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

Percentage Accurate: 79.4% → 85.7%

Time: 8.4s

Alternatives: 17

Speedup: 0.7×

• 62.7% 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: 79.4% 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: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+223}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right), \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+100}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot z\right), \mathsf{min}\left(t, a\right), \mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{9 \cdot \mathsf{min}\left(x, y\right)}{c}, \frac{\mathsf{max}\left(x, y\right)}{z}, \mathsf{max}\left(t, a\right) \cdot \mathsf{fma}\left(-4, \frac{\mathsf{min}\left(t, a\right)}{c}, \frac{b}{\mathsf{max}\left(t, a\right) \cdot \left(c \cdot z\right)}\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.4e+223)
   (/ (fma -4.0 (* (fmax t a) (fmin t a)) (/ b z)) c)
   (if (<= z 3.1e+100)
     (/
      (/
       (fma
        (* (fmax t a) (* -4.0 z))
        (fmin t a)
        (fma (* (fmax x y) (fmin x y)) 9.0 b))
       c)
      z)
     (fma
      (/ (* 9.0 (fmin x y)) c)
      (/ (fmax x y) z)
      (*
       (fmax t a)
       (fma -4.0 (/ (fmin t a) c) (/ b (* (fmax t a) (* c z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.4e+223) {
		tmp = fma(-4.0, (fmax(t, a) * fmin(t, a)), (b / z)) / c;
	} else if (z <= 3.1e+100) {
		tmp = (fma((fmax(t, a) * (-4.0 * z)), fmin(t, a), fma((fmax(x, y) * fmin(x, y)), 9.0, b)) / c) / z;
	} else {
		tmp = fma(((9.0 * fmin(x, y)) / c), (fmax(x, y) / z), (fmax(t, a) * fma(-4.0, (fmin(t, a) / c), (b / (fmax(t, a) * (c * z))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.4e+223)
		tmp = Float64(fma(-4.0, Float64(fmax(t, a) * fmin(t, a)), Float64(b / z)) / c);
	elseif (z <= 3.1e+100)
		tmp = Float64(Float64(fma(Float64(fmax(t, a) * Float64(-4.0 * z)), fmin(t, a), fma(Float64(fmax(x, y) * fmin(x, y)), 9.0, b)) / c) / z);
	else
		tmp = fma(Float64(Float64(9.0 * fmin(x, y)) / c), Float64(fmax(x, y) / z), Float64(fmax(t, a) * fma(-4.0, Float64(fmin(t, a) / c), Float64(b / Float64(fmax(t, a) * Float64(c * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.4e+223], N[(N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.1e+100], N[(N[(N[(N[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * z), $MachinePrecision]), $MachinePrecision] * N[Min[t, a], $MachinePrecision] + N[(N[(N[Max[x, y], $MachinePrecision] * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / z), $MachinePrecision] + N[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(N[Max[t, a], $MachinePrecision] * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999e223

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 63.7%

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

   9. Applied rewrites 63.7%

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

   if -1.3999999999999999e223 < z < 3.1000000000000001e100

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   if 3.1000000000000001e100 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 71.7%

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

   6. Applied rewrites 71.7%

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

Alternative 2: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, \mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right), \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+108}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot z\right), \mathsf{min}\left(t, a\right), \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* (fmax t a) (fmin t a)) (/ b z)) c)))
   (if (<= z -1.4e+223)
     t_1
     (if (<= z 3.1e+108)
       (/
        (/ (fma (* (fmax t a) (* -4.0 z)) (fmin t a) (fma (* y x) 9.0 b)) c)
        z)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (fmax(t, a) * fmin(t, a)), (b / z)) / c;
	double tmp;
	if (z <= -1.4e+223) {
		tmp = t_1;
	} else if (z <= 3.1e+108) {
		tmp = (fma((fmax(t, a) * (-4.0 * z)), fmin(t, a), fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(fmax(t, a) * fmin(t, a)), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.4e+223)
		tmp = t_1;
	elseif (z <= 3.1e+108)
		tmp = Float64(Float64(fma(Float64(fmax(t, a) * Float64(-4.0 * z)), fmin(t, a), fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.4e+223], t$95$1, If[LessEqual[z, 3.1e+108], N[(N[(N[(N[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * z), $MachinePrecision]), $MachinePrecision] * N[Min[t, a], $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e223 or 3.1000000000000001e108 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 63.7%

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

   9. Applied rewrites 63.7%

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

   if -1.3999999999999999e223 < z < 3.1000000000000001e108

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

Alternative 3: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, \mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right), \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot \mathsf{max}\left(t, a\right), \mathsf{min}\left(t, a\right), \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* (fmax t a) (fmin t a)) (/ b z)) c)))
   (if (<= z -1.45e+191)
     t_1
     (if (<= z 2.7e+157)
       (/
        (fma (* (* -4.0 z) (fmax t a)) (fmin t a) (fma (* y x) 9.0 b))
        (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (fmax(t, a) * fmin(t, a)), (b / z)) / c;
	double tmp;
	if (z <= -1.45e+191) {
		tmp = t_1;
	} else if (z <= 2.7e+157) {
		tmp = fma(((-4.0 * z) * fmax(t, a)), fmin(t, a), fma((y * x), 9.0, b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(fmax(t, a) * fmin(t, a)), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.45e+191)
		tmp = t_1;
	elseif (z <= 2.7e+157)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * fmax(t, a)), fmin(t, a), fma(Float64(y * x), 9.0, b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.45e+191], t$95$1, If[LessEqual[z, 2.7e+157], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[Min[t, a], $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e191 or 2.7e157 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 63.7%

