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

Percentage Accurate: 79.4% → 90.9%

Time: 5.3s

Alternatives: 14

Speedup: 0.7×

• 37.5% 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: 79.4% 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: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\frac{x}{z}, 9, \frac{b}{z \cdot y}\right) \cdot y\right)}{c}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(\frac{x}{z}, -9, -\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{y}\right) \cdot y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= z -1.8e+80)
   (/ (fma (* -4.0 a) t (* (fma (/ x z) 9.0 (/ b (* z y))) y)) c)
   (if (<= z 4.4e-20)
     (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))
     (/ (- (* (fma (/ x z) -9.0 (- (/ (fma (* a t) -4.0 (/ b z)) y))) y)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -1.8e+80) {
		tmp = fma((-4.0 * a), t, (fma((x / z), 9.0, (b / (z * y))) * y)) / c;
	} else if (z <= 4.4e-20) {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = -(fma((x / z), -9.0, -(fma((a * t), -4.0, (b / z)) / y)) * y) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -1.8e+80)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(x / z), 9.0, Float64(b / Float64(z * y))) * y)) / c);
	elseif (z <= 4.4e-20)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(-Float64(fma(Float64(x / z), -9.0, Float64(-Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / y))) * y)) / 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.
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[z, -1.8e+80], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x / z), $MachinePrecision] * 9.0 + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 4.4e-20], 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], N[((-N[(N[(N[(x / z), $MachinePrecision] * -9.0 + (-N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision])), $MachinePrecision] * y), $MachinePrecision]) / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999997e80

   1. Initial program 57.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 67.8%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 88.2

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

   6. Applied rewrites 88.2%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 91.1

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

   9. Applied rewrites 91.1%

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

   if -1.79999999999999997e80 < z < 4.39999999999999982e-20

   1. Initial program 93.9%

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

   if 4.39999999999999982e-20 < z

   1. Initial program 63.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 71.4%

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

   4. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   6. Applied rewrites 84.6%

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

Alternative 2: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+215}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+189}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-173}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+252}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -5e+215)
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_1 -1e+189)
       (* (* (/ a c) -4.0) t)
       (if (<= t_1 -1e-63)
         (/ (fma (* y x) 9.0 b) (* z c))
         (if (<= t_1 5e-173)
           (/ (fma (* (* t z) a) -4.0 b) (* c z))
           (if (<= t_1 5e+252)
             (/ (/ (fma (* 9.0 x) y b) c) z)
             (* (* (/ x c) 9.0) (/ y z)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -5e+215) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_1 <= -1e+189) {
		tmp = ((a / c) * -4.0) * t;
	} else if (t_1 <= -1e-63) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 5e-173) {
		tmp = fma(((t * z) * a), -4.0, b) / (c * z);
	} else if (t_1 <= 5e+252) {
		tmp = (fma((9.0 * x), y, b) / c) / z;
	} 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])
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 <= -5e+215)
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_1 <= -1e+189)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	elseif (t_1 <= -1e-63)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 5e-173)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(c * z));
	elseif (t_1 <= 5e+252)
		tmp = Float64(Float64(fma(Float64(9.0 * x), y, b) / c) / z);
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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, -5e+215], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+189], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, -1e-63], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-173], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+252], N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000001e215

   1. Initial program 70.9%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.3

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

   4. Applied rewrites 80.3%

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

   if -5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e189

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 75.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 26.7

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

   7. Applied rewrites 26.7%

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

   if -1e189 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000007e-63

   1. Initial program 83.5%

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

   2. Taylor expanded in z around 0

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

      1. +-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 62.1

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

   4. Applied rewrites 62.1%

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

   if -1.00000000000000007e-63 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000002e-173

   1. Initial program 80.7%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 79.9

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

   4. Applied rewrites 79.9%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l/ N/A

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

      8. lower-/.f64 N/A

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

   6. Applied rewrites 78.1%

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

   if 5.0000000000000002e-173 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e252

   1. Initial program 81.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 80.5%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 90.0

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

   6. Applied rewrites 90.0%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 90.0

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

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in z around 0

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

       1. associate-/r* N/A

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

       2. lower-/.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. +-commutative N/A

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

       5. associate-*r* N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-*.f64 61.3

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

   11. Applied rewrites 61.3%

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

   if 4.9999999999999997e252 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.1%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.6

