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

Percentage Accurate: 79.7% → 89.2%

Time: 5.4s

Alternatives: 15

Speedup: 0.6×

• 62.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 79.7% accurate, 1.0× speedup

Math

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

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: 89.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \left|c\right| \cdot \left(\mathsf{min}\left(t, a\right) \cdot z\right)\\ \mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;\left|c\right| \leq 4.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot 9, \mathsf{min}\left(x, y\right), \mathsf{fma}\left(-4, \left(\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)\right) \cdot z, b\right)\right)}{z \cdot \left|c\right|}\\ \mathbf{elif}\;\left|c\right| \leq 7.6 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \mathsf{max}\left(t, a\right), \frac{\mathsf{min}\left(t, a\right)}{\left|c\right|}, \frac{\mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)}{\left|c\right| \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{min}\left(t, a\right) \cdot \mathsf{fma}\left(-4, \frac{\mathsf{max}\left(t, a\right)}{\left|c\right|}, \mathsf{fma}\left(9, \frac{\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)}{t\_1}, \frac{b}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fabs c) (* (fmin t a) z))))
   (*
    (copysign 1.0 c)
    (if (<= (fabs c) 4.5e-111)
      (/
       (fma
        (* (fmax x y) 9.0)
        (fmin x y)
        (fma -4.0 (* (* (fmax t a) (fmin t a)) z) b))
       (* z (fabs c)))
      (if (<= (fabs c) 7.6e+200)
        (fma
         (* -4.0 (fmax t a))
         (/ (fmin t a) (fabs c))
         (/ (fma (* (fmax x y) (fmin x y)) 9.0 b) (* (fabs c) z)))
        (*
         (fmin t a)
         (fma
          -4.0
          (/ (fmax t a) (fabs c))
          (fma 9.0 (/ (* (fmin x y) (fmax x y)) t_1) (/ b t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fabs(c) * (fmin(t, a) * z);
	double tmp;
	if (fabs(c) <= 4.5e-111) {
		tmp = fma((fmax(x, y) * 9.0), fmin(x, y), fma(-4.0, ((fmax(t, a) * fmin(t, a)) * z), b)) / (z * fabs(c));
	} else if (fabs(c) <= 7.6e+200) {
		tmp = fma((-4.0 * fmax(t, a)), (fmin(t, a) / fabs(c)), (fma((fmax(x, y) * fmin(x, y)), 9.0, b) / (fabs(c) * z)));
	} else {
		tmp = fmin(t, a) * fma(-4.0, (fmax(t, a) / fabs(c)), fma(9.0, ((fmin(x, y) * fmax(x, y)) / t_1), (b / t_1)));
	}
	return copysign(1.0, c) * tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(abs(c) * Float64(fmin(t, a) * z))
	tmp = 0.0
	if (abs(c) <= 4.5e-111)
		tmp = Float64(fma(Float64(fmax(x, y) * 9.0), fmin(x, y), fma(-4.0, Float64(Float64(fmax(t, a) * fmin(t, a)) * z), b)) / Float64(z * abs(c)));
	elseif (abs(c) <= 7.6e+200)
		tmp = fma(Float64(-4.0 * fmax(t, a)), Float64(fmin(t, a) / abs(c)), Float64(fma(Float64(fmax(x, y) * fmin(x, y)), 9.0, b) / Float64(abs(c) * z)));
	else
		tmp = Float64(fmin(t, a) * fma(-4.0, Float64(fmax(t, a) / abs(c)), fma(9.0, Float64(Float64(fmin(x, y) * fmax(x, y)) / t_1), Float64(b / t_1))));
	end
	return Float64(copysign(1.0, c) * tmp)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Abs[c], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[c], $MachinePrecision], 4.5e-111], N[(N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Min[x, y], $MachinePrecision] + N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[c], $MachinePrecision], 7.6e+200], N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[Max[x, y], $MachinePrecision] * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[Abs[c], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Min[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if c < 4.49999999999999994e-111

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. add-flip-rev N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. add-flip-rev N/A

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

   3. Applied rewrites 80.7%

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

   if 4.49999999999999994e-111 < c < 7.59999999999999963e200

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 79.2%

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

      11. lift-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-/l* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