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

   9. Applied rewrites 63.7%

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

   if -1.4500000000000001e191 < z < 2.7e157

   1. Initial program 79.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   3. Applied rewrites 79.6%

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

Alternative 4: 85.2% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       (+
        (-
         (* (* (fmin x y) 9.0) (fmax x y))
         (* (* (* z 4.0) (fmin t a)) (fmax t a)))
        b)
       (* z c))
      INFINITY)
   (/
    (fma
     (* (fmax x y) 9.0)
     (fmin x y)
     (fma -4.0 (* (* (fmax t a) (fmin t a)) z) b))
    (* z c))
   (fma -4.0 (* (fmin t a) (/ (fmax t a) c)) (/ b (* c z)))))

C

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

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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)) <= Inf)
		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 * c));
	else
		tmp = fma(-4.0, Float64(fmin(t, a) * Float64(fmax(t, a) / c)), Float64(b / Float64(c * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], Infinity], 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], N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] * N[(N[Max[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 +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 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 63.4%

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

   8. Applied rewrites 63.4%

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

Alternative 5: 85.1% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       (+ (- (* (* x 9.0) y) (* (* (* z 4.0) (fmin t a)) (fmax t a))) b)
       (* z c))
      INFINITY)
   (/ (fma (* 9.0 x) y (fma -4.0 (* (* (fmax t a) (fmin t a)) z) b)) (* z c))
   (fma -4.0 (* (fmin t a) (/ (fmax t a) c)) (/ b (* c z)))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 79.4%

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

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. add-flip-rev N/A

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

   3. Applied rewrites 80.7%

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

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

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 63.4%

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

   8. Applied rewrites 63.4%

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

Alternative 6: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot 9\\ t_2 := t\_1 \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{t\_1}{c}, \mathsf{max}\left(x, y\right), \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot \mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right)}{c \cdot z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fmin x y) 9.0)) (t_2 (* t_1 (fmax x y))))
   (if (<= t_2 -1e-12)
     (/ (fma (/ t_1 c) (fmax x y) (/ b c)) z)
     (if (<= t_2 2e+71)
       (fma -4.0 (* t (/ a c)) (/ b (* c z)))
       (/
        (fma (* 9.0 (fmin x y)) (fmax x y) (* (* (* t z) a) -4.0))
        (* c 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;
	double t_2 = t_1 * fmax(x, y);
	double tmp;
	if (t_2 <= -1e-12) {
		tmp = fma((t_1 / c), fmax(x, y), (b / c)) / z;
	} else if (t_2 <= 2e+71) {
		tmp = fma(-4.0, (t * (a / c)), (b / (c * z)));
	} else {
		tmp = fma((9.0 * fmin(x, y)), fmax(x, y), (((t * z) * a) * -4.0)) / (c * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmin(x, y) * 9.0)
	t_2 = Float64(t_1 * fmax(x, y))
	tmp = 0.0
	if (t_2 <= -1e-12)
		tmp = Float64(fma(Float64(t_1 / c), fmax(x, y), Float64(b / c)) / z);
	elseif (t_2 <= 2e+71)
		tmp = fma(-4.0, Float64(t * Float64(a / c)), Float64(b / Float64(c * z)));
	else
		tmp = Float64(fma(Float64(9.0 * fmin(x, y)), fmax(x, y), Float64(Float64(Float64(t * z) * a) * -4.0)) / Float64(c * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-12], N[(N[(N[(t$95$1 / c), $MachinePrecision] * N[Max[x, y], $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 2e+71], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * N[Max[x, y], $MachinePrecision] + N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999998e-13

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l/ N/A

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

      9. lift-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 59.3%

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

   8. Applied rewrites 59.3%

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

   if -9.9999999999999998e-13 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000001e71

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 63.4%

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

   8. Applied rewrites 63.4%

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

   if 2.0000000000000001e71 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

   2. 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 56.1%

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

   4. Applied rewrites 56.1%

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

      1. lift--.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. lift-*.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. distribute-lft-neg-out N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lower-fma.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. lift-*.f64 N/A

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

      23. lift-*.f64 N/A

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

   6. Applied rewrites 56.5%

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

Alternative 7: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot 9\\ t_2 := t\_1 \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{t\_1}{c}, \mathsf{max}\left(x, y\right), \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)}{c}}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fmin x y) 9.0)) (t_2 (* t_1 (fmax x y))))
   (if (<= t_2 -1e-12)
     (/ (fma (/ t_1 c) (fmax x y) (/ b c)) z)
     (if (<= t_2 1e+99)
       (fma -4.0 (* t (/ a c)) (/ b (* c z)))
       (/ (/ (fma (* (fmax x y) (fmin x y)) 9.0 b) c) 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;
	double t_2 = t_1 * fmax(x, y);
	double tmp;
	if (t_2 <= -1e-12) {
		tmp = fma((t_1 / c), fmax(x, y), (b / c)) / z;
	} else if (t_2 <= 1e+99) {
		tmp = fma(-4.0, (t * (a / c)), (b / (c * z)));
	} else {
		tmp = (fma((fmax(x, y) * fmin(x, y)), 9.0, b) / c) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmin(x, y) * 9.0)
	t_2 = Float64(t_1 * fmax(x, y))
	tmp = 0.0
	if (t_2 <= -1e-12)
		tmp = Float64(fma(Float64(t_1 / c), fmax(x, y), Float64(b / c)) / z);
	elseif (t_2 <= 1e+99)
		tmp = fma(-4.0, Float64(t * Float64(a / c)), Float64(b / Float64(c * z)));
	else
		tmp = Float64(Float64(fma(Float64(fmax(x, y) * fmin(x, y)), 9.0, b) / c) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-12], N[(N[(N[(t$95$1 / c), $MachinePrecision] * N[Max[x, y], $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+99], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Max[x, y], $MachinePrecision] * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999998e-13

