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

Percentage Accurate: 79.2% → 87.9%

Time: 13.3s

Alternatives: 19

Speedup: 0.9×

• 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

real(8) function code(x, y, z, t, a, b, c)
    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: 79.2% 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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(a \cdot z\right) \cdot c}\right) \cdot a\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
         (fma
          (/ (* x 9.0) z)
          (/ y c)
          (* (fma (/ t c) -4.0 (/ b (* (* a z) c))) a))))
   (if (<= z -3.5e+96)
     t_1
     (if (<= z 1.2e+20)
       (/ (fma (* (* t z) -4.0) a (fma (* y x) 9.0 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 = fma(((x * 9.0) / z), (y / c), (fma((t / c), -4.0, (b / ((a * z) * c))) * a));
	double tmp;
	if (z <= -3.5e+96) {
		tmp = t_1;
	} else if (z <= 1.2e+20) {
		tmp = fma(((t * z) * -4.0), a, fma((y * x), 9.0, 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 = fma(Float64(Float64(x * 9.0) / z), Float64(y / c), Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(a * z) * c))) * a))
	tmp = 0.0
	if (z <= -3.5e+96)
		tmp = t_1;
	elseif (z <= 1.2e+20)
		tmp = Float64(fma(Float64(Float64(t * z) * -4.0), a, fma(Float64(y * x), 9.0, b)) / Float64(c * z));
	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[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision] + N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(a * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+96], t$95$1, If[LessEqual[z, 1.2e+20], N[(N[(N[(N[(t * z), $MachinePrecision] * -4.0), $MachinePrecision] * a + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e96 or 1.2e20 < z

   1. Initial program 56.2%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 63.7%

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

   5. Taylor expanded in a around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 84.8

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

   7. Applied rewrites 84.8%

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

   if -3.4999999999999999e96 < z < 1.2e20

   1. Initial program 92.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. lower-fma.f64 N/A

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

   4. Applied rewrites 92.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(a \cdot z\right) \cdot c}\right) \cdot a\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(a \cdot z\right) \cdot c}\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{-238}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{c}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \frac{\left(t \cdot a\right) \cdot 4}{-c}\right)\\ \end{array} \end{array} \]

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 (/ (+ (- (* y (* x 9.0)) (* (* (* 4.0 z) t) a)) b) (* c z))))
   (if (<= t_1 -5e+249)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) z) c)
     (if (<= t_1 1e-238)
       (/ (fma (/ (* y x) c) 9.0 (/ (fma -4.0 (* (* t z) a) b) c)) z)
       (if (<= t_1 INFINITY)
         t_1
         (fma (/ (* x 9.0) z) (/ y c) (/ (* (* t a) 4.0) (- 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 t_1 = (((y * (x * 9.0)) - (((4.0 * z) * t) * a)) + b) / (c * z);
	double tmp;
	if (t_1 <= -5e+249) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / z) / c;
	} else if (t_1 <= 1e-238) {
		tmp = fma(((y * x) / c), 9.0, (fma(-4.0, ((t * z) * a), b) / c)) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(((x * 9.0) / z), (y / c), (((t * a) * 4.0) / -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)
	t_1 = Float64(Float64(Float64(Float64(y * Float64(x * 9.0)) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -5e+249)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / z) / c);
	elseif (t_1 <= 1e-238)
		tmp = Float64(fma(Float64(Float64(y * x) / c), 9.0, Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / c)) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(Float64(Float64(x * 9.0) / z), Float64(y / c), Float64(Float64(Float64(t * a) * 4.0) / Float64(-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_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+249], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e-238], N[(N[(N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision] * 9.0 + N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision] / (-c)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999996e249

   1. Initial program 78.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 86.0%

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

   if -4.9999999999999996e249 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 9.9999999999999999e-239

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 93.3%

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

   if 9.9999999999999999e-239 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.5%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 29.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 89.1