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

   4. Applied rewrites 83.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.0

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

   6. Applied rewrites 84.0%

      \[\leadsto \left(\frac{x}{c} \cdot 9\right) \cdot \frac{\color{blue}{y}}{z} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 3: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+215}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+189}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{t\_1}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-173}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+252}:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (fma (* y x) 9.0 b)) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -5e+215)
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_2 -1e+189)
       (* (* (/ a c) -4.0) t)
       (if (<= t_2 -1e-63)
         (/ t_1 (* z c))
         (if (<= t_2 5e-173)
           (/ (fma (* (* t z) a) -4.0 b) (* c z))
           (if (<= t_2 5e+252)
             (/ (/ t_1 c) z)
             (* (* (/ x c) 9.0) (/ y z)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = fma((y * x), 9.0, b);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+215) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_2 <= -1e+189) {
		tmp = ((a / c) * -4.0) * t;
	} else if (t_2 <= -1e-63) {
		tmp = t_1 / (z * c);
	} else if (t_2 <= 5e-173) {
		tmp = fma(((t * z) * a), -4.0, b) / (c * z);
	} else if (t_2 <= 5e+252) {
		tmp = (t_1 / c) / z;
	} 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])
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 = fma(Float64(y * x), 9.0, b)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -5e+215)
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_2 <= -1e+189)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	elseif (t_2 <= -1e-63)
		tmp = Float64(t_1 / Float64(z * c));
	elseif (t_2 <= 5e-173)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(c * z));
	elseif (t_2 <= 5e+252)
		tmp = Float64(Float64(t_1 / c) / z);
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+215], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e+189], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, -1e-63], N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-173], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+252], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000001e215

   1. Initial program 70.9%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.3

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

   4. Applied rewrites 80.3%

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

   if -5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e189

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 75.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 26.7

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

   7. Applied rewrites 26.7%

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

   if -1e189 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000007e-63

   1. Initial program 83.5%

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

   2. Taylor expanded in z around 0

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

      1. +-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 62.1

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

   4. Applied rewrites 62.1%

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

   if -1.00000000000000007e-63 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000002e-173

   1. Initial program 80.7%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 79.9

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

   4. Applied rewrites 79.9%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l/ N/A

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

      8. lower-/.f64 N/A

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

   6. Applied rewrites 78.1%

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

   if 5.0000000000000002e-173 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e252

   1. Initial program 81.2%

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

   2. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 61.3

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

   4. Applied rewrites 61.3%

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

   if 4.9999999999999997e252 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.1%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.6

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

   4. Applied rewrites 83.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.0

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

   6. Applied rewrites 84.0%

      \[\leadsto \left(\frac{x}{c} \cdot 9\right) \cdot \frac{\color{blue}{y}}{z} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 4: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+211}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\left(x \cdot y\right) \cdot 9}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+252}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -5e+211)
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_1 -2e-53)
       (/ (fma (* -4.0 a) t (/ (* (* x y) 9.0) z)) c)
       (if (<= t_1 0.02)
         (/ (fma (* -4.0 a) t (/ b z)) c)
         (if (<= t_1 5e+252)
           (/ (/ (fma (* 9.0 x) y b) c) z)
           (* (* (/ x c) 9.0) (/ y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -5e+211) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_1 <= -2e-53) {
		tmp = fma((-4.0 * a), t, (((x * y) * 9.0) / z)) / c;
	} else if (t_1 <= 0.02) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else if (t_1 <= 5e+252) {
		tmp = (fma((9.0 * x), y, b) / c) / z;
	} 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])
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 <= -5e+211)
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_1 <= -2e-53)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(Float64(x * y) * 9.0) / z)) / c);
	elseif (t_1 <= 0.02)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	elseif (t_1 <= 5e+252)
		tmp = Float64(Float64(fma(Float64(9.0 * x), y, b) / c) / z);
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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, -5e+211], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-53], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x * y), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+252], N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 71.1%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.1

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

   4. Applied rewrites 80.1%

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

   if -4.9999999999999995e211 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000006e-53

   1. Initial program 83.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 79.2%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 70.8

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

   9. Applied rewrites 70.8%

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

   if -2.00000000000000006e-53 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0200000000000000004

   1. Initial program 80.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 81.6%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 91.2

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

   6. Applied rewrites 91.2%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 85.3%

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

   if 0.0200000000000000004 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e252

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 79.9%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 89.2