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l/ N/A

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

      9. lift-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 59.3%

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

   8. Applied rewrites 59.3%

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

   if -9.9999999999999998e-13 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 63.4%

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

   8. Applied rewrites 63.4%

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

   if 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 60.5%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 60.5%

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

   8. Applied rewrites 60.5%

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

Alternative 8: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (/ (/ (fma (* y x) 9.0 b) c) z)))
   (if (<= t_1 -1e-12)
     t_2
     (if (<= t_1 1e+99) (fma -4.0 (* t (/ a c)) (/ b (* c z))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (fma((y * x), 9.0, b) / c) / z;
	double tmp;
	if (t_1 <= -1e-12) {
		tmp = t_2;
	} else if (t_1 <= 1e+99) {
		tmp = fma(-4.0, (t * (a / c)), (b / (c * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z)
	tmp = 0.0
	if (t_1 <= -1e-12)
		tmp = t_2;
	elseif (t_1 <= 1e+99)
		tmp = fma(-4.0, Float64(t * Float64(a / c)), Float64(b / Float64(c * z)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-12], t$95$2, If[LessEqual[t$95$1, 1e+99], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999998e-13 or 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 60.5%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 60.5%

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

   8. Applied rewrites 60.5%

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

   if -9.9999999999999998e-13 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 63.4%

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

   8. Applied rewrites 63.4%

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

Alternative 9: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (/ (/ (fma (* y x) 9.0 b) c) z)))
   (if (<= t_1 -2e-6)
     t_2
     (if (<= t_1 1e+99) (/ (fma -4.0 (* a t) (/ b z)) c) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (fma((y * x), 9.0, b) / c) / z;
	double tmp;
	if (t_1 <= -2e-6) {
		tmp = t_2;
	} else if (t_1 <= 1e+99) {
		tmp = fma(-4.0, (a * t), (b / z)) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z)
	tmp = 0.0
	if (t_1 <= -2e-6)
		tmp = t_2;
	elseif (t_1 <= 1e+99)
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(b / z)) / c);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-6], t$95$2, If[LessEqual[t$95$1, 1e+99], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e-6 or 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 60.5%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 60.5%

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

   8. Applied rewrites 60.5%

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

   if -1.9999999999999999e-6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 63.7%

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

   9. Applied rewrites 63.7%

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

Alternative 10: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot 9\\ t_2 := t\_1 \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+128}:\\ \;\;\;\;\frac{\mathsf{max}\left(x, y\right) \cdot \frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right) \cdot 9}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fmin x y) 9.0)) (t_2 (* t_1 (fmax x y))))
   (if (<= t_2 -5e+128)
     (/ (* (fmax x y) (/ t_1 c)) z)
     (if (<= t_2 1e+99)
       (/ (fma -4.0 (* a t) (/ b z)) c)
       (* (fmin x y) (/ (* (fmax x y) 9.0) (* 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;
	double t_2 = t_1 * fmax(x, y);
	double tmp;
	if (t_2 <= -5e+128) {
		tmp = (fmax(x, y) * (t_1 / c)) / z;
	} else if (t_2 <= 1e+99) {
		tmp = fma(-4.0, (a * t), (b / z)) / c;
	} else {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmin(x, y) * 9.0)
	t_2 = Float64(t_1 * fmax(x, y))
	tmp = 0.0
	if (t_2 <= -5e+128)
		tmp = Float64(Float64(fmax(x, y) * Float64(t_1 / c)) / z);
	elseif (t_2 <= 1e+99)
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(b / z)) / c);
	else
		tmp = Float64(fmin(x, y) * Float64(Float64(fmax(x, y) * 9.0) / Float64(z * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+128], N[(N[(N[Max[x, y], $MachinePrecision] * N[(t$95$1 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+99], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[Min[x, y], $MachinePrecision] * N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e128

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. lift-/.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 36.8%

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 36.8%

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

   8. Applied rewrites 36.8%

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

   if -5e128 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate--l+ N/A

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

      8. div-add N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. times-frac N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1%

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 63.7%

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

   9. Applied rewrites 63.7%

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

   if 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 37.6%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 37.6%

