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

Percentage Accurate: 79.4% → 89.4%

Time: 6.9s

Alternatives: 16

Speedup: 0.5×

• 36.9% 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: 89.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{1}{\frac{-c}{\mathsf{max}\left(x, y\right) \cdot \left(\mathsf{fma}\left(-9, \frac{\mathsf{min}\left(x, y\right)}{z}, 4 \cdot \frac{a \cdot t}{\mathsf{max}\left(x, y\right)}\right) - \frac{b}{\mathsf{max}\left(x, y\right) \cdot z}\right)}}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(z \cdot t\right) \cdot -4, a, \mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          1.0
          (/
           (- c)
           (*
            (fmax x y)
            (-
             (fma -9.0 (/ (fmin x y) z) (* 4.0 (/ (* a t) (fmax x y))))
             (/ b (* (fmax x y) z))))))))
   (if (<= z -4.4e+114)
     t_1
     (if (<= z 1.2e+80)
       (/
        (/ (fma (* (* z t) -4.0) a (fma (* (fmax x y) (fmin x y)) 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 = 1.0 / (-c / (fmax(x, y) * (fma(-9.0, (fmin(x, y) / z), (4.0 * ((a * t) / fmax(x, y)))) - (b / (fmax(x, y) * z)))));
	double tmp;
	if (z <= -4.4e+114) {
		tmp = t_1;
	} else if (z <= 1.2e+80) {
		tmp = (fma(((z * t) * -4.0), a, fma((fmax(x, y) * fmin(x, y)), 9.0, b)) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(Float64(-c) / Float64(fmax(x, y) * Float64(fma(-9.0, Float64(fmin(x, y) / z), Float64(4.0 * Float64(Float64(a * t) / fmax(x, y)))) - Float64(b / Float64(fmax(x, y) * z))))))
	tmp = 0.0
	if (z <= -4.4e+114)
		tmp = t_1;
	elseif (z <= 1.2e+80)
		tmp = Float64(Float64(fma(Float64(Float64(z * t) * -4.0), a, fma(Float64(fmax(x, y) * fmin(x, y)), 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[(1.0 / N[((-c) / N[(N[Max[x, y], $MachinePrecision] * N[(N[(-9.0 * N[(N[Min[x, y], $MachinePrecision] / z), $MachinePrecision] + N[(4.0 * N[(N[(a * t), $MachinePrecision] / N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[Max[x, y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+114], t$95$1, If[LessEqual[z, 1.2e+80], N[(N[(N[(N[(N[(z * t), $MachinePrecision] * -4.0), $MachinePrecision] * a + N[(N[(N[Max[x, y], $MachinePrecision] * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000001e114 or 1.1999999999999999e80 < 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

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 75.0

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

   6. Applied rewrites 75.0%

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

   if -4.4000000000000001e114 < z < 1.1999999999999999e80

   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 80.8%

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

   5. Applied rewrites 80.1%

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

Alternative 2: 87.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := z \cdot \left|c\right|\\ t_2 := \frac{\mathsf{fma}\left(9 \cdot \mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), \mathsf{fma}\left(-4, \left(a \cdot t\right) \cdot z, b\right)\right)}{t\_1}\\ t_3 := \frac{\left(\left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{t\_1}\\ \mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+227}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(z \cdot t\right) \cdot -4, a, \mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)\right)}{\left|c\right|}}{z}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{-0.25 \cdot \frac{\left|c\right|}{a \cdot t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (fabs c)))
        (t_2
         (/
          (fma (* 9.0 (fmin x y)) (fmax x y) (fma -4.0 (* (* a t) z) b))
          t_1))
        (t_3
         (/
          (+ (- (* (* (fmin x y) 9.0) (fmax x y)) (* (* (* z 4.0) t) a)) b)
          t_1)))
   (*
    (copysign 1.0 c)
    (if (<= t_3 -2e-251)
      t_2
      (if (<= t_3 2e+227)
        (/
         (/
          (fma (* (* z t) -4.0) a (fma (* (fmax x y) (fmin x y)) 9.0 b))
          (fabs c))
         z)
        (if (<= t_3 INFINITY) t_2 (/ 1.0 (* -0.25 (/ (fabs c) (* a t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * fabs(c);
	double t_2 = fma((9.0 * fmin(x, y)), fmax(x, y), fma(-4.0, ((a * t) * z), b)) / t_1;
	double t_3 = ((((fmin(x, y) * 9.0) * fmax(x, y)) - (((z * 4.0) * t) * a)) + b) / t_1;
	double tmp;
	if (t_3 <= -2e-251) {
		tmp = t_2;
	} else if (t_3 <= 2e+227) {
		tmp = (fma(((z * t) * -4.0), a, fma((fmax(x, y) * fmin(x, y)), 9.0, b)) / fabs(c)) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = 1.0 / (-0.25 * (fabs(c) / (a * t)));
	}
	return copysign(1.0, c) * tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * abs(c))
	t_2 = Float64(fma(Float64(9.0 * fmin(x, y)), fmax(x, y), fma(-4.0, Float64(Float64(a * t) * z), b)) / t_1)
	t_3 = Float64(Float64(Float64(Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / t_1)
	tmp = 0.0
	if (t_3 <= -2e-251)
		tmp = t_2;
	elseif (t_3 <= 2e+227)
		tmp = Float64(Float64(fma(Float64(Float64(z * t) * -4.0), a, fma(Float64(fmax(x, y) * fmin(x, y)), 9.0, b)) / abs(c)) / z);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(1.0 / Float64(-0.25 * Float64(abs(c) / Float64(a * t))));
	end
	return Float64(copysign(1.0, c) * tmp)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * N[Max[x, y], $MachinePrecision] + N[(-4.0 * N[(N[(a * t), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$3, -2e-251], t$95$2, If[LessEqual[t$95$3, 2e+227], N[(N[(N[(N[(N[(z * t), $MachinePrecision] * -4.0), $MachinePrecision] * a + N[(N[(N[Max[x, y], $MachinePrecision] * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(1.0 / N[(-0.25 * N[(N[Abs[c], $MachinePrecision] / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -2.00000000000000003e-251 or 2.0000000000000002e227 < (/.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 80.8%

