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

Percentage Accurate: 79.5% → 87.9%

Time: 9.1s

Alternatives: 15

Speedup: 0.8×

• 38.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+71} \lor \neg \left(z \leq 2.7 \cdot 10^{+131}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, t, \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}}{a}\right) \cdot \frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.2e+71) (not (<= z 2.7e+131)))
   (* (fma -4.0 t (/ (/ (fma (* x y) 9.0 b) z) a)) (/ a c))
   (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.2e+71) || !(z <= 2.7e+131)) {
		tmp = fma(-4.0, t, ((fma((x * y), 9.0, b) / z) / a)) * (a / c);
	} else {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.2e+71) || !(z <= 2.7e+131))
		tmp = Float64(fma(-4.0, t, Float64(Float64(fma(Float64(x * y), 9.0, b) / z) / a)) * Float64(a / c));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.2e+71], N[Not[LessEqual[z, 2.7e+131]], $MachinePrecision]], N[(N[(-4.0 * t + N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1999999999999999e71 or 2.70000000000000004e131 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 90.5%

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

   if -1.1999999999999999e71 < z < 2.70000000000000004e131

   1. Initial program 93.1%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+71} \lor \neg \left(z \leq 2.7 \cdot 10^{+131}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, t, \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}}{a}\right) \cdot \frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_2 (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))))
   (if (<= t_1 -5e-160)
     t_2
     (if (<= t_1 0.0)
       (/ (/ (fma (* y x) 9.0 b) z) c)
       (if (<= t_1 INFINITY) t_2 (* (* (/ t c) -4.0) a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	double tmp;
	if (t_1 <= -5e-160) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-160)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(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]}, Block[{t$95$2 = N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-160], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $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)) < -4.99999999999999994e-160 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 92.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 93.5%

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

   if -4.99999999999999994e-160 < (/.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 51.1%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 93.8

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

   5. Applied rewrites 93.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 63.4

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

   8. Applied rewrites 63.4%

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

Alternative 3: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+23}:\\ \;\;\;\;\left(9 \cdot x\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-95}:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-304}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-75}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{x}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+23)
     (* (* 9.0 x) (/ y (* z c)))
     (if (<= t_1 -1e-95)
       (* (* -4.0 t) (/ a c))
       (if (<= t_1 -5e-304)
         (/ (/ b z) c)
         (if (<= t_1 2e-75)
           (* (* (/ t c) -4.0) a)
           (* (* y 9.0) (/ x (* c z)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+23) {
		tmp = (9.0 * x) * (y / (z * c));
	} else if (t_1 <= -1e-95) {
		tmp = (-4.0 * t) * (a / c);
	} else if (t_1 <= -5e-304) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e-75) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (y * 9.0) * (x / (c * z));
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    if (t_1 <= (-2d+23)) then
        tmp = (9.0d0 * x) * (y / (z * c))
    else if (t_1 <= (-1d-95)) then
        tmp = ((-4.0d0) * t) * (a / c)
    else if (t_1 <= (-5d-304)) then
        tmp = (b / z) / c
    else if (t_1 <= 2d-75) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = (y * 9.0d0) * (x / (c * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+23) {
		tmp = (9.0 * x) * (y / (z * c));
	} else if (t_1 <= -1e-95) {
		tmp = (-4.0 * t) * (a / c);
	} else if (t_1 <= -5e-304) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e-75) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (y * 9.0) * (x / (c * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -2e+23:
		tmp = (9.0 * x) * (y / (z * c))
	elif t_1 <= -1e-95:
		tmp = (-4.0 * t) * (a / c)
	elif t_1 <= -5e-304:
		tmp = (b / z) / c
	elif t_1 <= 2e-75:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = (y * 9.0) * (x / (c * z))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+23)
		tmp = Float64(Float64(9.0 * x) * Float64(y / Float64(z * c)));
	elseif (t_1 <= -1e-95)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c));
	elseif (t_1 <= -5e-304)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 2e-75)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = Float64(Float64(y * 9.0) * Float64(x / Float64(c * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -2e+23)
		tmp = (9.0 * x) * (y / (z * c));
	elseif (t_1 <= -1e-95)
		tmp = (-4.0 * t) * (a / c);
	elseif (t_1 <= -5e-304)
		tmp = (b / z) / c;
	elseif (t_1 <= 2e-75)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = (y * 9.0) * (x / (c * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+23], N[(N[(9.0 * x), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-95], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-304], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e-75], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], N[(N[(y * 9.0), $MachinePrecision] * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e23

   1. Initial program 80.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 65.4

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

   5. Applied rewrites 65.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. frac-times N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 63.5

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 63.5

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

   7. Applied rewrites 63.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 65.2

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 65.2

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

   9. Applied rewrites 65.2%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lift-*.f64 N/A

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

       5. associate-*l* N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. lift-*.f64 N/A