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

   8. Applied rewrites 37.6%

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

Alternative 11: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot 9\\ t_2 := t\_1 \cdot \mathsf{max}\left(x, y\right)\\ t_3 := \mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\frac{\mathsf{max}\left(x, y\right) \cdot \frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{1}{\frac{c}{b}}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right) \cdot 9}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fmin x y) 9.0))
        (t_2 (* t_1 (fmax x y)))
        (t_3 (* (fmax t a) (* -4.0 (/ (fmin t a) c)))))
   (if (<= t_2 -1e+69)
     (/ (* (fmax x y) (/ t_1 c)) z)
     (if (<= t_2 -5e-160)
       t_3
       (if (<= t_2 -2e-301)
         (/ (/ 1.0 (/ c b)) z)
         (if (<= t_2 1e+99)
           t_3
           (* (fmin x y) (/ (* (fmax x y) 9.0) (* 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;
	double t_2 = t_1 * fmax(x, y);
	double t_3 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double tmp;
	if (t_2 <= -1e+69) {
		tmp = (fmax(x, y) * (t_1 / c)) / z;
	} else if (t_2 <= -5e-160) {
		tmp = t_3;
	} else if (t_2 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_2 <= 1e+99) {
		tmp = t_3;
	} else {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	}
	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 = fmin(x, y) * 9.0d0
    t_2 = t_1 * fmax(x, y)
    t_3 = fmax(t, a) * ((-4.0d0) * (fmin(t, a) / c))
    if (t_2 <= (-1d+69)) then
        tmp = (fmax(x, y) * (t_1 / c)) / z
    else if (t_2 <= (-5d-160)) then
        tmp = t_3
    else if (t_2 <= (-2d-301)) then
        tmp = (1.0d0 / (c / b)) / z
    else if (t_2 <= 1d+99) then
        tmp = t_3
    else
        tmp = fmin(x, y) * ((fmax(x, y) * 9.0d0) / (z * c))
    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;
	double t_2 = t_1 * fmax(x, y);
	double t_3 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double tmp;
	if (t_2 <= -1e+69) {
		tmp = (fmax(x, y) * (t_1 / c)) / z;
	} else if (t_2 <= -5e-160) {
		tmp = t_3;
	} else if (t_2 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_2 <= 1e+99) {
		tmp = t_3;
	} else {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = fmin(x, y) * 9.0
	t_2 = t_1 * fmax(x, y)
	t_3 = fmax(t, a) * (-4.0 * (fmin(t, a) / c))
	tmp = 0
	if t_2 <= -1e+69:
		tmp = (fmax(x, y) * (t_1 / c)) / z
	elif t_2 <= -5e-160:
		tmp = t_3
	elif t_2 <= -2e-301:
		tmp = (1.0 / (c / b)) / z
	elif t_2 <= 1e+99:
		tmp = t_3
	else:
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmin(x, y) * 9.0)
	t_2 = Float64(t_1 * fmax(x, y))
	t_3 = Float64(fmax(t, a) * Float64(-4.0 * Float64(fmin(t, a) / c)))
	tmp = 0.0
	if (t_2 <= -1e+69)
		tmp = Float64(Float64(fmax(x, y) * Float64(t_1 / c)) / z);
	elseif (t_2 <= -5e-160)
		tmp = t_3;
	elseif (t_2 <= -2e-301)
		tmp = Float64(Float64(1.0 / Float64(c / b)) / z);
	elseif (t_2 <= 1e+99)
		tmp = t_3;
	else
		tmp = Float64(fmin(x, y) * Float64(Float64(fmax(x, y) * 9.0) / Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = min(x, y) * 9.0;
	t_2 = t_1 * max(x, y);
	t_3 = max(t, a) * (-4.0 * (min(t, a) / c));
	tmp = 0.0;
	if (t_2 <= -1e+69)
		tmp = (max(x, y) * (t_1 / c)) / z;
	elseif (t_2 <= -5e-160)
		tmp = t_3;
	elseif (t_2 <= -2e-301)
		tmp = (1.0 / (c / b)) / z;
	elseif (t_2 <= 1e+99)
		tmp = t_3;
	else
		tmp = min(x, y) * ((max(x, y) * 9.0) / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+69], N[(N[(N[Max[x, y], $MachinePrecision] * N[(t$95$1 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, -5e-160], t$95$3, If[LessEqual[t$95$2, -2e-301], N[(N[(1.0 / N[(c / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+99], t$95$3, N[(N[Min[x, y], $MachinePrecision] * N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.0000000000000001e69

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. lift-/.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 36.8%

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 36.8%

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

   8. Applied rewrites 36.8%

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

   if -1.0000000000000001e69 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-160 or -2.0000000000000001e-301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

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

   2. 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 56.1%

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 59.3%

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

   7. Applied rewrites 59.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 40.1%

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

   10. Applied rewrites 40.1%

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

   if -4.9999999999999999e-160 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.0000000000000001e-301

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 34.8%

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

       1. lift-/.f64 N/A

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

       2. div-flip N/A

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

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

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

       4. lower-unsound-/.f64 34.8%

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

   11. Applied rewrites 34.8%

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

   if 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 37.6%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 37.6%