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

   if -2.00000000000000003e-251 < (/.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)) < 2.0000000000000002e227

   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 80.8%

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

   5. Applied rewrites 80.1%

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

   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

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{-1}{4} \cdot \frac{c}{a \cdot t}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \color{blue}{\frac{c}{a \cdot t}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \frac{c}{\color{blue}{a \cdot t}}} \]

      3. lower-*.f64 38.8

         \[\leadsto \frac{1}{-0.25 \cdot \frac{c}{a \cdot \color{blue}{t}}} \]

   6. Applied rewrites 38.8%

      \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.1% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;\left|c\right| \leq 7.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4, \left(a \cdot t\right) \cdot z, b\right)\right)}{z \cdot \left|c\right|}\\ \mathbf{elif}\;\left|c\right| \leq 1.75 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot 9, \frac{y}{\left|c\right| \cdot z}, t \cdot \mathsf{fma}\left(-4, \frac{a}{\left|c\right|}, \frac{b}{\left|c\right| \cdot \left(t \cdot z\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{\left|c\right|}, 9 \cdot x, \frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, b\right)}{\left|c\right|}\right)}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (*
  (copysign 1.0 c)
  (if (<= (fabs c) 7.5e-20)
    (/ (fma (* 9.0 x) y (fma -4.0 (* (* a t) z) b)) (* z (fabs c)))
    (if (<= (fabs c) 1.75e+119)
      (fma
       (* x 9.0)
       (/ y (* (fabs c) z))
       (* t (fma -4.0 (/ a (fabs c)) (/ b (* (fabs c) (* t z))))))
      (/
       (fma (/ y (fabs c)) (* 9.0 x) (/ (fma (* (* t z) -4.0) a b) (fabs c)))
       z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (fabs(c) <= 7.5e-20) {
		tmp = fma((9.0 * x), y, fma(-4.0, ((a * t) * z), b)) / (z * fabs(c));
	} else if (fabs(c) <= 1.75e+119) {
		tmp = fma((x * 9.0), (y / (fabs(c) * z)), (t * fma(-4.0, (a / fabs(c)), (b / (fabs(c) * (t * z))))));
	} else {
		tmp = fma((y / fabs(c)), (9.0 * x), (fma(((t * z) * -4.0), a, b) / fabs(c))) / z;
	}
	return copysign(1.0, c) * tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (abs(c) <= 7.5e-20)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(-4.0, Float64(Float64(a * t) * z), b)) / Float64(z * abs(c)));
	elseif (abs(c) <= 1.75e+119)
		tmp = fma(Float64(x * 9.0), Float64(y / Float64(abs(c) * z)), Float64(t * fma(-4.0, Float64(a / abs(c)), Float64(b / Float64(abs(c) * Float64(t * z))))));
	else
		tmp = Float64(fma(Float64(y / abs(c)), Float64(9.0 * x), Float64(fma(Float64(Float64(t * z) * -4.0), a, b) / abs(c))) / z);
	end
	return Float64(copysign(1.0, c) * tmp)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[c], $MachinePrecision], 7.5e-20], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(-4.0 * N[(N[(a * t), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[c], $MachinePrecision], 1.75e+119], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(N[Abs[c], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * N[(a / N[Abs[c], $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[Abs[c], $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / N[Abs[c], $MachinePrecision]), $MachinePrecision] * N[(9.0 * x), $MachinePrecision] + N[(N[(N[(N[(t * z), $MachinePrecision] * -4.0), $MachinePrecision] * a + b), $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if c < 7.49999999999999981e-20

   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 80.8%

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

   if 7.49999999999999981e-20 < c < 1.75e119

   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 80.8%

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

      1. lift-/.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. div-add N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 73.8

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

      14. lift-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 73.8

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 73.8

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 73.8

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lift-*.f64 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 72.8

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

   8. Applied rewrites 72.8%

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

   if 1.75e119 < 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

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

      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 79.9%

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

   5. Applied rewrites 77.2%

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

Alternative 4: 85.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(\left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(9 \cdot \mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), \mathsf{fma}\left(-4, \left(a \cdot t\right) \cdot z, b\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{-c}{\frac{4 \cdot \left(a \cdot \left(t \cdot z\right)\right) - b}{z}}}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{-0.25 \cdot \frac{c}{a \cdot t}}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          (+ (- (* (* (fmin x y) 9.0) (fmax x y)) (* (* (* z 4.0) t) a)) b)
          (* z c)))
        (t_2
         (/
          (fma (* 9.0 (fmin x y)) (fmax x y) (fma -4.0 (* (* a t) z) b))
          (* z c))))
   (if (<= t_1 -2e-251)
     t_2
     (if (<= t_1 0.0)
       (/ 1.0 (/ (- c) (/ (- (* 4.0 (* a (* t z))) b) z)))
       (if (<= t_1 INFINITY) t_2 (/ 1.0 (* -0.25 (/ c (* a t)))))))))