   6. Applied rewrites 85.0%

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

   if 7.59999999999999963e200 < c

   1. Initial program 79.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 70.1%

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

   4. Applied rewrites 70.1%

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

Alternative 2: 88.0% accurate, 0.6× speedup

Math

\[\mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;\left|c\right| \leq 4.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot 9, \mathsf{min}\left(x, y\right), \mathsf{fma}\left(-4, \left(a \cdot t\right) \cdot z, b\right)\right)}{z \cdot \left|c\right|}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{\left|c\right|}, \frac{\mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)}{\left|c\right| \cdot z}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (*
  (copysign 1.0 c)
  (if (<= (fabs c) 4.5e-111)
    (/
     (fma (* (fmax x y) 9.0) (fmin x y) (fma -4.0 (* (* a t) z) b))
     (* z (fabs c)))
    (fma
     (* -4.0 a)
     (/ t (fabs c))
     (/ (fma (* (fmax x y) (fmin x y)) 9.0 b) (* (fabs c) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (fabs(c) <= 4.5e-111) {
		tmp = fma((fmax(x, y) * 9.0), fmin(x, y), fma(-4.0, ((a * t) * z), b)) / (z * fabs(c));
	} else {
		tmp = fma((-4.0 * a), (t / fabs(c)), (fma((fmax(x, y) * fmin(x, y)), 9.0, b) / (fabs(c) * z)));
	}
	return copysign(1.0, c) * tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (abs(c) <= 4.5e-111)
		tmp = Float64(fma(Float64(fmax(x, y) * 9.0), fmin(x, y), fma(-4.0, Float64(Float64(a * t) * z), b)) / Float64(z * abs(c)));
	else
		tmp = fma(Float64(-4.0 * a), Float64(t / abs(c)), Float64(fma(Float64(fmax(x, y) * fmin(x, y)), 9.0, b) / Float64(abs(c) * z)));
	end
	return Float64(copysign(1.0, c) * tmp)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[c], $MachinePrecision], 4.5e-111], N[(N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Min[x, y], $MachinePrecision] + N[(-4.0 * N[(N[(a * t), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / N[Abs[c], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[Max[x, y], $MachinePrecision] * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[Abs[c], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 4.49999999999999994e-111

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. add-flip-rev N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. add-flip-rev N/A

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

   3. Applied rewrites 80.7%

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

   if 4.49999999999999994e-111 < c

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 79.2%

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

      11. lift-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-/l* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

   6. Applied rewrites 85.0%

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

Alternative 3: 87.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot 9, \mathsf{min}\left(x, y\right), \mathsf{fma}\left(-4, \left(\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)\right) \cdot z, b\right)\right)}{z \cdot c}\\ t_2 := \frac{\left(\left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right) - \left(\left(z \cdot 4\right) \cdot \mathsf{min}\left(t, a\right)\right) \cdot \mathsf{max}\left(t, a\right)\right) + b}{z \cdot c}\\ t_3 := -4 \cdot \mathsf{max}\left(t, a\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\mathsf{min}\left(t, a\right) \cdot t\_3, z, \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)\right)}{z}}{c}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, \frac{\mathsf{min}\left(t, a\right)}{c}, \frac{b}{c \cdot z}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          (fma
           (* (fmax x y) 9.0)
           (fmin x y)
           (fma -4.0 (* (* (fmax t a) (fmin t a)) z) b))
          (* z c)))
        (t_2
         (/
          (+
           (-
            (* (* (fmin x y) 9.0) (fmax x y))
            (* (* (* z 4.0) (fmin t a)) (fmax t a)))
           b)
          (* z c)))
        (t_3 (* -4.0 (fmax t a))))
   (if (<= t_2 -5e-223)
     t_1
     (if (<= t_2 0.0)
       (/ (/ (fma (* (fmin t a) t_3) z (* (fmax x y) (* 9.0 (fmin x y)))) z) c)
       (if (<= t_2 INFINITY) t_1 (fma t_3 (/ (fmin t a) c) (/ b (* c z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((fmax(x, y) * 9.0), fmin(x, y), fma(-4.0, ((fmax(t, a) * fmin(t, a)) * z), b)) / (z * c);
	double t_2 = ((((fmin(x, y) * 9.0) * fmax(x, y)) - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / (z * c);
	double t_3 = -4.0 * fmax(t, a);
	double tmp;
	if (t_2 <= -5e-223) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = (fma((fmin(t, a) * t_3), z, (fmax(x, y) * (9.0 * fmin(x, y)))) / z) / c;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(t_3, (fmin(t, a) / c), (b / (c * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(fmax(x, y) * 9.0), fmin(x, y), fma(-4.0, Float64(Float64(fmax(t, a) * fmin(t, a)) * z), b)) / Float64(z * c))
	t_2 = Float64(Float64(Float64(Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y)) - Float64(Float64(Float64(z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / Float64(z * c))
	t_3 = Float64(-4.0 * fmax(t, a))
	tmp = 0.0
	if (t_2 <= -5e-223)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(fma(Float64(fmin(t, a) * t_3), z, Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) / z) / c);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = fma(t_3, Float64(fmin(t, a) / c), Float64(b / Float64(c * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Min[x, y], $MachinePrecision] + N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-223], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(N[Min[t, a], $MachinePrecision] * t$95$3), $MachinePrecision] * z + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(t$95$3 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.00000000000000024e-223 or -0.0 < (/.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)) < +inf.0