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

   8. Applied rewrites 37.6%

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

Alternative 12: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{max}\left(t, a\right) \leq -1.65 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \frac{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}{c}\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 2.4 \cdot 10^{-171}:\\ \;\;\;\;9 \cdot \frac{\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{z}}{c}\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 2 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right) \cdot 9}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (fmax t a) -1.65e-113)
   (* -4.0 (/ (* (fmax t a) (fmin t a)) c))
   (if (<= (fmax t a) 2.4e-171)
     (* 9.0 (/ (* (fmin x y) (/ (fmax x y) z)) c))
     (if (<= (fmax t a) 2.8e-22)
       (/ b (* c z))
       (if (<= (fmax t a) 2e+180)
         (* (fmin x y) (/ (* (fmax x y) 9.0) (* z c)))
         (* (fmax t a) (* -4.0 (/ (fmin t a) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (fmax(t, a) <= -1.65e-113) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (fmax(t, a) <= 2.4e-171) {
		tmp = 9.0 * ((fmin(x, y) * (fmax(x, y) / z)) / c);
	} else if (fmax(t, a) <= 2.8e-22) {
		tmp = b / (c * z);
	} else if (fmax(t, a) <= 2e+180) {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	} else {
		tmp = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	}
	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 (fmax(t, a) <= (-1.65d-113)) then
        tmp = (-4.0d0) * ((fmax(t, a) * fmin(t, a)) / c)
    else if (fmax(t, a) <= 2.4d-171) then
        tmp = 9.0d0 * ((fmin(x, y) * (fmax(x, y) / z)) / c)
    else if (fmax(t, a) <= 2.8d-22) then
        tmp = b / (c * z)
    else if (fmax(t, a) <= 2d+180) then
        tmp = fmin(x, y) * ((fmax(x, y) * 9.0d0) / (z * c))
    else
        tmp = fmax(t, a) * ((-4.0d0) * (fmin(t, a) / c))
    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 (fmax(t, a) <= -1.65e-113) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (fmax(t, a) <= 2.4e-171) {
		tmp = 9.0 * ((fmin(x, y) * (fmax(x, y) / z)) / c);
	} else if (fmax(t, a) <= 2.8e-22) {
		tmp = b / (c * z);
	} else if (fmax(t, a) <= 2e+180) {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	} else {
		tmp = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if fmax(t, a) <= -1.65e-113:
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c)
	elif fmax(t, a) <= 2.4e-171:
		tmp = 9.0 * ((fmin(x, y) * (fmax(x, y) / z)) / c)
	elif fmax(t, a) <= 2.8e-22:
		tmp = b / (c * z)
	elif fmax(t, a) <= 2e+180:
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c))
	else:
		tmp = fmax(t, a) * (-4.0 * (fmin(t, a) / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (fmax(t, a) <= -1.65e-113)
		tmp = Float64(-4.0 * Float64(Float64(fmax(t, a) * fmin(t, a)) / c));
	elseif (fmax(t, a) <= 2.4e-171)
		tmp = Float64(9.0 * Float64(Float64(fmin(x, y) * Float64(fmax(x, y) / z)) / c));
	elseif (fmax(t, a) <= 2.8e-22)
		tmp = Float64(b / Float64(c * z));
	elseif (fmax(t, a) <= 2e+180)
		tmp = Float64(fmin(x, y) * Float64(Float64(fmax(x, y) * 9.0) / Float64(z * c)));
	else
		tmp = Float64(fmax(t, a) * Float64(-4.0 * Float64(fmin(t, a) / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (max(t, a) <= -1.65e-113)
		tmp = -4.0 * ((max(t, a) * min(t, a)) / c);
	elseif (max(t, a) <= 2.4e-171)
		tmp = 9.0 * ((min(x, y) * (max(x, y) / z)) / c);
	elseif (max(t, a) <= 2.8e-22)
		tmp = b / (c * z);
	elseif (max(t, a) <= 2e+180)
		tmp = min(x, y) * ((max(x, y) * 9.0) / (z * c));
	else
		tmp = max(t, a) * (-4.0 * (min(t, a) / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[Max[t, a], $MachinePrecision], -1.65e-113], N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Max[t, a], $MachinePrecision], 2.4e-171], N[(9.0 * N[(N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Max[t, a], $MachinePrecision], 2.8e-22], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Max[t, a], $MachinePrecision], 2e+180], N[(N[Min[x, y], $MachinePrecision] * N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.6500000000000001e-113

   1. Initial program 79.4%

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

   2. 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 38.5%

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

   4. Applied rewrites 38.5%

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

   if -1.6500000000000001e-113 < a < 2.3999999999999999e-171

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. 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. lift-*.f64 N/A

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

      4. times-frac N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 35.1%

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

   8. Applied rewrites 35.1%

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

   if 2.3999999999999999e-171 < a < 2.7999999999999999e-22

   1. Initial program 79.4%

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

   2. 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 35.6%

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

   4. Applied rewrites 35.6%

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

   if 2.7999999999999999e-22 < a < 2e180

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 37.6%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 37.6%