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)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = fma((9.0 * fmin(x, y)), fmax(x, y), fma(-4.0, ((a * t) * z), b)) / (z * c);
	double tmp;
	if (t_1 <= -2e-251) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / (-c / (((4.0 * (a * (t * z))) - b) / z));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = 1.0 / (-0.25 * (c / (a * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = Float64(fma(Float64(9.0 * fmin(x, y)), fmax(x, y), fma(-4.0, Float64(Float64(a * t) * z), b)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-251)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(1.0 / Float64(Float64(-c) / Float64(Float64(Float64(4.0 * Float64(a * Float64(t * z))) - b) / z)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(1.0 / Float64(-0.25 * Float64(c / Float64(a * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * N[Max[x, y], $MachinePrecision] + N[(-4.0 * N[(N[(a * t), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-251], t$95$2, If[LessEqual[t$95$1, 0.0], N[(1.0 / N[((-c) / N[(N[(N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(1.0 / N[(-0.25 * N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -2.00000000000000003e-251 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 80.8%

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

   if -2.00000000000000003e-251 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 79.4%

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

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 56.7

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

   6. Applied rewrites 56.7%

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

   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

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

      3. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{-1}{4} \cdot \frac{c}{a \cdot t}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \color{blue}{\frac{c}{a \cdot t}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \frac{c}{\color{blue}{a \cdot t}}} \]

      3. lower-*.f64 38.8

         \[\leadsto \frac{1}{-0.25 \cdot \frac{c}{a \cdot \color{blue}{t}}} \]

   6. Applied rewrites 38.8%

      \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.6% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;\left|c\right| \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot \mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), \mathsf{fma}\left(-4, \left(\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)\right) \cdot z, b\right)\right)}{z \cdot \left|c\right|}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\mathsf{max}\left(t, a\right) \cdot \left(-4 \cdot z\right), \mathsf{min}\left(t, a\right), \mathsf{fma}\left(\mathsf{max}\left(x, y\right) \cdot \mathsf{min}\left(x, y\right), 9, b\right)\right)}{\left|c\right|}}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (*
  (copysign 1.0 c)
  (if (<= (fabs c) 2e+28)
    (/
     (fma
      (* 9.0 (fmin x y))
      (fmax x y)
      (fma -4.0 (* (* (fmax t a) (fmin t a)) z) b))
     (* z (fabs c)))
    (/
     (/
      (fma
       (* (fmax t a) (* -4.0 z))
       (fmin t a)
       (fma (* (fmax x y) (fmin x y)) 9.0 b))
      (fabs c))
     z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (fabs(c) <= 2e+28) {
		tmp = fma((9.0 * fmin(x, y)), fmax(x, y), fma(-4.0, ((fmax(t, a) * fmin(t, a)) * z), b)) / (z * fabs(c));
	} else {
		tmp = (fma((fmax(t, a) * (-4.0 * z)), fmin(t, a), fma((fmax(x, y) * fmin(x, y)), 9.0, b)) / fabs(c)) / z;
	}
	return copysign(1.0, c) * tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (abs(c) <= 2e+28)
		tmp = Float64(fma(Float64(9.0 * fmin(x, y)), fmax(x, y), fma(-4.0, Float64(Float64(fmax(t, a) * fmin(t, a)) * z), b)) / Float64(z * abs(c)));
	else
		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)) / abs(c)) / z);
	end
	return Float64(copysign(1.0, c) * tmp)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[c], $MachinePrecision], 2e+28], N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * N[Max[x, y], $MachinePrecision] + N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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] / N[Abs[c], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.99999999999999992e28

   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 80.8%

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

   if 1.99999999999999992e28 < 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

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

      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 79.9%

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

Alternative 6: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ b (* 9.0 (* x y)))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -5e+79)
     (/ (/ t_1 c) z)
     (if (<= t_2 5e+22)
       (/ (/ (fma (* (* t a) z) -4.0 b) z) c)
       (/ t_1 (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+79) {
		tmp = (t_1 / c) / z;
	} else if (t_2 <= 5e+22) {
		tmp = (fma(((t * a) * z), -4.0, b) / z) / c;
	} else {
		tmp = t_1 / (z * c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -5e+79)
		tmp = Float64(Float64(t_1 / c) / z);
	elseif (t_2 <= 5e+22)
		tmp = Float64(Float64(fma(Float64(Float64(t * a) * z), -4.0, b) / z) / c);
	else
		tmp = Float64(t_1 / Float64(z * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+79], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 5e+22], N[(N[(N[(N[(N[(t * a), $MachinePrecision] * z), $MachinePrecision] * -4.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e79

   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 80.8%

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]
   7. 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 60.4

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

   8. Applied rewrites 60.4%

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

   if -5e79 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999996e22

   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 79.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 56.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   8. Applied rewrites 59.8%

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

   if 4.9999999999999996e22 < (*.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 z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

Alternative 7: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ b (* 9.0 (* x y)))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -5e+79)
     (/ (/ t_1 c) z)
     (if (<= t_2 5e+22)
       (/ (fma (* (* -4.0 z) a) t b) (* z c))
       (/ t_1 (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+79) {
		tmp = (t_1 / c) / z;
	} else if (t_2 <= 5e+22) {
		tmp = fma(((-4.0 * z) * a), t, b) / (z * c);
	} else {
		tmp = t_1 / (z * c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -5e+79)
		tmp = Float64(Float64(t_1 / c) / z);
	elseif (t_2 <= 5e+22)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, b) / Float64(z * c));
	else
		tmp = Float64(t_1 / Float64(z * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+79], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 5e+22], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e79