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. add-flip-rev N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. add-flip-rev N/A

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

   3. Applied rewrites 80.7%

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

   if -5.00000000000000024e-223 < (/.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)) < -0.0

   1. Initial program 79.7%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 55.9%

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

   4. Applied rewrites 55.9%

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

   6. Applied rewrites 58.3%

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

   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 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 79.2%

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

      11. lift-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-/l* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

   6. Applied rewrites 85.0%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.9%

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

   9. Applied rewrites 63.9%

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

Alternative 4: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_2 := -4 \cdot \mathsf{max}\left(t, a\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\left(\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t\_2}{c}, \mathsf{min}\left(t, a\right), \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\mathsf{min}\left(t, a\right) \cdot t\_2, z, \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)\right)}{z}}{c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))) (t_2 (* -4.0 (fmax t a))))
   (if (<= t_1 -2e+212)
     (/ (* (* (fmin x y) (/ (fmax x y) c)) 9.0) z)
     (if (<= t_1 5e+50)
       (fma (/ t_2 c) (fmin t a) (/ b (* c z)))
       (/
        (/ (fma (* (fmin t a) t_2) z (* (fmax x y) (* 9.0 (fmin x y)))) z)
        c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = -4.0 * fmax(t, a);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= 5e+50) {
		tmp = fma((t_2 / c), fmin(t, a), (b / (c * z)));
	} else {
		tmp = (fma((fmin(t, a) * t_2), z, (fmax(x, y) * (9.0 * fmin(x, y)))) / z) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	t_2 = Float64(-4.0 * fmax(t, a))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / c)) * 9.0) / z);
	elseif (t_1 <= 5e+50)
		tmp = fma(Float64(t_2 / c), fmin(t, a), Float64(b / Float64(c * z)));
	else
		tmp = Float64(Float64(fma(Float64(fmin(t, a) * t_2), z, Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) / z) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+50], N[(N[(t$95$2 / c), $MachinePrecision] * N[Min[t, a], $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Min[t, a], $MachinePrecision] * t$95$2), $MachinePrecision] * z + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e212

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 36.1%

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

   8. Applied rewrites 36.1%

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

   if -1.9999999999999998e212 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e50

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 79.2%

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

      11. lift-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-/l* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

   6. Applied rewrites 85.0%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.9%

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

   9. Applied rewrites 63.9%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. mult-flip N/A

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

       5. lift-/.f64 N/A

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

       6. associate-*r* N/A

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(\frac{1}{c} \cdot \left(-4 \cdot a\right), \color{blue}{t}, \frac{b}{c \cdot z}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\frac{1}{c} \cdot \left(-4 \cdot a\right), t, \frac{b}{c \cdot z}\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\left(-4 \cdot a\right) \cdot \frac{1}{c}, t, \frac{b}{c \cdot z}\right) \]

       12. lift-/.f64 N/A

           \[\leadsto \mathsf{fma}\left(\left(-4 \cdot a\right) \cdot \frac{1}{c}, t, \frac{b}{c \cdot z}\right) \]

       13. mult-flip-rev N/A

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

       14. lower-/.f64 64.2%

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

   11. Applied rewrites 64.2%

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

   if 5e50 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 55.9%

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

   4. Applied rewrites 55.9%

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

   6. Applied rewrites 58.3%

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

Alternative 5: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\left(\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4 \cdot \mathsf{max}\left(t, a\right)}{c}, \mathsf{min}\left(t, a\right), \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x, y\right) \cdot \frac{\frac{\mathsf{min}\left(x, y\right)}{c} \cdot 9}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))))
   (if (<= t_1 -2e+212)
     (/ (* (* (fmin x y) (/ (fmax x y) c)) 9.0) z)
     (if (<= t_1 5e+121)
       (fma (/ (* -4.0 (fmax t a)) c) (fmin t a) (/ b (* c z)))
       (* (fmax x y) (/ (* (/ (fmin x y) c) 9.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= 5e+121) {
		tmp = fma(((-4.0 * fmax(t, a)) / c), fmin(t, a), (b / (c * z)));
	} else {
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / c)) * 9.0) / z);
	elseif (t_1 <= 5e+121)
		tmp = fma(Float64(Float64(-4.0 * fmax(t, a)) / c), fmin(t, a), Float64(b / Float64(c * z)));
	else
		tmp = Float64(fmax(x, y) * Float64(Float64(Float64(fmin(x, y) / c) * 9.0) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+121], N[(N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * N[Min[t, a], $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] * N[(N[(N[(N[Min[x, y], $MachinePrecision] / c), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e212