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

       9. *-commutative N/A

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

       10. lift-*.f64 N/A

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

       11. associate-/l* N/A

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

       12. lower-*.f64 N/A

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

       13. lower-/.f64 65.2

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

   11. Applied rewrites 65.2%

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

   if -1.9999999999999998e23 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999989e-96

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 53.3

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

   7. Applied rewrites 53.3%

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

   if -9.99999999999999989e-96 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999965e-304

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 68.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 71.0

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

   7. Applied rewrites 71.0%

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

   if -4.99999999999999965e-304 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e-75

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 59.0

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

   8. Applied rewrites 59.0%

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

   if 1.9999999999999999e-75 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 62.9

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

   5. Applied rewrites 62.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. frac-times N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 62.7

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 62.7

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

   7. Applied rewrites 62.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 66.3

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 66.3

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

   9. Applied rewrites 66.3%

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

Alternative 4: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(9 \cdot x\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-95}:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-304}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-75}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* 9.0 x) (/ y (* z c)))))
   (if (<= t_1 -2e+23)
     t_2
     (if (<= t_1 -1e-95)
       (* (* -4.0 t) (/ a c))
       (if (<= t_1 -5e-304)
         (/ (/ b z) c)
         (if (<= t_1 2e-75) (* (* (/ t c) -4.0) a) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (9.0 * x) * (y / (z * c));
	double tmp;
	if (t_1 <= -2e+23) {
		tmp = t_2;
	} else if (t_1 <= -1e-95) {
		tmp = (-4.0 * t) * (a / c);
	} else if (t_1 <= -5e-304) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e-75) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = (9.0d0 * x) * (y / (z * c))
    if (t_1 <= (-2d+23)) then
        tmp = t_2
    else if (t_1 <= (-1d-95)) then
        tmp = ((-4.0d0) * t) * (a / c)
    else if (t_1 <= (-5d-304)) then
        tmp = (b / z) / c
    else if (t_1 <= 2d-75) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (9.0 * x) * (y / (z * c));
	double tmp;
	if (t_1 <= -2e+23) {
		tmp = t_2;
	} else if (t_1 <= -1e-95) {
		tmp = (-4.0 * t) * (a / c);
	} else if (t_1 <= -5e-304) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e-75) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = (9.0 * x) * (y / (z * c))
	tmp = 0
	if t_1 <= -2e+23:
		tmp = t_2
	elif t_1 <= -1e-95:
		tmp = (-4.0 * t) * (a / c)
	elif t_1 <= -5e-304:
		tmp = (b / z) / c
	elif t_1 <= 2e-75:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(9.0 * x) * Float64(y / Float64(z * c)))
	tmp = 0.0
	if (t_1 <= -2e+23)
		tmp = t_2;
	elseif (t_1 <= -1e-95)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c));
	elseif (t_1 <= -5e-304)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 2e-75)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = (9.0 * x) * (y / (z * c));
	tmp = 0.0;
	if (t_1 <= -2e+23)
		tmp = t_2;
	elseif (t_1 <= -1e-95)
		tmp = (-4.0 * t) * (a / c);
	elseif (t_1 <= -5e-304)
		tmp = (b / z) / c;
	elseif (t_1 <= 2e-75)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * x), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+23], t$95$2, If[LessEqual[t$95$1, -1e-95], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-304], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e-75], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e23 or 1.9999999999999999e-75 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 64.0

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

   5. Applied rewrites 64.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. frac-times N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 63.0

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 63.0

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

   7. Applied rewrites 63.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 65.8

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 65.8

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

   9. Applied rewrites 65.8%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lift-*.f64 N/A

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

       5. associate-*l* N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. lift-*.f64 N/A

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

       9. *-commutative N/A

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

       10. lift-*.f64 N/A

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

       11. associate-/l* N/A

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

       12. lower-*.f64 N/A

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

       13. lower-/.f64 66.5

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

   11. Applied rewrites 66.5%

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

   if -1.9999999999999998e23 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999989e-96

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 46.9

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

   5. Applied rewrites 46.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 53.3

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

   7. Applied rewrites 53.3%

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

   if -9.99999999999999989e-96 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999965e-304

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 68.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 71.0

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

   7. Applied rewrites 71.0%

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

   if -4.99999999999999965e-304 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e-75