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

   7. Applied rewrites 89.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq 10^{-238}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \frac{\left(t \cdot a\right) \cdot 4}{-c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -8 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+32}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (fma (* y x) 9.0 b) (* c z))) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -8e+187)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_2 -4e+77)
       t_1
       (if (<= t_2 1e+32)
         (/ (fma -4.0 (* (* t z) a) b) (* c z))
         (if (<= t_2 5e+275) t_1 (* (* (/ 9.0 z) x) (/ 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 t_1 = fma((y * x), 9.0, b) / (c * z);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -8e+187) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_2 <= -4e+77) {
		tmp = t_1;
	} else if (t_2 <= 1e+32) {
		tmp = fma(-4.0, ((t * z) * a), b) / (c * z);
	} else if (t_2 <= 5e+275) {
		tmp = t_1;
	} else {
		tmp = ((9.0 / z) * x) * (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)
	t_1 = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -8e+187)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_2 <= -4e+77)
		tmp = t_1;
	elseif (t_2 <= 1e+32)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(c * z));
	elseif (t_2 <= 5e+275)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(9.0 / z) * x) * Float64(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_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -8e+187], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e+77], t$95$1, If[LessEqual[t$95$2, 1e+32], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+275], t$95$1, N[(N[(N[(9.0 / z), $MachinePrecision] * x), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -7.99999999999999926e187

   1. Initial program 58.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if -7.99999999999999926e187 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999993e77 or 1.00000000000000005e32 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000003e275

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 73.9

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

   5. Applied rewrites 73.9%

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

   if -3.99999999999999993e77 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000005e32

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. inv-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 71.1

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

      10. lift-+.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.2

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

   7. Applied rewrites 71.2%

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

   9. Applied rewrites 99.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -8 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+32}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(c \cdot z\right) \cdot t}\right) \cdot t\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \end{array} \]

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 -3.5e+96)
   (fma (/ (* x 9.0) z) (/ y c) (* (fma (/ a c) -4.0 (/ b (* (* c z) t))) t))
   (if (<= z 5.5e+99)
     (/ (fma (* (* t z) -4.0) a (fma (* y x) 9.0 b)) (* c z))
     (fma (* (/ x (* c z)) 9.0) y (fma (/ (* t a) c) -4.0 (/ b (* c 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 tmp;
	if (z <= -3.5e+96) {
		tmp = fma(((x * 9.0) / z), (y / c), (fma((a / c), -4.0, (b / ((c * z) * t))) * t));
	} else if (z <= 5.5e+99) {
		tmp = fma(((t * z) * -4.0), a, fma((y * x), 9.0, b)) / (c * z);
	} else {
		tmp = fma(((x / (c * z)) * 9.0), y, fma(((t * a) / c), -4.0, (b / (c * 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)
	tmp = 0.0
	if (z <= -3.5e+96)
		tmp = fma(Float64(Float64(x * 9.0) / z), Float64(y / c), Float64(fma(Float64(a / c), -4.0, Float64(b / Float64(Float64(c * z) * t))) * t));
	elseif (z <= 5.5e+99)
		tmp = Float64(fma(Float64(Float64(t * z) * -4.0), a, fma(Float64(y * x), 9.0, b)) / Float64(c * z));
	else
		tmp = fma(Float64(Float64(x / Float64(c * z)) * 9.0), y, fma(Float64(Float64(t * a) / c), -4.0, Float64(b / Float64(c * 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_] := If[LessEqual[z, -3.5e+96], N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision] + N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(c * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+99], N[(N[(N[(N[(t * z), $MachinePrecision] * -4.0), $MachinePrecision] * a + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0 + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999999e96

   1. Initial program 52.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 60.1%

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

   5. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 77.6

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

   7. Applied rewrites 77.6%

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

   if -3.4999999999999999e96 < z < 5.5000000000000002e99

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. lower-fma.f64 N/A

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

   4. Applied rewrites 92.5%

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

   if 5.5000000000000002e99 < z

   1. Initial program 43.8%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-/.f64 N/A

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

      19. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(c \cdot z\right) \cdot t}\right) \cdot t\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+77}:\\ \;\;\;\;\frac{1}{\frac{c}{\mathsf{fma}\left(9, y \cdot x, b\right)} \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -2e+77)
     (/ 1.0 (* (/ c (fma 9.0 (* y x) b)) z))
     (if (<= t_1 5e+16)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (if (<= t_1 5e+275)
         (/ (fma (* y x) 9.0 b) (* c z))
         (* (* (/ 9.0 z) x) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+77) {
		tmp = 1.0 / ((c / fma(9.0, (y * x), b)) * z);
	} else if (t_1 <= 5e+16) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else if (t_1 <= 5e+275) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = ((9.0 / z) * x) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+77)
		tmp = Float64(1.0 / Float64(Float64(c / fma(9.0, Float64(y * x), b)) * z));
	elseif (t_1 <= 5e+16)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 5e+275)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(9.0 / z) * x) * Float64(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_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+77], N[(1.0 / N[(N[(c / N[(9.0 * N[(y * x), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+16], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+275], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 / z), $MachinePrecision] * x), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999997e77