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 36.1%

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

   8. Applied rewrites 36.1%

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

   if -1.9999999999999998e212 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000007e121

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 79.2%

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

      11. lift-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-/l* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

   6. Applied rewrites 85.0%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.9%

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

   9. Applied rewrites 63.9%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. mult-flip N/A

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

       5. lift-/.f64 N/A

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

       6. associate-*r* N/A

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-fma.f64 64.2%

          \[\leadsto \mathsf{fma}\left(\frac{1}{c} \cdot \left(-4 \cdot a\right), \color{blue}{t}, \frac{b}{c \cdot z}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\frac{1}{c} \cdot \left(-4 \cdot a\right), t, \frac{b}{c \cdot z}\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\left(-4 \cdot a\right) \cdot \frac{1}{c}, t, \frac{b}{c \cdot z}\right) \]

       12. lift-/.f64 N/A

           \[\leadsto \mathsf{fma}\left(\left(-4 \cdot a\right) \cdot \frac{1}{c}, t, \frac{b}{c \cdot z}\right) \]

       13. mult-flip-rev N/A

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

       14. lower-/.f64 64.2%

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

   11. Applied rewrites 64.2%

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

   if 5.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 37.4%

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

   8. Applied rewrites 37.4%

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

Alternative 6: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\left(\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x, y\right) \cdot \frac{\frac{\mathsf{min}\left(x, y\right)}{c} \cdot 9}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))))
   (if (<= t_1 -2e+212)
     (/ (* (* (fmin x y) (/ (fmax x y) c)) 9.0) z)
     (if (<= t_1 5e+121)
       (fma (* -4.0 a) (/ t c) (/ b (* c z)))
       (* (fmax x y) (/ (* (/ (fmin x y) c) 9.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= 5e+121) {
		tmp = fma((-4.0 * a), (t / c), (b / (c * z)));
	} else {
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / c)) * 9.0) / z);
	elseif (t_1 <= 5e+121)
		tmp = fma(Float64(-4.0 * a), Float64(t / c), Float64(b / Float64(c * z)));
	else
		tmp = Float64(fmax(x, y) * Float64(Float64(Float64(fmin(x, y) / c) * 9.0) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+121], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] * N[(N[(N[(N[Min[x, y], $MachinePrecision] / c), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e212

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 36.1%

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

   8. Applied rewrites 36.1%

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

   if -1.9999999999999998e212 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000007e121

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 79.2%

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

      11. lift-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-/l* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

   6. Applied rewrites 85.0%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.9%

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

   9. Applied rewrites 63.9%

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

   if 5.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 37.4%

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

   8. Applied rewrites 37.4%

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

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\left(\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x, y\right) \cdot \frac{\frac{\mathsf{min}\left(x, y\right)}{c} \cdot 9}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))))
   (if (<= t_1 -2e+212)
     (/ (* (* (fmin x y) (/ (fmax x y) c)) 9.0) z)
     (if (<= t_1 5e+121)
       (fma -4.0 (/ (* a t) c) (/ b (* c z)))
       (* (fmax x y) (/ (* (/ (fmin x y) c) 9.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= 5e+121) {
		tmp = fma(-4.0, ((a * t) / c), (b / (c * z)));
	} else {
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = Float64(Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / c)) * 9.0) / z);
	elseif (t_1 <= 5e+121)
		tmp = fma(-4.0, Float64(Float64(a * t) / c), Float64(b / Float64(c * z)));
	else
		tmp = Float64(fmax(x, y) * Float64(Float64(Float64(fmin(x, y) / c) * 9.0) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], N[(N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+121], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] * N[(N[(N[(N[Min[x, y], $MachinePrecision] / c), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e212

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 36.1%

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

   8. Applied rewrites 36.1%

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

   if -1.9999999999999998e212 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000007e121

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 78.8%

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.4%

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

   7. Applied rewrites 63.4%

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

   if 5.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 37.4%

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

   8. Applied rewrites 37.4%

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

Alternative 8: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+142}:\\ \;\;\;\;\frac{\left(\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot \mathsf{max}\left(t, a\right), \mathsf{min}\left(t, a\right), b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x, y\right) \cdot \frac{\frac{\mathsf{min}\left(x, y\right)}{c} \cdot 9}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))))
   (if (<= t_1 -1e+142)
     (/ (* (* (fmin x y) (/ (fmax x y) c)) 9.0) z)
     (if (<= t_1 5e+121)
       (/ (fma (* (* -4.0 z) (fmax t a)) (fmin t a) b) (* c z))
       (* (fmax x y) (/ (* (/ (fmin x y) c) 9.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -1e+142) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= 5e+121) {
		tmp = fma(((-4.0 * z) * fmax(t, a)), fmin(t, a), b) / (c * z);
	} else {
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -1e+142)
		tmp = Float64(Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / c)) * 9.0) / z);
	elseif (t_1 <= 5e+121)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * fmax(t, a)), fmin(t, a), b) / Float64(c * z));
	else
		tmp = Float64(fmax(x, y) * Float64(Float64(Float64(fmin(x, y) / c) * 9.0) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+142], N[(N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+121], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[Min[t, a], $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] * N[(N[(N[(N[Min[x, y], $MachinePrecision] / c), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000005e142