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

   6. Applied rewrites 89.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 89.1

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in z around 0

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

       1. associate-/r* N/A

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

       2. lower-/.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. +-commutative N/A

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

       5. associate-*r* N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-*.f64 67.0

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

   11. Applied rewrites 67.0%

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

   if 4.9999999999999997e252 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.1%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.6

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

   4. Applied rewrites 83.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.0

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

   6. Applied rewrites 84.0%

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

Alternative 5: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+215}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+189}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+176}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -5e+215)
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_1 -1e+189)
       (* (* (/ a c) -4.0) t)
       (if (<= t_1 -1e-63)
         (/ (fma (* y x) 9.0 b) (* z c))
         (if (<= t_1 1e+176)
           (/ (fma (* (* t z) a) -4.0 b) (* c z))
           (* (* (/ x c) 9.0) (/ y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -5e+215) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_1 <= -1e+189) {
		tmp = ((a / c) * -4.0) * t;
	} else if (t_1 <= -1e-63) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 1e+176) {
		tmp = fma(((t * z) * a), -4.0, b) / (c * z);
	} 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])
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 <= -5e+215)
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_1 <= -1e+189)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	elseif (t_1 <= -1e-63)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 1e+176)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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, -5e+215], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+189], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, -1e-63], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+176], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000001e215

   1. Initial program 70.9%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.3

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

   4. Applied rewrites 80.3%

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

   if -5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e189

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 75.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 26.7

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

   7. Applied rewrites 26.7%

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

   if -1e189 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000007e-63

   1. Initial program 83.5%

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

   2. Taylor expanded in z around 0

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

      1. +-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 62.1

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

   4. Applied rewrites 62.1%

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

   if -1.00000000000000007e-63 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e176

   1. Initial program 81.1%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 71.9

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

   4. Applied rewrites 71.9%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l/ N/A

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

      8. lower-/.f64 N/A

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

   6. Applied rewrites 70.9%

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

   if 1e176 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.4%

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

   2. Taylor expanded in x around inf

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

      1. 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. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 78.1

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

   4. Applied rewrites 78.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.4

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

   6. Applied rewrites 78.4%

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

Alternative 6: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+247}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+252}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -4e+247)
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_1 0.02)
       (/ (fma (* -4.0 a) t (/ b z)) c)
       (if (<= t_1 5e+252)
         (/ (/ (fma (* 9.0 x) y b) c) z)
         (* (* (/ x c) 9.0) (/ y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -4e+247) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_1 <= 0.02) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else if (t_1 <= 5e+252) {
		tmp = (fma((9.0 * x), y, b) / c) / z;
	} 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])
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 <= -4e+247)
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_1 <= 0.02)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	elseif (t_1 <= 5e+252)
		tmp = Float64(Float64(fma(Float64(9.0 * x), y, b) / c) / z);
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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, -4e+247], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+252], N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999981e247

   1. Initial program 68.8%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.9

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

   4. Applied rewrites 83.9%

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

   if -3.99999999999999981e247 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0200000000000000004

   1. Initial program 81.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 80.7%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 90.1

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

   6. Applied rewrites 90.1%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 76.1%

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

   if 0.0200000000000000004 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e252

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 79.9%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 89.2

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

   6. Applied rewrites 89.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 89.1

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in z around 0

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

       1. associate-/r* N/A

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

       2. lower-/.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. +-commutative N/A

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

       5. associate-*r* N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-*.f64 67.0

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

   11. Applied rewrites 67.0%

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

   if 4.9999999999999997e252 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.1%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.6

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

   4. Applied rewrites 83.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.0

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

   6. Applied rewrites 84.0%

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

Alternative 7: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+260}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (- INFINITY))
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_1 1e+260)
       (/ (fma (* -4.0 a) t (/ (fma (* x y) 9.0 b) z)) c)
       (* (* (/ x c) 9.0) (/ y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -((double) INFINITY)) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_1 <= 1e+260) {
		tmp = fma((-4.0 * a), t, (fma((x * y), 9.0, 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])
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 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_1 <= 1e+260)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(x * y), 9.0, b) / z)) / c);
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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, (-Infinity)], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+260], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   1. Initial program 62.7%

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

   2. Taylor expanded in x around inf

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

      1. 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. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 89.2

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

   4. Applied rewrites 89.2%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000007e260

   1. Initial program 81.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 80.4%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 89.6