   1. Initial program 70.6%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

   7. Applied rewrites 68.9%

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

   if -1.99999999999999997e77 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e16

   1. Initial program 83.2%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 79.7%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 80.8

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

   7. Applied rewrites 80.8%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 84.9

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

   10. Applied rewrites 84.9%

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

   if 5e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000003e275

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. inv-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 71.1

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

      10. lift-+.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.2

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

   7. Applied rewrites 71.2%

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

   9. Applied rewrites 99.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+77}:\\ \;\;\;\;\frac{1}{\frac{c}{\mathsf{fma}\left(9, y \cdot x, b\right)} \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -4e+77)
     (/ (/ (fma (* x 9.0) y b) c) z)
     (if (<= t_1 5e+16)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (if (<= t_1 5e+275)
         (/ (fma (* y x) 9.0 b) (* c z))
         (* (* (/ 9.0 z) x) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e+77) {
		tmp = (fma((x * 9.0), y, b) / c) / z;
	} else if (t_1 <= 5e+16) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else if (t_1 <= 5e+275) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = ((9.0 / z) * x) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -4e+77)
		tmp = Float64(Float64(fma(Float64(x * 9.0), y, b) / c) / z);
	elseif (t_1 <= 5e+16)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 5e+275)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(9.0 / z) * x) * Float64(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_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+77], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+16], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+275], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 / z), $MachinePrecision] * x), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999993e77

   1. Initial program 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 79.0%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 67.6

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

   7. Applied rewrites 67.6%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 67.3

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

   10. Applied rewrites 67.3%

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

   if -3.99999999999999993e77 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e16

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 80.9

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

   7. Applied rewrites 80.9%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 85.0

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

   10. Applied rewrites 85.0%

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

   if 5e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000003e275

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. inv-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 71.1

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

      10. lift-+.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.2

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

   7. Applied rewrites 71.2%

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

   9. Applied rewrites 99.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{t\_1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (fma (* y x) 9.0 b)) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -4e+77)
     (/ (/ t_1 c) z)
     (if (<= t_2 5e+16)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (if (<= t_2 5e+275) (/ t_1 (* c z)) (* (* (/ 9.0 z) x) (/ 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 t_1 = fma((y * x), 9.0, b);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -4e+77) {
		tmp = (t_1 / c) / z;
	} else if (t_2 <= 5e+16) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else if (t_2 <= 5e+275) {
		tmp = t_1 / (c * z);
	} else {
		tmp = ((9.0 / z) * x) * (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)
	t_1 = fma(Float64(y * x), 9.0, b)
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -4e+77)
		tmp = Float64(Float64(t_1 / c) / z);
	elseif (t_2 <= 5e+16)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	elseif (t_2 <= 5e+275)
		tmp = Float64(t_1 / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(9.0 / z) * x) * Float64(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_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+77], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 5e+16], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 5e+275], N[(t$95$1 / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 / z), $MachinePrecision] * x), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999993e77

   1. Initial program 69.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -3.99999999999999993e77 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e16

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 80.9

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

   7. Applied rewrites 80.9%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 85.0

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

   10. Applied rewrites 85.0%

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

   if 5e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000003e275

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. inv-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 71.1

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

      10. lift-+.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.2

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

   7. Applied rewrites 71.2%

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

   9. Applied rewrites 99.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -8 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -8e+187)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 5e+16)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (if (<= t_1 5e+275)
         (/ (fma (* y x) 9.0 b) (* c z))
         (* (* (/ 9.0 z) x) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -8e+187) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= 5e+16) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else if (t_1 <= 5e+275) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = ((9.0 / z) * x) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -8e+187)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= 5e+16)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 5e+275)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(9.0 / z) * x) * Float64(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_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -8e+187], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+16], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+275], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 / z), $MachinePrecision] * x), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -7.99999999999999926e187