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 36.1%

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

   8. Applied rewrites 36.1%

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

   if -1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000007e121

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. mult-flip N/A

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

      3. lower-*.f64 N/A

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \color{blue}{b}\right) \cdot \frac{1}{c \cdot z} \]
   5. Step-by-step derivation

   6. Applied rewrites 57.1%

      \[\leadsto \mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \color{blue}{b}\right) \cdot \frac{1}{c \cdot z} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, b\right) \cdot \frac{1}{c \cdot z}} \]

      2. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, b\right) \cdot \color{blue}{\frac{1}{c \cdot z}} \]

      3. mult-flip-rev N/A

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

      4. lower-/.f64 57.1%

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 57.1%

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

   8. Applied rewrites 57.1%

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

   if 5.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 37.4%

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

   8. Applied rewrites 37.4%

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

Alternative 9: 63.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c))))
   (if (<= t -1.26e+141)
     t_1
     (if (<= t 1.8e-25) (/ (+ b (* 9.0 (* x y))) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double tmp;
	if (t <= -1.26e+141) {
		tmp = t_1;
	} else if (t <= 1.8e-25) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (-4.0d0) * ((a * t) / c)
    if (t <= (-1.26d+141)) then
        tmp = t_1
    else if (t <= 1.8d-25) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t_1
    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 = -4.0 * ((a * t) / c);
	double tmp;
	if (t <= -1.26e+141) {
		tmp = t_1;
	} else if (t <= 1.8e-25) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	tmp = 0
	if t <= -1.26e+141:
		tmp = t_1
	elif t <= 1.8e-25:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (t <= -1.26e+141)
		tmp = t_1;
	elseif (t <= 1.8e-25)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (t <= -1.26e+141)
		tmp = t_1;
	elseif (t <= 1.8e-25)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+141], t$95$1, If[LessEqual[t, 1.8e-25], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25999999999999994e141 or 1.8e-25 < t

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -1.25999999999999994e141 < t < 1.8e-25

   1. Initial program 79.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

Alternative 10: 53.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+48}:\\ \;\;\;\;\frac{\left(\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-296}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x, y\right) \cdot \frac{\frac{\mathsf{min}\left(x, y\right)}{c} \cdot 9}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))) (t_2 (* -4.0 (/ (* a t) c))))
   (if (<= t_1 -5e+48)
     (/ (* (* (fmin x y) (/ (fmax x y) c)) 9.0) z)
     (if (<= t_1 -1e-203)
       t_2
       (if (<= t_1 1e-296)
         (/ 1.0 (/ c (/ b z)))
         (if (<= t_1 5e+87)
           t_2
           (* (fmax x y) (/ (* (/ (fmin x y) c) 9.0) z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (t_1 <= -5e+48) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= -1e-203) {
		tmp = t_2;
	} else if (t_1 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_1 <= 5e+87) {
		tmp = t_2;
	} else {
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z);
	}
	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) :: tmp
    t_1 = (fmin(x, y) * 9.0d0) * fmax(x, y)
    t_2 = (-4.0d0) * ((a * t) / c)
    if (t_1 <= (-5d+48)) then
        tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0d0) / z
    else if (t_1 <= (-1d-203)) then
        tmp = t_2
    else if (t_1 <= 1d-296) then
        tmp = 1.0d0 / (c / (b / z))
    else if (t_1 <= 5d+87) then
        tmp = t_2
    else
        tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0d0) / z)
    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 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (t_1 <= -5e+48) {
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z;
	} else if (t_1 <= -1e-203) {
		tmp = t_2;
	} else if (t_1 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_1 <= 5e+87) {
		tmp = t_2;
	} else {
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmin(x, y) * 9.0) * fmax(x, y)
	t_2 = -4.0 * ((a * t) / c)
	tmp = 0
	if t_1 <= -5e+48:
		tmp = ((fmin(x, y) * (fmax(x, y) / c)) * 9.0) / z
	elif t_1 <= -1e-203:
		tmp = t_2
	elif t_1 <= 1e-296:
		tmp = 1.0 / (c / (b / z))
	elif t_1 <= 5e+87:
		tmp = t_2
	else:
		tmp = fmax(x, y) * (((fmin(x, y) / c) * 9.0) / z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (t_1 <= -5e+48)
		tmp = Float64(Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / c)) * 9.0) / z);
	elseif (t_1 <= -1e-203)
		tmp = t_2;
	elseif (t_1 <= 1e-296)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (t_1 <= 5e+87)
		tmp = t_2;
	else
		tmp = Float64(fmax(x, y) * Float64(Float64(Float64(fmin(x, y) / c) * 9.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (min(x, y) * 9.0) * max(x, y);
	t_2 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (t_1 <= -5e+48)
		tmp = ((min(x, y) * (max(x, y) / c)) * 9.0) / z;
	elseif (t_1 <= -1e-203)
		tmp = t_2;
	elseif (t_1 <= 1e-296)
		tmp = 1.0 / (c / (b / z));
	elseif (t_1 <= 5e+87)
		tmp = t_2;
	else
		tmp = max(x, y) * (((min(x, y) / c) * 9.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+48], N[(N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e-203], t$95$2, If[LessEqual[t$95$1, 1e-296], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+87], t$95$2, N[(N[Max[x, y], $MachinePrecision] * N[(N[(N[(N[Min[x, y], $MachinePrecision] / c), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999973e48

