
      (/ (fma (* (/ x z) 9.0) y (* -4.0 (* a t))) c_m)
      (if (<= t_2 -5e+69)
        (/ (/ t_1 c_m) z)
        (if (<= t_2 1e-55)
          (fma (* -4.0 t) (/ a c_m) (/ b (* z c_m)))
          (/ t_1 (* z c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = fma((y * x), 9.0, b);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+211) {
		tmp = fma(((x / z) * 9.0), y, (-4.0 * (a * t))) / c_m;
	} else if (t_2 <= -5e+69) {
		tmp = (t_1 / c_m) / z;
	} else if (t_2 <= 1e-55) {
		tmp = fma((-4.0 * t), (a / c_m), (b / (z * c_m)));
	} else {
		tmp = t_1 / (z * c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = fma(Float64(y * x), 9.0, b)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -5e+211)
		tmp = Float64(fma(Float64(Float64(x / z) * 9.0), y, Float64(-4.0 * Float64(a * t))) / c_m);
	elseif (t_2 <= -5e+69)
		tmp = Float64(Float64(t_1 / c_m) / z);
	elseif (t_2 <= 1e-55)
		tmp = fma(Float64(-4.0 * t), Float64(a / c_m), Float64(b / Float64(z * c_m)));
	else
		tmp = Float64(t_1 / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -5e+211], N[(N[(N[(N[(x / z), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$2, -5e+69], N[(N[(t$95$1 / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e-55], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999995e211

   1. Initial program 69.0%

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 88.4%

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

   if -4.9999999999999995e211 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000036e69

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 85.9%

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

   6. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 92.2

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

   8. Applied rewrites 92.2%

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

   if -5.00000000000000036e69 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999995e-56

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 90.8%

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

   7. Applied rewrites 89.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 84.8%

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

   if 9.99999999999999995e-56 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 75.1

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

   5. Applied rewrites 75.1%

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

Alternative 6: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+39} \lor \neg \left(z \leq 2.2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -3.6e+39) (not (<= z 2.2e+30)))
    (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c_m)
    (/ (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) c_m) z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.6e+39) || !(z <= 2.2e+30)) {
		tmp = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c_m;
	} else {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / c_m) / z;
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -3.6e+39) || !(z <= 2.2e+30))
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c_m);
	else
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / c_m) / z);
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -3.6e+39], N[Not[LessEqual[z, 2.2e+30]], $MachinePrecision]], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999984e39 or 2.2e30 < z

   1. Initial program 58.7%

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 92.5%

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

   if -3.59999999999999984e39 < z < 2.2e30

   1. Initial program 93.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 94.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+39} \lor \neg \left(z \leq 2.2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 4.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-4 \cdot t}{c\_m}, \frac{\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{c\_m}}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 4.6e-60)
    (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c_m)
    (fma a (/ (* -4.0 t) c_m) (/ (/ (fma (* y 9.0) x b) c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 4.6e-60) {
		tmp = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c_m;
	} else {
		tmp = fma(a, ((-4.0 * t) / c_m), ((fma((y * 9.0), x, b) / c_m) / z));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 4.6e-60)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c_m);
	else
		tmp = fma(a, Float64(Float64(-4.0 * t) / c_m), Float64(Float64(fma(Float64(y * 9.0), x, b) / c_m) / z));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 4.6e-60], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(N[(N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 4.6000000000000003e-60

   1. Initial program 78.2%

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

   3. Taylor expanded in 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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 87.7%

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

   if 4.6000000000000003e-60 < c

   1. Initial program 80.6%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 93.1%

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

Alternative 8: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+40} \lor \neg \left(z \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -1.1e+40) (not (<= z 2e+30)))
    (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c_m)
    (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1.1e+40) || !(z <= 2e+30)) {
		tmp = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c_m;
	} else {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -1.1e+40) || !(z <= 2e+30))
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c_m);
	else
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -1.1e+40], N[Not[LessEqual[z, 2e+30]], $MachinePrecision]], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e40 or 2e30 < z