   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 80.8%

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]
   7. 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 60.4

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

   8. Applied rewrites 60.4%

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

   if -5e79 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999996e22

   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 79.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 56.7%

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

   if 4.9999999999999996e22 < (*.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 z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

Alternative 8: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{1}{-0.25 \cdot \frac{c}{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}}\\ \mathbf{if}\;\mathsf{max}\left(t, a\right) \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 10^{-186}:\\ \;\;\;\;\frac{\frac{-9 \cdot \left(x \cdot y\right) - b}{-z}}{c}\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 1.15 \cdot 10^{+227}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* -0.25 (/ c (* (fmax t a) (fmin t a)))))))
   (if (<= (fmax t a) -2.7e-17)
     t_1
     (if (<= (fmax t a) 1e-186)
       (/ (/ (- (* -9.0 (* x y)) b) (- z)) c)
       (if (<= (fmax t a) 1.15e+227) (/ (+ b (* 9.0 (* x y))) (* z c)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))));
	double tmp;
	if (fmax(t, a) <= -2.7e-17) {
		tmp = t_1;
	} else if (fmax(t, a) <= 1e-186) {
		tmp = (((-9.0 * (x * y)) - b) / -z) / c;
	} else if (fmax(t, a) <= 1.15e+227) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((-0.25d0) * (c / (fmax(t, a) * fmin(t, a))))
    if (fmax(t, a) <= (-2.7d-17)) then
        tmp = t_1
    else if (fmax(t, a) <= 1d-186) then
        tmp = ((((-9.0d0) * (x * y)) - b) / -z) / c
    else if (fmax(t, a) <= 1.15d+227) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))));
	double tmp;
	if (fmax(t, a) <= -2.7e-17) {
		tmp = t_1;
	} else if (fmax(t, a) <= 1e-186) {
		tmp = (((-9.0 * (x * y)) - b) / -z) / c;
	} else if (fmax(t, a) <= 1.15e+227) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))))
	tmp = 0
	if fmax(t, a) <= -2.7e-17:
		tmp = t_1
	elif fmax(t, a) <= 1e-186:
		tmp = (((-9.0 * (x * y)) - b) / -z) / c
	elif fmax(t, a) <= 1.15e+227:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(-0.25 * Float64(c / Float64(fmax(t, a) * fmin(t, a)))))
	tmp = 0.0
	if (fmax(t, a) <= -2.7e-17)
		tmp = t_1;
	elseif (fmax(t, a) <= 1e-186)
		tmp = Float64(Float64(Float64(Float64(-9.0 * Float64(x * y)) - b) / Float64(-z)) / c);
	elseif (fmax(t, a) <= 1.15e+227)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (-0.25 * (c / (max(t, a) * min(t, a))));
	tmp = 0.0;
	if (max(t, a) <= -2.7e-17)
		tmp = t_1;
	elseif (max(t, a) <= 1e-186)
		tmp = (((-9.0 * (x * y)) - b) / -z) / c;
	elseif (max(t, a) <= 1.15e+227)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(-0.25 * N[(c / N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Max[t, a], $MachinePrecision], -2.7e-17], t$95$1, If[LessEqual[N[Max[t, a], $MachinePrecision], 1e-186], N[(N[(N[(N[(-9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] / (-z)), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[N[Max[t, a], $MachinePrecision], 1.15e+227], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7000000000000001e-17 or 1.1499999999999999e227 < 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. 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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{-1}{4} \cdot \frac{c}{a \cdot t}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \color{blue}{\frac{c}{a \cdot t}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \frac{c}{\color{blue}{a \cdot t}}} \]

      3. lower-*.f64 38.8

         \[\leadsto \frac{1}{-0.25 \cdot \frac{c}{a \cdot \color{blue}{t}}} \]

   6. Applied rewrites 38.8%

      \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]

   if -2.7000000000000001e-17 < a < 9.9999999999999991e-187

   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{-c}{\frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-c}{\frac{-9 \cdot \left(x \cdot y\right) - b}{z}}} \]

      3. lower-*.f64 58.0

         \[\leadsto \frac{1}{\frac{-c}{\frac{-9 \cdot \left(x \cdot y\right) - b}{z}}} \]

   6. Applied rewrites 58.0%

      \[\leadsto \frac{1}{\frac{-c}{\frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. frac-2neg N/A

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

      5. lift-neg.f64 N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

   8. Applied rewrites 58.1%

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

   if 9.9999999999999991e-187 < a < 1.1499999999999999e227

   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 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