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 36.1%

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

   8. Applied rewrites 36.1%

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

   if -4.99999999999999973e48 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203 or 1e-296 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e87

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-296

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 36.1%

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

   4. Applied rewrites 36.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 34.1%

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

   6. Applied rewrites 34.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      4. lower-unsound-/.f64 34.1%

         \[\leadsto \frac{1}{\frac{c}{\color{blue}{\frac{b}{z}}}} \]

   8. Applied rewrites 34.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

   if 4.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 37.4%

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

   8. Applied rewrites 37.4%

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

Alternative 11: 53.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := y \cdot \frac{\frac{x}{c} \cdot 9}{z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-296}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c)))
        (t_2 (* (* x 9.0) y))
        (t_3 (* y (/ (* (/ x c) 9.0) z))))
   (if (<= t_2 -1e+43)
     t_3
     (if (<= t_2 -1e-203)
       t_1
       (if (<= t_2 1e-296)
         (/ 1.0 (/ c (/ b z)))
         (if (<= t_2 5e+87) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double t_3 = y * (((x / c) * 9.0) / z);
	double tmp;
	if (t_2 <= -1e+43) {
		tmp = t_3;
	} else if (t_2 <= -1e-203) {
		tmp = t_1;
	} else if (t_2 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_2 <= 5e+87) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: tmp
    t_1 = (-4.0d0) * ((a * t) / c)
    t_2 = (x * 9.0d0) * y
    t_3 = y * (((x / c) * 9.0d0) / z)
    if (t_2 <= (-1d+43)) then
        tmp = t_3
    else if (t_2 <= (-1d-203)) then
        tmp = t_1
    else if (t_2 <= 1d-296) then
        tmp = 1.0d0 / (c / (b / z))
    else if (t_2 <= 5d+87) then
        tmp = t_1
    else
        tmp = t_3
    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 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double t_3 = y * (((x / c) * 9.0) / z);
	double tmp;
	if (t_2 <= -1e+43) {
		tmp = t_3;
	} else if (t_2 <= -1e-203) {
		tmp = t_1;
	} else if (t_2 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_2 <= 5e+87) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	t_2 = (x * 9.0) * y
	t_3 = y * (((x / c) * 9.0) / z)
	tmp = 0
	if t_2 <= -1e+43:
		tmp = t_3
	elif t_2 <= -1e-203:
		tmp = t_1
	elif t_2 <= 1e-296:
		tmp = 1.0 / (c / (b / z))
	elif t_2 <= 5e+87:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(y * Float64(Float64(Float64(x / c) * 9.0) / z))
	tmp = 0.0
	if (t_2 <= -1e+43)
		tmp = t_3;
	elseif (t_2 <= -1e-203)
		tmp = t_1;
	elseif (t_2 <= 1e-296)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (t_2 <= 5e+87)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	t_2 = (x * 9.0) * y;
	t_3 = y * (((x / c) * 9.0) / z);
	tmp = 0.0;
	if (t_2 <= -1e+43)
		tmp = t_3;
	elseif (t_2 <= -1e-203)
		tmp = t_1;
	elseif (t_2 <= 1e-296)
		tmp = 1.0 / (c / (b / z));
	elseif (t_2 <= 5e+87)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+43], t$95$3, If[LessEqual[t$95$2, -1e-203], t$95$1, If[LessEqual[t$95$2, 1e-296], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+87], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000001e43 or 4.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 36.5%