   1. Initial program 58.7%

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 92.5%

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

   if -1.0999999999999999e40 < z < 2e30

   1. Initial program 93.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 93.6%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+40} \lor \neg \left(z \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c\_m}, \frac{b}{z \cdot c\_m}\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{z} \cdot 9, y, -4 \cdot \left(a \cdot t\right)\right)}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -2.95e+131)
    (fma (* -4.0 t) (/ a c_m) (/ b (* z c_m)))
    (if (<= z 4.4e+63)
      (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c_m))
      (/ (fma (* (/ x z) 9.0) y (* -4.0 (* a t))) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2.95e+131) {
		tmp = fma((-4.0 * t), (a / c_m), (b / (z * c_m)));
	} else if (z <= 4.4e+63) {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c_m);
	} else {
		tmp = fma(((x / z) * 9.0), y, (-4.0 * (a * t))) / c_m;
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -2.95e+131)
		tmp = fma(Float64(-4.0 * t), Float64(a / c_m), Float64(b / Float64(z * c_m)));
	elseif (z <= 4.4e+63)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c_m));
	else
		tmp = Float64(fma(Float64(Float64(x / z) * 9.0), y, Float64(-4.0 * Float64(a * t))) / c_m);
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -2.95e+131], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+63], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / z), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.94999999999999992e131

   1. Initial program 55.5%

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 90.2%

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

   7. Applied rewrites 71.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 81.4%

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

   if -2.94999999999999992e131 < z < 4.3999999999999997e63

   1. Initial program 92.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 91.6%

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

   if 4.3999999999999997e63 < z

   1. Initial program 49.3%

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 82.1%

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

Alternative 10: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140} \lor \neg \left(z \leq 1.15 \cdot 10^{-38}\right):\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c\_m}, \frac{b}{z \cdot c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -8.2e+140) (not (<= z 1.15e-38)))
    (fma (* -4.0 t) (/ a c_m) (/ b (* z c_m)))
    (/ (/ (fma (* y x) 9.0 b) c_m) z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -8.2e+140) || !(z <= 1.15e-38)) {
		tmp = fma((-4.0 * t), (a / c_m), (b / (z * c_m)));
	} else {
		tmp = (fma((y * x), 9.0, b) / c_m) / z;
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -8.2e+140) || !(z <= 1.15e-38))
		tmp = fma(Float64(-4.0 * t), Float64(a / c_m), Float64(b / Float64(z * c_m)));
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c_m) / z);
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -8.2e+140], N[Not[LessEqual[z, 1.15e-38]], $MachinePrecision]], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999998e140 or 1.15000000000000001e-38 < z

   1. Initial program 62.0%

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 92.5%

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

   7. Applied rewrites 80.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 79.2%

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

   if -8.1999999999999998e140 < z < 1.15000000000000001e-38

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 82.2

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

   8. Applied rewrites 82.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140} \lor \neg \left(z \leq 1.15 \cdot 10^{-38}\right):\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+140}:\\ \;\;\;\;\left(t \cdot \frac{a}{c\_m}\right) \cdot -4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -9.2e+140)
    (* (* t (/ a c_m)) -4.0)
    (if (<= z 4.5e+40)
      (/ (/ (fma (* y x) 9.0 b) c_m) z)
      (* -4.0 (/ (* a t) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -9.2e+140) {
		tmp = (t * (a / c_m)) * -4.0;
	} else if (z <= 4.5e+40) {
		tmp = (fma((y * x), 9.0, b) / c_m) / z;
	} else {
		tmp = -4.0 * ((a * t) / c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -9.2e+140)
		tmp = Float64(Float64(t * Float64(a / c_m)) * -4.0);
	elseif (z <= 4.5e+40)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c_m) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -9.2e+140], N[(N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 4.5e+40], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999961e140