   1. Initial program 58.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if -7.99999999999999926e187 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e16

   1. Initial program 83.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 78.2%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 77.0

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

   7. Applied rewrites 77.0%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 80.5

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

   10. Applied rewrites 80.5%

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

   if 5e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000003e275

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. inv-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 71.1

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

      10. lift-+.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.2

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

   7. Applied rewrites 71.2%

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

   9. Applied rewrites 99.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -8 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
         (fma (* (/ x (* c z)) 9.0) y (fma (/ (* t a) c) -4.0 (/ b (* c z))))))
   (if (<= z -2.3e+24)
     t_1
     (if (<= z 9.2e+109)
       (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 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 = fma(((x / (c * z)) * 9.0), y, fma(((t * a) / c), -4.0, (b / (c * z))));
	double tmp;
	if (z <= -2.3e+24) {
		tmp = t_1;
	} else if (z <= 9.2e+109) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, 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 = fma(Float64(Float64(x / Float64(c * z)) * 9.0), y, fma(Float64(Float64(t * a) / c), -4.0, Float64(b / Float64(c * z))))
	tmp = 0.0
	if (z <= -2.3e+24)
		tmp = t_1;
	elseif (z <= 9.2e+109)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	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[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0 + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+24], t$95$1, If[LessEqual[z, 9.2e+109], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e24 or 9.20000000000000042e109 < z

   1. Initial program 56.7%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-/.f64 N/A

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

      19. lower-*.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -2.2999999999999999e24 < z < 9.20000000000000042e109

   1. Initial program 92.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 93.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \frac{\left(t \cdot a\right) \cdot 4}{-c}\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+139}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (fma (/ (* x 9.0) z) (/ y c) (/ (* (* t a) 4.0) (- c)))))
   (if (<= z -1.2e+124)
     t_1
     (if (<= z 6.4e+139)
       (/ (fma (* (* t z) -4.0) a (fma (* y x) 9.0 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 = fma(((x * 9.0) / z), (y / c), (((t * a) * 4.0) / -c));
	double tmp;
	if (z <= -1.2e+124) {
		tmp = t_1;
	} else if (z <= 6.4e+139) {
		tmp = fma(((t * z) * -4.0), a, fma((y * x), 9.0, 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 = fma(Float64(Float64(x * 9.0) / z), Float64(y / c), Float64(Float64(Float64(t * a) * 4.0) / Float64(-c)))
	tmp = 0.0
	if (z <= -1.2e+124)
		tmp = t_1;
	elseif (z <= 6.4e+139)
		tmp = Float64(fma(Float64(Float64(t * z) * -4.0), a, fma(Float64(y * x), 9.0, b)) / Float64(c * z));
	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[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision] / (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+124], t$95$1, If[LessEqual[z, 6.4e+139], N[(N[(N[(N[(t * z), $MachinePrecision] * -4.0), $MachinePrecision] * a + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000003e124 or 6.4000000000000002e139 < z

   1. Initial program 45.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 57.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 79.3

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

   7. Applied rewrites 79.3%

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

   if -1.20000000000000003e124 < z < 6.4000000000000002e139

   1. Initial program 90.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. lower-fma.f64 N/A

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

   4. Applied rewrites 90.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \frac{\left(t \cdot a\right) \cdot 4}{-c}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+139}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot 9}{z}, \frac{y}{c}, \frac{\left(t \cdot a\right) \cdot 4}{-c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (fma (* t a) -4.0 (/ b z)) c)))
   (if (<= z -7e+96)
     t_1
     (if (<= z 1.15e+123)
       (/ (fma (* (* t z) -4.0) a (fma (* y x) 9.0 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 = fma((t * a), -4.0, (b / z)) / c;
	double tmp;
	if (z <= -7e+96) {
		tmp = t_1;
	} else if (z <= 1.15e+123) {
		tmp = fma(((t * z) * -4.0), a, fma((y * x), 9.0, 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(fma(Float64(t * a), -4.0, Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -7e+96)
		tmp = t_1;
	elseif (z <= 1.15e+123)
		tmp = Float64(fma(Float64(Float64(t * z) * -4.0), a, fma(Float64(y * x), 9.0, b)) / Float64(c * z));
	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[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -7e+96], t$95$1, If[LessEqual[z, 1.15e+123], N[(N[(N[(N[(t * z), $MachinePrecision] * -4.0), $MachinePrecision] * a + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999998e96 or 1.14999999999999995e123 < z