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

   6. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 37.4%

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

   8. Applied rewrites 37.4%

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

   if -1.00000000000000001e43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203 or 1e-296 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e87

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-296

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 36.1%

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

   4. Applied rewrites 36.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 34.1%

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

   6. Applied rewrites 34.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      4. lower-unsound-/.f64 34.1%

         \[\leadsto \frac{1}{\frac{c}{\color{blue}{\frac{b}{z}}}} \]

   8. Applied rewrites 34.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\mathsf{max}\left(x, y\right)}{c \cdot z} \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)\\ t_2 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_3 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-296}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t\_2 \leq 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ (fmax x y) (* c z)) (* 9.0 (fmin x y))))
        (t_2 (* (* (fmin x y) 9.0) (fmax x y)))
        (t_3 (* -4.0 (/ (* a t) c))))
   (if (<= t_2 -1e+142)
     t_1
     (if (<= t_2 -1e-203)
       t_3
       (if (<= t_2 1e-296)
         (/ 1.0 (/ c (/ b z)))
         (if (<= t_2 1e+79) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmax(x, y) / (c * z)) * (9.0 * fmin(x, y));
	double t_2 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_3 = -4.0 * ((a * t) / c);
	double tmp;
	if (t_2 <= -1e+142) {
		tmp = t_1;
	} else if (t_2 <= -1e-203) {
		tmp = t_3;
	} else if (t_2 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_2 <= 1e+79) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (fmax(x, y) / (c * z)) * (9.0d0 * fmin(x, y))
    t_2 = (fmin(x, y) * 9.0d0) * fmax(x, y)
    t_3 = (-4.0d0) * ((a * t) / c)
    if (t_2 <= (-1d+142)) then
        tmp = t_1
    else if (t_2 <= (-1d-203)) then
        tmp = t_3
    else if (t_2 <= 1d-296) then
        tmp = 1.0d0 / (c / (b / z))
    else if (t_2 <= 1d+79) then
        tmp = t_3
    else
        tmp = t_1
    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 = (fmax(x, y) / (c * z)) * (9.0 * fmin(x, y));
	double t_2 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_3 = -4.0 * ((a * t) / c);
	double tmp;
	if (t_2 <= -1e+142) {
		tmp = t_1;
	} else if (t_2 <= -1e-203) {
		tmp = t_3;
	} else if (t_2 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_2 <= 1e+79) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmax(x, y) / (c * z)) * (9.0 * fmin(x, y))
	t_2 = (fmin(x, y) * 9.0) * fmax(x, y)
	t_3 = -4.0 * ((a * t) / c)
	tmp = 0
	if t_2 <= -1e+142:
		tmp = t_1
	elif t_2 <= -1e-203:
		tmp = t_3
	elif t_2 <= 1e-296:
		tmp = 1.0 / (c / (b / z))
	elif t_2 <= 1e+79:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmax(x, y) / Float64(c * z)) * Float64(9.0 * fmin(x, y)))
	t_2 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	t_3 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (t_2 <= -1e+142)
		tmp = t_1;
	elseif (t_2 <= -1e-203)
		tmp = t_3;
	elseif (t_2 <= 1e-296)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (t_2 <= 1e+79)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (max(x, y) / (c * z)) * (9.0 * min(x, y));
	t_2 = (min(x, y) * 9.0) * max(x, y);
	t_3 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (t_2 <= -1e+142)
		tmp = t_1;
	elseif (t_2 <= -1e-203)
		tmp = t_3;
	elseif (t_2 <= 1e-296)
		tmp = 1.0 / (c / (b / z));
	elseif (t_2 <= 1e+79)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Max[x, y], $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+142], t$95$1, If[LessEqual[t$95$2, -1e-203], t$95$3, If[LessEqual[t$95$2, 1e-296], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+79], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000005e142 or 9.99999999999999967e78 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lift-/.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 37.4%

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

   6. Applied rewrites 37.4%

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

   if -1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203 or 1e-296 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999967e78

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-296

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 36.1%

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

   4. Applied rewrites 36.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 34.1%

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

   6. Applied rewrites 34.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      4. lower-unsound-/.f64 34.1%

         \[\leadsto \frac{1}{\frac{c}{\color{blue}{\frac{b}{z}}}} \]