   1. Initial program 59.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   8. Applied rewrites 64.8%

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

   if -9.19999999999999961e140 < z < 4.50000000000000032e40

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

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

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 80.6

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

   8. Applied rewrites 80.6%

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

   if 4.50000000000000032e40 < z

   1. Initial program 54.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

Alternative 12: 67.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+45} \lor \neg \left(a \leq 6.2 \cdot 10^{+123}\right):\\ \;\;\;\;\left(t \cdot \frac{a}{c\_m}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= a -5.5e+45) (not (<= a 6.2e+123)))
    (* (* t (/ a c_m)) -4.0)
    (/ (fma (* y x) 9.0 b) (* z c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((a <= -5.5e+45) || !(a <= 6.2e+123)) {
		tmp = (t * (a / c_m)) * -4.0;
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((a <= -5.5e+45) || !(a <= 6.2e+123))
		tmp = Float64(Float64(t * Float64(a / c_m)) * -4.0);
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[a, -5.5e+45], N[Not[LessEqual[a, 6.2e+123]], $MachinePrecision]], N[(N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < -5.5000000000000001e45 or 6.20000000000000013e123 < a

   1. Initial program 75.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 66.2

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

   8. Applied rewrites 66.2%

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

   if -5.5000000000000001e45 < a < 6.20000000000000013e123

   1. Initial program 81.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+45} \lor \neg \left(a \leq 6.2 \cdot 10^{+123}\right):\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{-64} \lor \neg \left(a \leq 1.85 \cdot 10^{+96}\right):\\ \;\;\;\;\left(t \cdot \frac{a}{c\_m}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= a -1.36e-64) (not (<= a 1.85e+96)))
    (* (* t (/ a c_m)) -4.0)
    (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((a <= -1.36e-64) || !(a <= 1.85e+96)) {
		tmp = (t * (a / c_m)) * -4.0;
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m =     private
c\_s =     private
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m 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(c_s, x, y, z, t, a, b, c_m)
use fmin_fmax_functions
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((a <= (-1.36d-64)) .or. (.not. (a <= 1.85d+96))) then
        tmp = (t * (a / c_m)) * (-4.0d0)
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((a <= -1.36e-64) || !(a <= 1.85e+96)) {
		tmp = (t * (a / c_m)) * -4.0;
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (a <= -1.36e-64) or not (a <= 1.85e+96):
		tmp = (t * (a / c_m)) * -4.0
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((a <= -1.36e-64) || !(a <= 1.85e+96))
		tmp = Float64(Float64(t * Float64(a / c_m)) * -4.0);
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((a <= -1.36e-64) || ~((a <= 1.85e+96)))
		tmp = (t * (a / c_m)) * -4.0;
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[a, -1.36e-64], N[Not[LessEqual[a, 1.85e+96]], $MachinePrecision]], N[(N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < -1.35999999999999995e-64 or 1.84999999999999996e96 < a

   1. Initial program 78.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 56.2

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

   8. Applied rewrites 56.2%

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

   if -1.35999999999999995e-64 < a < 1.84999999999999996e96

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 43.0

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

   5. Applied rewrites 43.0%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{-64} \lor \neg \left(a \leq 1.85 \cdot 10^{+96}\right):\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+114} \lor \neg \left(z \leq 8.8 \cdot 10^{-15}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -2.35e+114) (not (<= z 8.8e-15)))
    (* -4.0 (/ (* a t) c_m))
    (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.35e+114) || !(z <= 8.8e-15)) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m =     private
c\_s =     private
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m 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(c_s, x, y, z, t, a, b, c_m)
use fmin_fmax_functions
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-2.35d+114)) .or. (.not. (z <= 8.8d-15))) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.35e+114) || !(z <= 8.8e-15)) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -2.35e+114) or not (z <= 8.8e-15):
		tmp = -4.0 * ((a * t) / c_m)
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -2.35e+114) || !(z <= 8.8e-15))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -2.35e+114) || ~((z <= 8.8e-15)))
		tmp = -4.0 * ((a * t) / c_m);
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -2.35e+114], N[Not[LessEqual[z, 8.8e-15]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.35e114 or 8.79999999999999942e-15 < z

   1. Initial program 58.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

   if -2.35e114 < z < 8.79999999999999942e-15

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 49.0

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

   5. Applied rewrites 49.0%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+114} \lor \neg \left(z \leq 8.8 \cdot 10^{-15}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m =     private
c\_s =     private
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m 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(c_s, x, y, z, t, a, b, c_m)
use fmin_fmax_functions
    real(8), intent (in) :: c_s
    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_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.0%

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

3. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 37.9

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

5. Applied rewrites 37.9%

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

Developer Target 1: 81.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025016 
(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)))