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 59.0

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

   8. Applied rewrites 59.0%

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

Alternative 5: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4 \cdot z, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e-80)
     (/ (fma (* y x) 9.0 b) (* z c))
     (if (<= t_1 1e+35)
       (/ (fma (* a t) (* -4.0 z) b) (* z c))
       (/ (fma (* -4.0 z) (* a t) (* (* y x) 9.0)) (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e-80) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 1e+35) {
		tmp = fma((a * t), (-4.0 * z), b) / (z * c);
	} else {
		tmp = fma((-4.0 * z), (a * t), ((y * x) * 9.0)) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e-80)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 1e+35)
		tmp = Float64(fma(Float64(a * t), Float64(-4.0 * z), b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(-4.0 * z), Float64(a * t), Float64(Float64(y * x) * 9.0)) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-80], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+35], N[(N[(N[(a * t), $MachinePrecision] * N[(-4.0 * z), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999992e-80

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -1.99999999999999992e-80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999997e34

   1. Initial program 83.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 85.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 82.1%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 84.0

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 84.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 84.0

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

   9. Applied rewrites 84.0%

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

   if 9.9999999999999997e34 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 87.4%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

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

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

      13. associate-*l* N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-fma.f64 N/A

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

   5. Applied rewrites 84.6%

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

Alternative 6: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot -4, \frac{t \cdot a}{c}, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(4, t, \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{a}}{-z}\right)}{-c} \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 5.6e-16)
   (/ (fma (* z -4.0) (/ (* t a) c) (/ (fma x (* 9.0 y) b) c)) z)
   (* (/ (fma 4.0 t (/ (/ (fma (* x y) 9.0 b) a) (- z))) (- c)) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 5.6e-16) {
		tmp = fma((z * -4.0), ((t * a) / c), (fma(x, (9.0 * y), b) / c)) / z;
	} else {
		tmp = (fma(4.0, t, ((fma((x * y), 9.0, b) / a) / -z)) / -c) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 5.6e-16)
		tmp = Float64(fma(Float64(z * -4.0), Float64(Float64(t * a) / c), Float64(fma(x, Float64(9.0 * y), b) / c)) / z);
	else
		tmp = Float64(Float64(fma(4.0, t, Float64(Float64(fma(Float64(x * y), 9.0, b) / a) / Float64(-z))) / Float64(-c)) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 5.6e-16], N[(N[(N[(z * -4.0), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(4.0 * t + N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / a), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.6000000000000003e-16

   1. Initial program 81.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 83.8%

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

      1. lift-/.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. div-add N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 85.2

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

   6. Applied rewrites 85.2%

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

   if 5.6000000000000003e-16 < a

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   8. Applied rewrites 98.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot -4, \frac{t \cdot a}{c}, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(4, t, \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{a}}{-z}\right)}{-c} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 9.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(4, t, \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{a}}{-z}\right)}{-c} \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 9.4e-14)
   (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))
   (* (/ (fma 4.0 t (/ (/ (fma (* x y) 9.0 b) a) (- z))) (- c)) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 9.4e-14) {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	} else {
		tmp = (fma(4.0, t, ((fma((x * y), 9.0, b) / a) / -z)) / -c) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 9.4e-14)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	else
		tmp = Float64(Float64(fma(4.0, t, Float64(Float64(fma(Float64(x * y), 9.0, b) / a) / Float64(-z))) / Float64(-c)) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 9.4e-14], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(4.0 * t + N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / a), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.4000000000000003e-14

   1. Initial program 81.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 84.2%

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

   if 9.4000000000000003e-14 < a

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   8. Applied rewrites 98.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(4, t, \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{a}}{-z}\right)}{-c} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+124}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4 \cdot z, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{x}{c} \cdot 9\right) \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e-80)
     (/ (fma (* y x) 9.0 b) (* z c))
     (if (<= t_1 1e+124)
       (/ (fma (* a t) (* -4.0 z) b) (* z c))
       (/ (* (* (/ x c) 9.0) y) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e-80) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 1e+124) {
		tmp = fma((a * t), (-4.0 * z), b) / (z * c);
	} else {
		tmp = (((x / c) * 9.0) * y) / z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e-80)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 1e+124)
		tmp = Float64(fma(Float64(a * t), Float64(-4.0 * z), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(Float64(x / c) * 9.0) * y) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-80], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+124], N[(N[(N[(a * t), $MachinePrecision] * N[(-4.0 * z), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999992e-80

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -1.99999999999999992e-80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999948e123

   1. Initial program 84.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 86.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 79.8%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 81.4

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 81.4

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 81.4

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

   9. Applied rewrites 81.4%

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

   if 9.99999999999999948e123 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 85.3

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

   5. Applied rewrites 85.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 85.3

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 85.3

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

   7. Applied rewrites 85.3%

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

Alternative 9: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+124}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{x}{c} \cdot 9\right) \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+23)
     (/ (fma (* 9.0 x) y b) (* z c))
     (if (<= t_1 1e+124)
       (/ (fma -4.0 (* (* t z) a) b) (* z c))
       (/ (* (* (/ x c) 9.0) y) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+23) {
		tmp = fma((9.0 * x), y, b) / (z * c);
	} else if (t_1 <= 1e+124) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else {
		tmp = (((x / c) * 9.0) * y) / z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+23)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	elseif (t_1 <= 1e+124)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(Float64(x / c) * 9.0) * y) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+23], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+124], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999998e23