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

   6. Applied rewrites 89.6%

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

   if 1.00000000000000007e260 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 69.6%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.8

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

   4. Applied rewrites 83.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.3

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

   6. Applied rewrites 84.3%

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

Alternative 8: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+260}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{c} \cdot 9\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (- INFINITY))
     (* (/ (* 9.0 x) c) (/ y z))
     (if (<= t_1 1e+260)
       (/ (fma (* -4.0 a) t (/ (fma (* 9.0 x) y b) z)) c)
       (* (* (/ x c) 9.0) (/ y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -((double) INFINITY)) {
		tmp = ((9.0 * x) / c) * (y / z);
	} else if (t_1 <= 1e+260) {
		tmp = fma((-4.0 * a), t, (fma((9.0 * x), y, 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])
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 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	elseif (t_1 <= 1e+260)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(9.0 * x), y, b) / z)) / c);
	else
		tmp = Float64(Float64(Float64(x / c) * 9.0) * Float64(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.
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, (-Infinity)], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+260], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   1. Initial program 62.7%

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

   2. Taylor expanded in x around inf

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

      1. 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. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 89.2

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

   4. Applied rewrites 89.2%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000007e260

   1. Initial program 81.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 80.4%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 89.6

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

   6. Applied rewrites 89.6%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 89.6

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

   8. Applied rewrites 89.6%

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

   if 1.00000000000000007e260 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 69.6%

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

   2. Taylor expanded in x around inf

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

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.8

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

   4. Applied rewrites 83.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.3

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

   6. Applied rewrites 84.3%

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

Alternative 9: 92.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\frac{x}{z}, 9, \frac{b}{z \cdot y}\right) \cdot y\right)}{c}\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{-69}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= z -1.8e+80)
   (/ (fma (* -4.0 a) t (* (fma (/ x z) 9.0 (/ b (* z y))) y)) c)
   (if (<= z 1.96e-69)
     (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))
     (/ (fma (* -4.0 a) t (/ (fma (* 9.0 x) y b) z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -1.8e+80) {
		tmp = fma((-4.0 * a), t, (fma((x / z), 9.0, (b / (z * y))) * y)) / c;
	} else if (z <= 1.96e-69) {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = fma((-4.0 * a), t, (fma((9.0 * x), y, b) / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -1.8e+80)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(x / z), 9.0, Float64(b / Float64(z * y))) * y)) / c);
	elseif (z <= 1.96e-69)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(9.0 * x), y, b) / 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.
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[z, -1.8e+80], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x / z), $MachinePrecision] * 9.0 + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.96e-69], 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], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999997e80

   1. Initial program 57.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 67.8%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 88.2

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

   6. Applied rewrites 88.2%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 91.1

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

   9. Applied rewrites 91.1%

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

   if -1.79999999999999997e80 < z < 1.96e-69

   1. Initial program 94.0%

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

   if 1.96e-69 < z

   1. Initial program 67.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 89.1

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

   6. Applied rewrites 89.1%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 89.1

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

   8. Applied rewrites 89.1%

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

Alternative 10: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* (* (/ a c) -4.0) t)))
   (if (<= t -4.8e+116)
     t_1
     (if (<= t 2.25e-39) (/ (fma (* y x) 9.0 b) (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = ((a / c) * -4.0) * t;
	double tmp;
	if (t <= -4.8e+116) {
		tmp = t_1;
	} else if (t <= 2.25e-39) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(a / c) * -4.0) * t)
	tmp = 0.0
	if (t <= -4.8e+116)
		tmp = t_1;
	elseif (t <= 2.25e-39)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.8e+116], t$95$1, If[LessEqual[t, 2.25e-39], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000001e116 or 2.25e-39 < t