Alternative 9: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{1}{-0.25 \cdot \frac{c}{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}}\\ \mathbf{if}\;\mathsf{max}\left(t, a\right) \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 1.15 \cdot 10^{+227}:\\ \;\;\;\;\frac{t\_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ b (* 9.0 (* x y))))
        (t_2 (/ 1.0 (* -0.25 (/ c (* (fmax t a) (fmin t a)))))))
   (if (<= (fmax t a) -2.7e-17)
     t_2
     (if (<= (fmax t a) -5e-294)
       (/ (/ t_1 c) z)
       (if (<= (fmax t a) 1.15e+227) (/ t_1 (* z c)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double t_2 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))));
	double tmp;
	if (fmax(t, a) <= -2.7e-17) {
		tmp = t_2;
	} else if (fmax(t, a) <= -5e-294) {
		tmp = (t_1 / c) / z;
	} else if (fmax(t, a) <= 1.15e+227) {
		tmp = t_1 / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b + (9.0d0 * (x * y))
    t_2 = 1.0d0 / ((-0.25d0) * (c / (fmax(t, a) * fmin(t, a))))
    if (fmax(t, a) <= (-2.7d-17)) then
        tmp = t_2
    else if (fmax(t, a) <= (-5d-294)) then
        tmp = (t_1 / c) / z
    else if (fmax(t, a) <= 1.15d+227) then
        tmp = t_1 / (z * c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double t_2 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))));
	double tmp;
	if (fmax(t, a) <= -2.7e-17) {
		tmp = t_2;
	} else if (fmax(t, a) <= -5e-294) {
		tmp = (t_1 / c) / z;
	} else if (fmax(t, a) <= 1.15e+227) {
		tmp = t_1 / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (x * y))
	t_2 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))))
	tmp = 0
	if fmax(t, a) <= -2.7e-17:
		tmp = t_2
	elif fmax(t, a) <= -5e-294:
		tmp = (t_1 / c) / z
	elif fmax(t, a) <= 1.15e+227:
		tmp = t_1 / (z * c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	t_2 = Float64(1.0 / Float64(-0.25 * Float64(c / Float64(fmax(t, a) * fmin(t, a)))))
	tmp = 0.0
	if (fmax(t, a) <= -2.7e-17)
		tmp = t_2;
	elseif (fmax(t, a) <= -5e-294)
		tmp = Float64(Float64(t_1 / c) / z);
	elseif (fmax(t, a) <= 1.15e+227)
		tmp = Float64(t_1 / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (x * y));
	t_2 = 1.0 / (-0.25 * (c / (max(t, a) * min(t, a))));
	tmp = 0.0;
	if (max(t, a) <= -2.7e-17)
		tmp = t_2;
	elseif (max(t, a) <= -5e-294)
		tmp = (t_1 / c) / z;
	elseif (max(t, a) <= 1.15e+227)
		tmp = t_1 / (z * c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(-0.25 * N[(c / N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Max[t, a], $MachinePrecision], -2.7e-17], t$95$2, If[LessEqual[N[Max[t, a], $MachinePrecision], -5e-294], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[Max[t, a], $MachinePrecision], 1.15e+227], N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7000000000000001e-17 or 1.1499999999999999e227 < 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. 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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{-1}{4} \cdot \frac{c}{a \cdot t}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \color{blue}{\frac{c}{a \cdot t}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \frac{c}{\color{blue}{a \cdot t}}} \]

      3. lower-*.f64 38.8

         \[\leadsto \frac{1}{-0.25 \cdot \frac{c}{a \cdot \color{blue}{t}}} \]

   6. Applied rewrites 38.8%

      \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]

   if -2.7000000000000001e-17 < a < -5.0000000000000003e-294

   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 80.8%

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}}{z} \]
   7. 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 60.4

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

   8. Applied rewrites 60.4%

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

   if -5.0000000000000003e-294 < a < 1.1499999999999999e227

   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 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

Alternative 10: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{1}{-0.25 \cdot \frac{c}{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}}\\ \mathbf{if}\;\mathsf{max}\left(t, a\right) \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\mathsf{max}\left(t, a\right) \leq 1.15 \cdot 10^{+227}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* -0.25 (/ c (* (fmax t a) (fmin t a)))))))
   (if (<= (fmax t a) -2.7e-17)
     t_1
     (if (<= (fmax t a) 1.15e+227) (/ (+ b (* 9.0 (* x y))) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))));
	double tmp;
	if (fmax(t, a) <= -2.7e-17) {
		tmp = t_1;
	} else if (fmax(t, a) <= 1.15e+227) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((-0.25d0) * (c / (fmax(t, a) * fmin(t, a))))
    if (fmax(t, a) <= (-2.7d-17)) then
        tmp = t_1
    else if (fmax(t, a) <= 1.15d+227) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))));
	double tmp;
	if (fmax(t, a) <= -2.7e-17) {
		tmp = t_1;
	} else if (fmax(t, a) <= 1.15e+227) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (-0.25 * (c / (fmax(t, a) * fmin(t, a))))
	tmp = 0
	if fmax(t, a) <= -2.7e-17:
		tmp = t_1
	elif fmax(t, a) <= 1.15e+227:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(-0.25 * Float64(c / Float64(fmax(t, a) * fmin(t, a)))))
	tmp = 0.0
	if (fmax(t, a) <= -2.7e-17)
		tmp = t_1;
	elseif (fmax(t, a) <= 1.15e+227)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (-0.25 * (c / (max(t, a) * min(t, a))));
	tmp = 0.0;
	if (max(t, a) <= -2.7e-17)
		tmp = t_1;
	elseif (max(t, a) <= 1.15e+227)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(-0.25 * N[(c / N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Max[t, a], $MachinePrecision], -2.7e-17], t$95$1, If[LessEqual[N[Max[t, a], $MachinePrecision], 1.15e+227], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7000000000000001e-17 or 1.1499999999999999e227 < 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. 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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{-1}{4} \cdot \frac{c}{a \cdot t}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \color{blue}{\frac{c}{a \cdot t}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \frac{c}{\color{blue}{a \cdot t}}} \]