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

   8. Applied rewrites 37.6%

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

   if 2e180 < a

   1. Initial program 79.4%

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

   2. 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 56.1%

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 59.3%

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

   7. Applied rewrites 59.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 40.1%

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

   10. Applied rewrites 40.1%

       \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 13: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_2 := \mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;9 \cdot \left(\mathsf{max}\left(x, y\right) \cdot \frac{\mathsf{min}\left(x, y\right)}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{1}{\frac{c}{b}}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right) \cdot 9}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y)))
        (t_2 (* (fmax t a) (* -4.0 (/ (fmin t a) c)))))
   (if (<= t_1 -1e+69)
     (* 9.0 (* (fmax x y) (/ (fmin x y) (* z c))))
     (if (<= t_1 -5e-160)
       t_2
       (if (<= t_1 -2e-301)
         (/ (/ 1.0 (/ c b)) z)
         (if (<= t_1 1e+99)
           t_2
           (* (fmin x y) (/ (* (fmax x y) 9.0) (* 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 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double tmp;
	if (t_1 <= -1e+69) {
		tmp = 9.0 * (fmax(x, y) * (fmin(x, y) / (z * c)));
	} else if (t_1 <= -5e-160) {
		tmp = t_2;
	} else if (t_1 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_1 <= 1e+99) {
		tmp = t_2;
	} else {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	}
	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 = fmax(t, a) * ((-4.0d0) * (fmin(t, a) / c))
    if (t_1 <= (-1d+69)) then
        tmp = 9.0d0 * (fmax(x, y) * (fmin(x, y) / (z * c)))
    else if (t_1 <= (-5d-160)) then
        tmp = t_2
    else if (t_1 <= (-2d-301)) then
        tmp = (1.0d0 / (c / b)) / z
    else if (t_1 <= 1d+99) then
        tmp = t_2
    else
        tmp = fmin(x, y) * ((fmax(x, y) * 9.0d0) / (z * c))
    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 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double tmp;
	if (t_1 <= -1e+69) {
		tmp = 9.0 * (fmax(x, y) * (fmin(x, y) / (z * c)));
	} else if (t_1 <= -5e-160) {
		tmp = t_2;
	} else if (t_1 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_1 <= 1e+99) {
		tmp = t_2;
	} else {
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmin(x, y) * 9.0) * fmax(x, y)
	t_2 = fmax(t, a) * (-4.0 * (fmin(t, a) / c))
	tmp = 0
	if t_1 <= -1e+69:
		tmp = 9.0 * (fmax(x, y) * (fmin(x, y) / (z * c)))
	elif t_1 <= -5e-160:
		tmp = t_2
	elif t_1 <= -2e-301:
		tmp = (1.0 / (c / b)) / z
	elif t_1 <= 1e+99:
		tmp = t_2
	else:
		tmp = fmin(x, y) * ((fmax(x, y) * 9.0) / (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(fmax(t, a) * Float64(-4.0 * Float64(fmin(t, a) / c)))
	tmp = 0.0
	if (t_1 <= -1e+69)
		tmp = Float64(9.0 * Float64(fmax(x, y) * Float64(fmin(x, y) / Float64(z * c))));
	elseif (t_1 <= -5e-160)
		tmp = t_2;
	elseif (t_1 <= -2e-301)
		tmp = Float64(Float64(1.0 / Float64(c / b)) / z);
	elseif (t_1 <= 1e+99)
		tmp = t_2;
	else
		tmp = Float64(fmin(x, y) * Float64(Float64(fmax(x, y) * 9.0) / Float64(z * c)));
	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 = max(t, a) * (-4.0 * (min(t, a) / c));
	tmp = 0.0;
	if (t_1 <= -1e+69)
		tmp = 9.0 * (max(x, y) * (min(x, y) / (z * c)));
	elseif (t_1 <= -5e-160)
		tmp = t_2;
	elseif (t_1 <= -2e-301)
		tmp = (1.0 / (c / b)) / z;
	elseif (t_1 <= 1e+99)
		tmp = t_2;
	else
		tmp = min(x, y) * ((max(x, y) * 9.0) / (z * c));
	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[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+69], N[(9.0 * N[(N[Max[x, y], $MachinePrecision] * N[(N[Min[x, y], $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-160], t$95$2, If[LessEqual[t$95$1, -2e-301], N[(N[(1.0 / N[(c / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+99], t$95$2, N[(N[Min[x, y], $MachinePrecision] * N[(N[(N[Max[x, y], $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.0000000000000001e69

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. 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%

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 37.6%

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

   8. Applied rewrites 37.6%

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

   if -1.0000000000000001e69 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-160 or -2.0000000000000001e-301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

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

   2. 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 56.1%

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 59.3%

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

   7. Applied rewrites 59.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 40.1%

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

   10. Applied rewrites 40.1%

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

   if -4.9999999999999999e-160 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.0000000000000001e-301

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 34.8%

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

       1. lift-/.f64 N/A

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

       2. div-flip N/A

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

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

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

       4. lower-unsound-/.f64 34.8%

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

   11. Applied rewrites 34.8%

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

   if 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

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

   6. Applied rewrites 35.6%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(9 \cdot x\right) \cdot y}{c \cdot z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(9 \cdot x\right) \cdot y}{c \cdot z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{c \cdot z} \]

      9. associate-*l* N/A

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{c} \cdot z} \]

      10. associate-/l* N/A

          \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      11. lower-*.f64 N/A

          \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      12. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{9 \cdot y}{\color{blue}{c \cdot z}} \]

      13. *-commutative N/A

          \[\leadsto x \cdot \frac{y \cdot 9}{\color{blue}{c} \cdot z} \]

      14. lower-*.f64 37.6%

          \[\leadsto x \cdot \frac{y \cdot 9}{\color{blue}{c} \cdot z} \]

      15. lift-*.f64 N/A

          \[\leadsto x \cdot \frac{y \cdot 9}{c \cdot \color{blue}{z}} \]

      16. *-commutative N/A

          \[\leadsto x \cdot \frac{y \cdot 9}{z \cdot \color{blue}{c}} \]

      17. lower-*.f64 37.6%

          \[\leadsto x \cdot \frac{y \cdot 9}{z \cdot \color{blue}{c}} \]