   1. Initial program 70.4%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 61.6

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

   7. Applied rewrites 61.6%

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

   if -4.8000000000000001e116 < t < 2.25e-39

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0

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

      1. +-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 70.6

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

   4. Applied rewrites 70.6%

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

Alternative 11: 49.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* (* (/ a c) -4.0) t)))
   (if (<= t -1.05e+116) t_1 (if (<= t 7.5e-40) (/ (/ b c) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = ((a / c) * -4.0) * t;
	double tmp;
	if (t <= -1.05e+116) {
		tmp = t_1;
	} else if (t <= 7.5e-40) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = ((a / c) * (-4.0d0)) * t
    if (t <= (-1.05d+116)) then
        tmp = t_1
    else if (t <= 7.5d-40) then
        tmp = (b / c) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = ((a / c) * -4.0) * t;
	double tmp;
	if (t <= -1.05e+116) {
		tmp = t_1;
	} else if (t <= 7.5e-40) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = ((a / c) * -4.0) * t
	tmp = 0
	if t <= -1.05e+116:
		tmp = t_1
	elif t <= 7.5e-40:
		tmp = (b / c) / z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(a / c) * -4.0) * t)
	tmp = 0.0
	if (t <= -1.05e+116)
		tmp = t_1;
	elseif (t <= 7.5e-40)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = ((a / c) * -4.0) * t;
	tmp = 0.0;
	if (t <= -1.05e+116)
		tmp = t_1;
	elseif (t <= 7.5e-40)
		tmp = (b / c) / z;
	else
		tmp = t_1;
	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.
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[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.05e+116], t$95$1, If[LessEqual[t, 7.5e-40], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0500000000000001e116 or 7.50000000000000069e-40 < t

   1. Initial program 70.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 61.5

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

   7. Applied rewrites 61.5%

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

   if -1.0500000000000001e116 < t < 7.50000000000000069e-40

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 56.3

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

   4. Applied rewrites 56.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 41.8%

      \[\leadsto \frac{\frac{b}{c}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 49.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* (* (/ a c) -4.0) t)))
   (if (<= t -1.05e+116) t_1 (if (<= t 7.5e-40) (/ b (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = ((a / c) * -4.0) * t;
	double tmp;
	if (t <= -1.05e+116) {
		tmp = t_1;
	} else if (t <= 7.5e-40) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = ((a / c) * (-4.0d0)) * t
    if (t <= (-1.05d+116)) then
        tmp = t_1
    else if (t <= 7.5d-40) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = ((a / c) * -4.0) * t;
	double tmp;
	if (t <= -1.05e+116) {
		tmp = t_1;
	} else if (t <= 7.5e-40) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = ((a / c) * -4.0) * t
	tmp = 0
	if t <= -1.05e+116:
		tmp = t_1
	elif t <= 7.5e-40:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(a / c) * -4.0) * t)
	tmp = 0.0
	if (t <= -1.05e+116)
		tmp = t_1;
	elseif (t <= 7.5e-40)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = ((a / c) * -4.0) * t;
	tmp = 0.0;
	if (t <= -1.05e+116)
		tmp = t_1;
	elseif (t <= 7.5e-40)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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.
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[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.05e+116], t$95$1, If[LessEqual[t, 7.5e-40], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0500000000000001e116 or 7.50000000000000069e-40 < t

   1. Initial program 70.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 61.5

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

   7. Applied rewrites 61.5%

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

   if -1.0500000000000001e116 < t < 7.50000000000000069e-40

   1. Initial program 84.6%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 42.0%

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

Alternative 13: 47.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ (* a t) c))))
   (if (<= t -1.06e+116) t_1 (if (<= t 7.5e-40) (/ b (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * ((a * t) / c);
	double tmp;
	if (t <= -1.06e+116) {
		tmp = t_1;
	} else if (t <= 7.5e-40) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = (-4.0d0) * ((a * t) / c)
    if (t <= (-1.06d+116)) then
        tmp = t_1
    else if (t <= 7.5d-40) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * ((a * t) / c);
	double tmp;
	if (t <= -1.06e+116) {
		tmp = t_1;
	} else if (t <= 7.5e-40) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * ((a * t) / c)
	tmp = 0
	if t <= -1.06e+116:
		tmp = t_1
	elif t <= 7.5e-40:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (t <= -1.06e+116)
		tmp = t_1;
	elseif (t <= 7.5e-40)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (t <= -1.06e+116)
		tmp = t_1;
	elseif (t <= 7.5e-40)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e+116], t$95$1, If[LessEqual[t, 7.5e-40], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05999999999999993e116 or 7.50000000000000069e-40 < t

   1. Initial program 70.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 56.8

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

   4. Applied rewrites 56.8%

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

   if -1.05999999999999993e116 < t < 7.50000000000000069e-40

   1. Initial program 84.6%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 42.0%

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

Alternative 14: 35.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 79.4%

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

2. Taylor expanded in b around inf

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

4. Applied rewrites 35.7%

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

Developer Target 1: 80.6% 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 2025093 
(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)))