      3. lower-*.f64 38.8

         \[\leadsto \frac{1}{-0.25 \cdot \frac{c}{a \cdot \color{blue}{t}}} \]

   6. Applied rewrites 38.8%

      \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]

   if -2.7000000000000001e-17 < a < 1.1499999999999999e227

   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 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

Alternative 11: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;\frac{\left(9 \cdot \mathsf{min}\left(x, y\right)\right) \cdot \mathsf{max}\left(x, y\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-257}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{-184}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{1}{-0.25 \cdot \frac{c}{a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\right)}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))))
   (if (<= t_1 -5e+79)
     (/ (* (* 9.0 (fmin x y)) (fmax x y)) (* z c))
     (if (<= t_1 -4e-257)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 1e-184)
         (/ b (* c z))
         (if (<= t_1 2e+27)
           (/ 1.0 (* -0.25 (/ c (* a t))))
           (/ (* 9.0 (* (fmin x y) (fmax x y))) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -5e+79) {
		tmp = ((9.0 * fmin(x, y)) * fmax(x, y)) / (z * c);
	} else if (t_1 <= -4e-257) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_1 <= 2e+27) {
		tmp = 1.0 / (-0.25 * (c / (a * t)));
	} else {
		tmp = (9.0 * (fmin(x, y) * fmax(x, y))) / (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) :: tmp
    t_1 = (fmin(x, y) * 9.0d0) * fmax(x, y)
    if (t_1 <= (-5d+79)) then
        tmp = ((9.0d0 * fmin(x, y)) * fmax(x, y)) / (z * c)
    else if (t_1 <= (-4d-257)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 1d-184) then
        tmp = b / (c * z)
    else if (t_1 <= 2d+27) then
        tmp = 1.0d0 / ((-0.25d0) * (c / (a * t)))
    else
        tmp = (9.0d0 * (fmin(x, y) * fmax(x, y))) / (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 tmp;
	if (t_1 <= -5e+79) {
		tmp = ((9.0 * fmin(x, y)) * fmax(x, y)) / (z * c);
	} else if (t_1 <= -4e-257) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_1 <= 2e+27) {
		tmp = 1.0 / (-0.25 * (c / (a * t)));
	} else {
		tmp = (9.0 * (fmin(x, y) * fmax(x, y))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmin(x, y) * 9.0) * fmax(x, y)
	tmp = 0
	if t_1 <= -5e+79:
		tmp = ((9.0 * fmin(x, y)) * fmax(x, y)) / (z * c)
	elif t_1 <= -4e-257:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 1e-184:
		tmp = b / (c * z)
	elif t_1 <= 2e+27:
		tmp = 1.0 / (-0.25 * (c / (a * t)))
	else:
		tmp = (9.0 * (fmin(x, y) * fmax(x, y))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -5e+79)
		tmp = Float64(Float64(Float64(9.0 * fmin(x, y)) * fmax(x, y)) / Float64(z * c));
	elseif (t_1 <= -4e-257)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 1e-184)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 2e+27)
		tmp = Float64(1.0 / Float64(-0.25 * Float64(c / Float64(a * t))));
	else
		tmp = Float64(Float64(9.0 * Float64(fmin(x, y) * fmax(x, y))) / 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);
	tmp = 0.0;
	if (t_1 <= -5e+79)
		tmp = ((9.0 * min(x, y)) * max(x, y)) / (z * c);
	elseif (t_1 <= -4e-257)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 1e-184)
		tmp = b / (c * z);
	elseif (t_1 <= 2e+27)
		tmp = 1.0 / (-0.25 * (c / (a * t)));
	else
		tmp = (9.0 * (min(x, y) * max(x, y))) / (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]}, If[LessEqual[t$95$1, -5e+79], N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-257], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-184], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+27], N[(1.0 / N[(-0.25 * N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e79

   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 80.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 35.5

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

   6. Applied rewrites 35.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lower-*.f64 35.5

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 35.5

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

   8. Applied rewrites 35.5%

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

   if -5e79 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-257

   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 38.9

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

   4. Applied rewrites 38.9%

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

   if -3.9999999999999999e-257 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e-184

   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 1.0000000000000001e-184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e27

   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. div-flip N/A

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

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

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

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

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

      8. lower-neg.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

   3. Applied rewrites 78.7%

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

   4. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{-1}{4} \cdot \frac{c}{a \cdot t}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \color{blue}{\frac{c}{a \cdot t}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{-1}{4} \cdot \frac{c}{\color{blue}{a \cdot t}}} \]

      3. lower-*.f64 38.8

         \[\leadsto \frac{1}{-0.25 \cdot \frac{c}{a \cdot \color{blue}{t}}} \]

   6. Applied rewrites 38.8%

      \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]

   if 2e27 < (*.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

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

      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 80.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 35.5