   8. Applied rewrites 37.6%

      \[\leadsto x \cdot \color{blue}{\frac{y \cdot 9}{z \cdot c}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := 9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{1}{\frac{c}{b}}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fmax t a) (* -4.0 (/ (fmin t a) c))))
        (t_2 (* (* x 9.0) y))
        (t_3 (* 9.0 (* y (/ x (* z c))))))
   (if (<= t_2 -1e+69)
     t_3
     (if (<= t_2 -5e-160)
       t_1
       (if (<= t_2 -2e-301)
         (/ (/ 1.0 (/ c b)) z)
         (if (<= t_2 1e+99) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (t_2 <= -1e+69) {
		tmp = t_3;
	} else if (t_2 <= -5e-160) {
		tmp = t_1;
	} else if (t_2 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_2 <= 1e+99) {
		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 = fmax(t, a) * ((-4.0d0) * (fmin(t, a) / c))
    t_2 = (x * 9.0d0) * y
    t_3 = 9.0d0 * (y * (x / (z * c)))
    if (t_2 <= (-1d+69)) then
        tmp = t_3
    else if (t_2 <= (-5d-160)) then
        tmp = t_1
    else if (t_2 <= (-2d-301)) then
        tmp = (1.0d0 / (c / b)) / z
    else if (t_2 <= 1d+99) 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 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (t_2 <= -1e+69) {
		tmp = t_3;
	} else if (t_2 <= -5e-160) {
		tmp = t_1;
	} else if (t_2 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_2 <= 1e+99) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = fmax(t, a) * (-4.0 * (fmin(t, a) / c))
	t_2 = (x * 9.0) * y
	t_3 = 9.0 * (y * (x / (z * c)))
	tmp = 0
	if t_2 <= -1e+69:
		tmp = t_3
	elif t_2 <= -5e-160:
		tmp = t_1
	elif t_2 <= -2e-301:
		tmp = (1.0 / (c / b)) / z
	elif t_2 <= 1e+99:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmax(t, a) * Float64(-4.0 * Float64(fmin(t, a) / c)))
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))))
	tmp = 0.0
	if (t_2 <= -1e+69)
		tmp = t_3;
	elseif (t_2 <= -5e-160)
		tmp = t_1;
	elseif (t_2 <= -2e-301)
		tmp = Float64(Float64(1.0 / Float64(c / b)) / z);
	elseif (t_2 <= 1e+99)
		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 = max(t, a) * (-4.0 * (min(t, a) / c));
	t_2 = (x * 9.0) * y;
	t_3 = 9.0 * (y * (x / (z * c)));
	tmp = 0.0;
	if (t_2 <= -1e+69)
		tmp = t_3;
	elseif (t_2 <= -5e-160)
		tmp = t_1;
	elseif (t_2 <= -2e-301)
		tmp = (1.0 / (c / b)) / z;
	elseif (t_2 <= 1e+99)
		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[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $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[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+69], t$95$3, If[LessEqual[t$95$2, -5e-160], t$95$1, If[LessEqual[t$95$2, -2e-301], N[(N[(1.0 / N[(c / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+99], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.0000000000000001e69 or 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   3. Applied rewrites 79.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. 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 35.6%

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot \color{blue}{z}} \]

   6. Applied rewrites 35.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. 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%

         \[\leadsto 9 \cdot \left(y \cdot \frac{x}{\color{blue}{c \cdot z}}\right) \]

      7. lift-*.f64 N/A

         \[\leadsto 9 \cdot \left(y \cdot \frac{x}{c \cdot \color{blue}{z}}\right) \]

      8. *-commutative N/A

         \[\leadsto 9 \cdot \left(y \cdot \frac{x}{z \cdot \color{blue}{c}}\right) \]

      9. lower-*.f64 37.6%

         \[\leadsto 9 \cdot \left(y \cdot \frac{x}{z \cdot \color{blue}{c}}\right) \]

   8. Applied rewrites 37.6%

      \[\leadsto 9 \cdot \left(y \cdot \color{blue}{\frac{x}{z \cdot c}}\right) \]

   if -1.0000000000000001e69 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-160 or -2.0000000000000001e-301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. 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 56.1%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot \color{blue}{z}} \]

   4. Applied rewrites 56.1%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c} + 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c} + \color{blue}{9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{\color{blue}{c}}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      8. lower-*.f64 59.3%

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

   7. Applied rewrites 59.3%

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c}\right) \]

      2. lower-/.f64 40.1%

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c}\right) \]

   10. Applied rewrites 40.1%

       \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]

   if -4.9999999999999999e-160 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.0000000000000001e-301

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   3. Applied rewrites 79.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}} \]

   4. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{c}}}{z} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      4. lower-*.f64 60.5%

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

   6. Applied rewrites 60.5%

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 34.8%

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{\frac{b}{\color{blue}{c}}}{z} \]

       2. div-flip N/A

          \[\leadsto \frac{\frac{1}{\color{blue}{\frac{c}{b}}}}{z} \]

       3. lower-unsound-/.f64 N/A

          \[\leadsto \frac{\frac{1}{\color{blue}{\frac{c}{b}}}}{z} \]

       4. lower-unsound-/.f64 34.8%

          \[\leadsto \frac{\frac{1}{\frac{c}{\color{blue}{b}}}}{z} \]

   11. Applied rewrites 34.8%

       \[\leadsto \frac{\frac{1}{\color{blue}{\frac{c}{b}}}}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 50.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{if}\;t\_2 \leq -1000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{1}{\frac{c}{b}}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c))))
        (t_2 (* (* x 9.0) y))
        (t_3 (* 9.0 (/ (* x y) (* c z)))))
   (if (<= t_2 -1000000000000.0)
     t_3
     (if (<= t_2 -5e-160)
       t_1
       (if (<= t_2 -2e-301)
         (/ (/ 1.0 (/ c b)) z)
         (if (<= t_2 1e+99) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (t_2 <= -1000000000000.0) {
		tmp = t_3;
	} else if (t_2 <= -5e-160) {
		tmp = t_1;
	} else if (t_2 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_2 <= 1e+99) {
		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 = a * ((-4.0d0) * (t / c))
    t_2 = (x * 9.0d0) * y
    t_3 = 9.0d0 * ((x * y) / (c * z))
    if (t_2 <= (-1000000000000.0d0)) then
        tmp = t_3
    else if (t_2 <= (-5d-160)) then
        tmp = t_1
    else if (t_2 <= (-2d-301)) then
        tmp = (1.0d0 / (c / b)) / z
    else if (t_2 <= 1d+99) 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 = a * (-4.0 * (t / c));
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (t_2 <= -1000000000000.0) {
		tmp = t_3;
	} else if (t_2 <= -5e-160) {
		tmp = t_1;
	} else if (t_2 <= -2e-301) {
		tmp = (1.0 / (c / b)) / z;
	} else if (t_2 <= 1e+99) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (-4.0 * (t / c))
	t_2 = (x * 9.0) * y
	t_3 = 9.0 * ((x * y) / (c * z))
	tmp = 0
	if t_2 <= -1000000000000.0:
		tmp = t_3
	elif t_2 <= -5e-160:
		tmp = t_1
	elif t_2 <= -2e-301:
		tmp = (1.0 / (c / b)) / z
	elif t_2 <= 1e+99:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c)))
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)))
	tmp = 0.0
	if (t_2 <= -1000000000000.0)
		tmp = t_3;
	elseif (t_2 <= -5e-160)
		tmp = t_1;
	elseif (t_2 <= -2e-301)
		tmp = Float64(Float64(1.0 / Float64(c / b)) / z);
	elseif (t_2 <= 1e+99)
		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 = a * (-4.0 * (t / c));
	t_2 = (x * 9.0) * y;
	t_3 = 9.0 * ((x * y) / (c * z));
	tmp = 0.0;
	if (t_2 <= -1000000000000.0)
		tmp = t_3;
	elseif (t_2 <= -5e-160)
		tmp = t_1;
	elseif (t_2 <= -2e-301)
		tmp = (1.0 / (c / b)) / z;
	elseif (t_2 <= 1e+99)
		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[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1000000000000.0], t$95$3, If[LessEqual[t$95$2, -5e-160], t$95$1, If[LessEqual[t$95$2, -2e-301], N[(N[(1.0 / N[(c / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+99], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e12 or 9.9999999999999997e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. 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 35.6%