   8. Applied rewrites 34.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 52.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := 9 \cdot \left(y \cdot \frac{x}{c \cdot z}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-296}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c)))
        (t_2 (* (* x 9.0) y))
        (t_3 (* 9.0 (* y (/ x (* c z))))))
   (if (<= t_2 -1e+142)
     t_3
     (if (<= t_2 -1e-203)
       t_1
       (if (<= t_2 1e-296)
         (/ 1.0 (/ c (/ b z)))
         (if (<= t_2 5e+87) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * (y * (x / (c * z)));
	double tmp;
	if (t_2 <= -1e+142) {
		tmp = t_3;
	} else if (t_2 <= -1e-203) {
		tmp = t_1;
	} else if (t_2 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_2 <= 5e+87) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: tmp
    t_1 = (-4.0d0) * ((a * t) / c)
    t_2 = (x * 9.0d0) * y
    t_3 = 9.0d0 * (y * (x / (c * z)))
    if (t_2 <= (-1d+142)) then
        tmp = t_3
    else if (t_2 <= (-1d-203)) then
        tmp = t_1
    else if (t_2 <= 1d-296) then
        tmp = 1.0d0 / (c / (b / z))
    else if (t_2 <= 5d+87) then
        tmp = t_1
    else
        tmp = t_3
    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 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * (y * (x / (c * z)));
	double tmp;
	if (t_2 <= -1e+142) {
		tmp = t_3;
	} else if (t_2 <= -1e-203) {
		tmp = t_1;
	} else if (t_2 <= 1e-296) {
		tmp = 1.0 / (c / (b / z));
	} else if (t_2 <= 5e+87) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	t_2 = (x * 9.0) * y
	t_3 = 9.0 * (y * (x / (c * z)))
	tmp = 0
	if t_2 <= -1e+142:
		tmp = t_3
	elif t_2 <= -1e-203:
		tmp = t_1
	elif t_2 <= 1e-296:
		tmp = 1.0 / (c / (b / z))
	elif t_2 <= 5e+87:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(9.0 * Float64(y * Float64(x / Float64(c * z))))
	tmp = 0.0
	if (t_2 <= -1e+142)
		tmp = t_3;
	elseif (t_2 <= -1e-203)
		tmp = t_1;
	elseif (t_2 <= 1e-296)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (t_2 <= 5e+87)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	t_2 = (x * 9.0) * y;
	t_3 = 9.0 * (y * (x / (c * z)));
	tmp = 0.0;
	if (t_2 <= -1e+142)
		tmp = t_3;
	elseif (t_2 <= -1e-203)
		tmp = t_1;
	elseif (t_2 <= 1e-296)
		tmp = 1.0 / (c / (b / z));
	elseif (t_2 <= 5e+87)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(y * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+142], t$95$3, If[LessEqual[t$95$2, -1e-203], t$95$1, If[LessEqual[t$95$2, 1e-296], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+87], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000005e142 or 4.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 35.3%

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

   4. Applied rewrites 35.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 37.6%

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

   6. Applied rewrites 37.6%

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

   if -1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-203 or 1e-296 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e87

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -1e-203 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-296

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 36.1%

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

   4. Applied rewrites 36.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 34.1%

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

   6. Applied rewrites 34.1%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]

      4. lower-unsound-/.f64 34.1%

         \[\leadsto \frac{1}{\frac{c}{\color{blue}{\frac{b}{z}}}} \]

   8. Applied rewrites 34.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{b}{z}}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+56}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.1e+78)
   (/ b (* c z))
   (if (<= b 1.8e+56) (* -4.0 (/ (* a t) c)) (/ (/ b c) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.1e+78) {
		tmp = b / (c * z);
	} else if (b <= 1.8e+56) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = (b / c) / z;
	}
	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) :: tmp
    if (b <= (-3.1d+78)) then
        tmp = b / (c * z)
    else if (b <= 1.8d+56) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = (b / c) / z
    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 tmp;
	if (b <= -3.1e+78) {
		tmp = b / (c * z);
	} else if (b <= 1.8e+56) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.1e+78:
		tmp = b / (c * z)
	elif b <= 1.8e+56:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.1e+78)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= 1.8e+56)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.1e+78)
		tmp = b / (c * z);
	elseif (b <= 1.8e+56)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.1e+78], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+56], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1e78

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 36.1%

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

   4. Applied rewrites 36.1%

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

   if -3.1e78 < b < 1.79999999999999999e56

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{\color{blue}{c}} \]

      3. lower-*.f64 38.7%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

   4. Applied rewrites 38.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if 1.79999999999999999e56 < b

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

      2. lower-*.f64 36.1%

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

   4. Applied rewrites 36.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

      5. lower-/.f64 35.6%

         \[\leadsto \frac{\frac{b}{c}}{z} \]

   6. Applied rewrites 35.6%

      \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 36.1% accurate, 3.8× speedup

Math

\[\frac{b}{c \cdot z} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

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 = b / (c * z)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Python

def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

2. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   2. lower-*.f64 36.1%

      \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

4. Applied rewrites 36.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025183 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64
  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))