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

   6. Applied rewrites 35.5%

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

Alternative 12: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;\frac{\left(9 \cdot \mathsf{min}\left(x, y\right)\right) \cdot \mathsf{max}\left(x, y\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-257}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-184}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\right)}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))) (t_2 (* -4.0 (/ (* a t) c))))
   (if (<= t_1 -5e+79)
     (/ (* (* 9.0 (fmin x y)) (fmax x y)) (* z c))
     (if (<= t_1 -4e-257)
       t_2
       (if (<= t_1 1e-184)
         (/ b (* c z))
         (if (<= t_1 2e+27)
           t_2
           (/ (* 9.0 (* (fmin x y) (fmax x y))) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (t_1 <= -5e+79) {
		tmp = ((9.0 * fmin(x, y)) * fmax(x, y)) / (z * c);
	} else if (t_1 <= -4e-257) {
		tmp = t_2;
	} else if (t_1 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_1 <= 2e+27) {
		tmp = t_2;
	} else {
		tmp = (9.0 * (fmin(x, y) * fmax(x, y))) / (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 = (-4.0d0) * ((a * t) / c)
    if (t_1 <= (-5d+79)) then
        tmp = ((9.0d0 * fmin(x, y)) * fmax(x, y)) / (z * c)
    else if (t_1 <= (-4d-257)) then
        tmp = t_2
    else if (t_1 <= 1d-184) then
        tmp = b / (c * z)
    else if (t_1 <= 2d+27) then
        tmp = t_2
    else
        tmp = (9.0d0 * (fmin(x, y) * fmax(x, y))) / (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 = -4.0 * ((a * t) / c);
	double tmp;
	if (t_1 <= -5e+79) {
		tmp = ((9.0 * fmin(x, y)) * fmax(x, y)) / (z * c);
	} else if (t_1 <= -4e-257) {
		tmp = t_2;
	} else if (t_1 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_1 <= 2e+27) {
		tmp = t_2;
	} else {
		tmp = (9.0 * (fmin(x, y) * fmax(x, y))) / (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 = -4.0 * ((a * t) / c)
	tmp = 0
	if t_1 <= -5e+79:
		tmp = ((9.0 * fmin(x, y)) * fmax(x, y)) / (z * c)
	elif t_1 <= -4e-257:
		tmp = t_2
	elif t_1 <= 1e-184:
		tmp = b / (c * z)
	elif t_1 <= 2e+27:
		tmp = t_2
	else:
		tmp = (9.0 * (fmin(x, y) * fmax(x, y))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (t_1 <= -5e+79)
		tmp = Float64(Float64(Float64(9.0 * fmin(x, y)) * fmax(x, y)) / Float64(z * c));
	elseif (t_1 <= -4e-257)
		tmp = t_2;
	elseif (t_1 <= 1e-184)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 2e+27)
		tmp = t_2;
	else
		tmp = Float64(Float64(9.0 * Float64(fmin(x, y) * fmax(x, y))) / 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 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (t_1 <= -5e+79)
		tmp = ((9.0 * min(x, y)) * max(x, y)) / (z * c);
	elseif (t_1 <= -4e-257)
		tmp = t_2;
	elseif (t_1 <= 1e-184)
		tmp = b / (c * z);
	elseif (t_1 <= 2e+27)
		tmp = t_2;
	else
		tmp = (9.0 * (min(x, y) * max(x, y))) / (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[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+79], N[(N[(N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-257], t$95$2, If[LessEqual[t$95$1, 1e-184], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+27], t$95$2, N[(N[(9.0 * N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e79

   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 80.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 35.5

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

   6. Applied rewrites 35.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lower-*.f64 35.5

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 35.5

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

   8. Applied rewrites 35.5%

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

   if -5e79 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-257 or 1.0000000000000001e-184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e27

   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 38.9

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

   4. Applied rewrites 38.9%

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

   if -3.9999999999999999e-257 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e-184

   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 2e27 < (*.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

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

      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 80.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 35.5

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

   6. Applied rewrites 35.5%

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

Alternative 13: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-184}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -5e+79)
     (* 9.0 (/ (* x y) (* c z)))
     (if (<= t_2 -4e-257)
       t_1
       (if (<= t_2 1e-184)
         (/ b (* c z))
         (if (<= t_2 2e+27) t_1 (/ (* 9.0 (* x y)) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+79) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (t_2 <= -4e-257) {
		tmp = t_1;
	} else if (t_2 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_2 <= 2e+27) {
		tmp = t_1;
	} else {
		tmp = (9.0 * (x * y)) / (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 = (-4.0d0) * ((a * t) / c)
    t_2 = (x * 9.0d0) * y
    if (t_2 <= (-5d+79)) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else if (t_2 <= (-4d-257)) then
        tmp = t_1
    else if (t_2 <= 1d-184) then
        tmp = b / (c * z)
    else if (t_2 <= 2d+27) then
        tmp = t_1
    else
        tmp = (9.0d0 * (x * y)) / (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 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+79) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (t_2 <= -4e-257) {
		tmp = t_1;
	} else if (t_2 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_2 <= 2e+27) {
		tmp = t_1;
	} else {
		tmp = (9.0 * (x * y)) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	t_2 = (x * 9.0) * y
	tmp = 0
	if t_2 <= -5e+79:
		tmp = 9.0 * ((x * y) / (c * z))
	elif t_2 <= -4e-257:
		tmp = t_1
	elif t_2 <= 1e-184:
		tmp = b / (c * z)
	elif t_2 <= 2e+27:
		tmp = t_1
	else:
		tmp = (9.0 * (x * y)) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -5e+79)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	elseif (t_2 <= -4e-257)
		tmp = t_1;
	elseif (t_2 <= 1e-184)
		tmp = Float64(b / Float64(c * z));
	elseif (t_2 <= 2e+27)
		tmp = t_1;
	else
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	t_2 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_2 <= -5e+79)
		tmp = 9.0 * ((x * y) / (c * z));
	elseif (t_2 <= -4e-257)
		tmp = t_1;
	elseif (t_2 <= 1e-184)
		tmp = b / (c * z);
	elseif (t_2 <= 2e+27)
		tmp = t_1;
	else
		tmp = (9.0 * (x * y)) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+79], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-257], t$95$1, If[LessEqual[t$95$2, 1e-184], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+27], t$95$1, N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e79