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot \color{blue}{z}} \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -1e12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-160 or -2.0000000000000001e-301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e98

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. 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 56.1%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot \color{blue}{z}} \]

   4. Applied rewrites 56.1%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c} + 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c} + \color{blue}{9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{\color{blue}{c}}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      8. lower-*.f64 59.3%

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

   7. Applied rewrites 59.3%

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c}\right) \]

      2. lower-/.f64 40.1%

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c}\right) \]

   10. Applied rewrites 40.1%

       \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]

   if -4.9999999999999999e-160 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.0000000000000001e-301

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   3. Applied rewrites 79.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}} \]

   4. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{c}}}{z} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      4. lower-*.f64 60.5%

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

   6. Applied rewrites 60.5%

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 34.8%

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \frac{\frac{b}{\color{blue}{c}}}{z} \]

       2. div-flip N/A

          \[\leadsto \frac{\frac{1}{\color{blue}{\frac{c}{b}}}}{z} \]

       3. lower-unsound-/.f64 N/A

          \[\leadsto \frac{\frac{1}{\color{blue}{\frac{c}{b}}}}{z} \]

       4. lower-unsound-/.f64 34.8%

          \[\leadsto \frac{\frac{1}{\frac{c}{\color{blue}{b}}}}{z} \]

   11. Applied rewrites 34.8%

       \[\leadsto \frac{\frac{1}{\color{blue}{\frac{c}{b}}}}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\right)\\ \mathbf{if}\;\mathsf{max}\left(t, a\right) \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 1.26 \cdot 10^{-36}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (fmax t a) (* -4.0 (/ (fmin t a) c)))))
   (if (<= (fmax t a) -7.5e-50)
     t_1
     (if (<= (fmax t a) 1.26e-36) (/ b (* c z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fmax(t, a) * (-4.0 * (fmin(t, a) / c));
	double tmp;
	if (fmax(t, a) <= -7.5e-50) {
		tmp = t_1;
	} else if (fmax(t, a) <= 1.26e-36) {
		tmp = b / (c * z);
	} 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 = fmax(t, a) * ((-4.0d0) * (fmin(t, a) / c))
    if (fmax(t, a) <= (-7.5d-50)) then
        tmp = t_1
    else if (fmax(t, a) <= 1.26d-36) then
        tmp = b / (c * z)
    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(t, a) * (-4.0 * (fmin(t, a) / c));
	double tmp;
	if (fmax(t, a) <= -7.5e-50) {
		tmp = t_1;
	} else if (fmax(t, a) <= 1.26e-36) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = fmax(t, a) * (-4.0 * (fmin(t, a) / c))
	tmp = 0
	if fmax(t, a) <= -7.5e-50:
		tmp = t_1
	elif fmax(t, a) <= 1.26e-36:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmax(t, a) * Float64(-4.0 * Float64(fmin(t, a) / c)))
	tmp = 0.0
	if (fmax(t, a) <= -7.5e-50)
		tmp = t_1;
	elseif (fmax(t, a) <= 1.26e-36)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = max(t, a) * (-4.0 * (min(t, a) / c));
	tmp = 0.0;
	if (max(t, a) <= -7.5e-50)
		tmp = t_1;
	elseif (max(t, a) <= 1.26e-36)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Max[t, a], $MachinePrecision] * N[(-4.0 * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Max[t, a], $MachinePrecision], -7.5e-50], t$95$1, If[LessEqual[N[Max[t, a], $MachinePrecision], 1.26e-36], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e-50 or 1.26e-36 < a

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. 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 56.1%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot \color{blue}{z}} \]

   4. Applied rewrites 56.1%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   5. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c} + 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c} + \color{blue}{9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{\color{blue}{c}}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

      8. lower-*.f64 59.3%

         \[\leadsto a \cdot \mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right) \]

   7. Applied rewrites 59.3%

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(-4, \frac{t}{c}, 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c}\right) \]

      2. lower-/.f64 40.1%

         \[\leadsto a \cdot \left(-4 \cdot \frac{t}{c}\right) \]

   10. Applied rewrites 40.1%

       \[\leadsto a \cdot \left(-4 \cdot \frac{t}{\color{blue}{c}}\right) \]

   if -7.5e-50 < a < 1.26e-36

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. 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 35.6%

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 35.6% 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 79.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

2. 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 35.6%

      \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

4. Applied rewrites 35.6%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025191 
(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)))