   1. Initial program 80.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 79.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 32.1%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 76.0

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

   10. Applied rewrites 76.0%

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

   if -1.9999999999999998e23 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999948e123

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if 9.99999999999999948e123 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 85.3

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

   5. Applied rewrites 85.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 85.3

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 85.3

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

   7. Applied rewrites 85.3%

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

Alternative 10: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{\left(a \cdot z\right) \cdot c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 1.5e-150)
   (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))
   (* (fma (/ t c) -4.0 (/ (fma x (* 9.0 y) b) (* (* a z) c))) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 1.5e-150) {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	} else {
		tmp = fma((t / c), -4.0, (fma(x, (9.0 * y), b) / ((a * z) * c))) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 1.5e-150)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(fma(x, Float64(9.0 * y), b) / Float64(Float64(a * z) * c))) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 1.5e-150], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / N[(N[(a * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.5000000000000001e-150

   1. Initial program 84.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 86.5%

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

   if 1.5000000000000001e-150 < a

   1. Initial program 83.2%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 81.7%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. lift-*.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

   7. Applied rewrites 87.8%

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

Alternative 11: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+39} \lor \neg \left(t \leq 3.2 \cdot 10^{-231}\right):\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.7e+39) (not (<= t 3.2e-231)))
   (* (* (/ t c) -4.0) a)
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.7e+39) || !(t <= 3.2e-231)) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-3.7d+39)) .or. (.not. (t <= 3.2d-231))) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.7e+39) || !(t <= 3.2e-231)) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.7e+39) or not (t <= 3.2e-231):
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.7e+39) || !(t <= 3.2e-231))
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3.7e+39) || ~((t <= 3.2e-231)))
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.7e+39], N[Not[LessEqual[t, 3.2e-231]], $MachinePrecision]], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.70000000000000012e39 or 3.20000000000000008e-231 < t

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 48.3

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

   8. Applied rewrites 48.3%

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

   if -3.70000000000000012e39 < t < 3.20000000000000008e-231

   1. Initial program 89.3%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.6%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+39} \lor \neg \left(t \leq 3.2 \cdot 10^{-231}\right):\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+39} \lor \neg \left(t \leq 3.2 \cdot 10^{-231}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.8e+39) (not (<= t 3.2e-231)))
   (* -4.0 (/ (* a t) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.8e+39) || !(t <= 3.2e-231)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-3.8d+39)) .or. (.not. (t <= 3.2d-231))) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.8e+39) || !(t <= 3.2e-231)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.8e+39) or not (t <= 3.2e-231):
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.8e+39) || !(t <= 3.2e-231))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3.8e+39) || ~((t <= 3.2e-231)))
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.8e+39], N[Not[LessEqual[t, 3.2e-231]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999998e39 or 3.20000000000000008e-231 < t

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 46.1

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

   5. Applied rewrites 46.1%

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

   if -3.7999999999999998e39 < t < 3.20000000000000008e-231

   1. Initial program 89.3%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.6%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+39} \lor \neg \left(t \leq 3.2 \cdot 10^{-231}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{+167}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 4.4e+167) (/ (fma (* y 9.0) x b) (* z c)) (* (* (/ t c) -4.0) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.4e+167) {
		tmp = fma((y * 9.0), x, b) / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 4.4e+167)
		tmp = Float64(fma(Float64(y * 9.0), x, b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 4.4e+167], N[(N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.40000000000000007e167

   1. Initial program 83.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 85.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 67.3

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

   10. Applied rewrites 67.3%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. associate-*l* N/A

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

       5. lift-*.f64 N/A

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

       6. lower-fma.f64 67.7

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

   12. Applied rewrites 67.7%

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

   if 4.40000000000000007e167 < a

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 91.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 74.7

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

   8. Applied rewrites 74.7%

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

Alternative 14: 63.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{+167}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 4.4e+167) (/ (fma (* 9.0 x) y b) (* z c)) (* (* (/ t c) -4.0) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.4e+167) {
		tmp = fma((9.0 * x), y, b) / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 4.4e+167)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 4.4e+167], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.40000000000000007e167

   1. Initial program 83.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 85.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 67.3

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

   10. Applied rewrites 67.3%

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

   if 4.40000000000000007e167 < a

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 91.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 74.7

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

   8. Applied rewrites 74.7%

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

Alternative 15: 35.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

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

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

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

3. Taylor expanded in b around inf

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

5. Applied rewrites 35.1%

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

Developer Target 1: 80.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025026 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))