   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 35.5

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

   4. Applied rewrites 35.5%

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

   if -5e79 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-257 or 1.0000000000000001e-184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e27

   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 38.9

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

   4. Applied rewrites 38.9%

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

   if -3.9999999999999999e-257 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e-184

   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 2e27 < (*.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

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

      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 80.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 35.5

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

   6. Applied rewrites 35.5%

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

Alternative 14: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-184}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c)))
        (t_2 (* (* x 9.0) y))
        (t_3 (* 9.0 (/ (* x y) (* c z)))))
   (if (<= t_2 -5e+79)
     t_3
     (if (<= t_2 -4e-257)
       t_1
       (if (<= t_2 1e-184) (/ b (* c z)) (if (<= t_2 2e+27) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (t_2 <= -5e+79) {
		tmp = t_3;
	} else if (t_2 <= -4e-257) {
		tmp = t_1;
	} else if (t_2 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_2 <= 2e+27) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-4.0d0) * ((a * t) / c)
    t_2 = (x * 9.0d0) * y
    t_3 = 9.0d0 * ((x * y) / (c * z))
    if (t_2 <= (-5d+79)) then
        tmp = t_3
    else if (t_2 <= (-4d-257)) then
        tmp = t_1
    else if (t_2 <= 1d-184) then
        tmp = b / (c * z)
    else if (t_2 <= 2d+27) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double t_2 = (x * 9.0) * y;
	double t_3 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (t_2 <= -5e+79) {
		tmp = t_3;
	} else if (t_2 <= -4e-257) {
		tmp = t_1;
	} else if (t_2 <= 1e-184) {
		tmp = b / (c * z);
	} else if (t_2 <= 2e+27) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	t_2 = (x * 9.0) * y
	t_3 = 9.0 * ((x * y) / (c * z))
	tmp = 0
	if t_2 <= -5e+79:
		tmp = t_3
	elif t_2 <= -4e-257:
		tmp = t_1
	elif t_2 <= 1e-184:
		tmp = b / (c * z)
	elif t_2 <= 2e+27:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)))
	tmp = 0.0
	if (t_2 <= -5e+79)
		tmp = t_3;
	elseif (t_2 <= -4e-257)
		tmp = t_1;
	elseif (t_2 <= 1e-184)
		tmp = Float64(b / Float64(c * z));
	elseif (t_2 <= 2e+27)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	t_2 = (x * 9.0) * y;
	t_3 = 9.0 * ((x * y) / (c * z));
	tmp = 0.0;
	if (t_2 <= -5e+79)
		tmp = t_3;
	elseif (t_2 <= -4e-257)
		tmp = t_1;
	elseif (t_2 <= 1e-184)
		tmp = b / (c * z);
	elseif (t_2 <= 2e+27)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+79], t$95$3, If[LessEqual[t$95$2, -4e-257], t$95$1, If[LessEqual[t$95$2, 1e-184], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+27], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e79 or 2e27 < (*.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 35.5

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

   4. Applied rewrites 35.5%

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

   if -5e79 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999999e-257 or 1.0000000000000001e-184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e27

   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 38.9

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

   4. Applied rewrites 38.9%

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

   if -3.9999999999999999e-257 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e-184

   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 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 47.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}{c}\\ \mathbf{if}\;\mathsf{min}\left(t, a\right) \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\mathsf{min}\left(t, a\right) \leq 2.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* (fmax t a) (fmin t a)) c))))
   (if (<= (fmin t a) -2.5e+106)
     t_1
     (if (<= (fmin t a) 2.5e-193) (/ 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 = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	double tmp;
	if (fmin(t, a) <= -2.5e+106) {
		tmp = t_1;
	} else if (fmin(t, a) <= 2.5e-193) {
		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 = (-4.0d0) * ((fmax(t, a) * fmin(t, a)) / c)
    if (fmin(t, a) <= (-2.5d+106)) then
        tmp = t_1
    else if (fmin(t, a) <= 2.5d-193) 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 = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	double tmp;
	if (fmin(t, a) <= -2.5e+106) {
		tmp = t_1;
	} else if (fmin(t, a) <= 2.5e-193) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((fmax(t, a) * fmin(t, a)) / c)
	tmp = 0
	if fmin(t, a) <= -2.5e+106:
		tmp = t_1
	elif fmin(t, a) <= 2.5e-193:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(fmax(t, a) * fmin(t, a)) / c))
	tmp = 0.0
	if (fmin(t, a) <= -2.5e+106)
		tmp = t_1;
	elseif (fmin(t, a) <= 2.5e-193)
		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 = -4.0 * ((max(t, a) * min(t, a)) / c);
	tmp = 0.0;
	if (min(t, a) <= -2.5e+106)
		tmp = t_1;
	elseif (min(t, a) <= 2.5e-193)
		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[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Min[t, a], $MachinePrecision], -2.5e+106], t$95$1, If[LessEqual[N[Min[t, a], $MachinePrecision], 2.5e-193], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999999e106 or 2.5000000000000002e-193 < t

   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 38.9

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

   4. Applied rewrites 38.9%

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

   if -2.4999999999999999e106 < t < 2.5000000000000002e-193

   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 16: 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 2025181 
(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)))