   1. Initial program 47.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. 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. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 73.6

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

   7. Applied rewrites 73.6%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 76.3

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

   10. Applied rewrites 76.3%

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

   if -6.9999999999999998e96 < z < 1.14999999999999995e123

   1. Initial program 91.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. lower-fma.f64 N/A

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

   4. Applied rewrites 91.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+96}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -4, a, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-223}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot x\right) \cdot 9\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= t -1.12e+39)
   (* (* (/ t c) a) -4.0)
   (if (<= t 6.2e-223)
     (* (* (/ y (* c z)) x) 9.0)
     (if (<= t 1.15e-82) (/ (/ b z) c) (* (* (/ -4.0 c) a) t)))))

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 (t <= -1.12e+39) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 6.2e-223) {
		tmp = ((y / (c * z)) * x) * 9.0;
	} else if (t <= 1.15e-82) {
		tmp = (b / z) / c;
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.12d+39)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t <= 6.2d-223) then
        tmp = ((y / (c * z)) * x) * 9.0d0
    else if (t <= 1.15d-82) then
        tmp = (b / z) / c
    else
        tmp = (((-4.0d0) / c) * a) * t
    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 tmp;
	if (t <= -1.12e+39) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 6.2e-223) {
		tmp = ((y / (c * z)) * x) * 9.0;
	} else if (t <= 1.15e-82) {
		tmp = (b / z) / c;
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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):
	tmp = 0
	if t <= -1.12e+39:
		tmp = ((t / c) * a) * -4.0
	elif t <= 6.2e-223:
		tmp = ((y / (c * z)) * x) * 9.0
	elif t <= 1.15e-82:
		tmp = (b / z) / c
	else:
		tmp = ((-4.0 / c) * a) * t
	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 (t <= -1.12e+39)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 6.2e-223)
		tmp = Float64(Float64(Float64(y / Float64(c * z)) * x) * 9.0);
	elseif (t <= 1.15e-82)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(Float64(-4.0 / c) * a) * t);
	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)
	tmp = 0.0;
	if (t <= -1.12e+39)
		tmp = ((t / c) * a) * -4.0;
	elseif (t <= 6.2e-223)
		tmp = ((y / (c * z)) * x) * 9.0;
	elseif (t <= 1.15e-82)
		tmp = (b / z) / c;
	else
		tmp = ((-4.0 / c) * a) * t;
	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_] := If[LessEqual[t, -1.12e+39], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 6.2e-223], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[t, 1.15e-82], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(-4.0 / c), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.12e39

   1. Initial program 77.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. inv-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 79.6

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

      10. lift-+.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 59.6

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

   7. Applied rewrites 59.6%

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

   9. Applied rewrites 67.7%

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

   if -1.12e39 < t < 6.20000000000000036e-223

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 84.2

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac N/A

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{9}{z}} \cdot \frac{x \cdot y}{c} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\frac{x \cdot y}{c}} \]

      7. *-commutative N/A

         \[\leadsto \frac{9}{z} \cdot \frac{\color{blue}{y \cdot x}}{c} \]

      8. lower-*.f64 45.6

         \[\leadsto \frac{9}{z} \cdot \frac{\color{blue}{y \cdot x}}{c} \]

   7. Applied rewrites 45.6%

      \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]
   8. Step-by-step derivation

   9. Applied rewrites 47.8%

      \[\leadsto -9 \cdot \color{blue}{\frac{\left(-y\right) \cdot x}{c \cdot z}} \]
   10. Step-by-step derivation

   11. Applied rewrites 48.1%

       \[\leadsto \left(\frac{y}{c \cdot z} \cdot x\right) \cdot \color{blue}{9} \]

   if 6.20000000000000036e-223 < t < 1.14999999999999998e-82

   1. Initial program 78.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 53.6

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 59.6%

      \[\leadsto \frac{\frac{b}{z}}{\color{blue}{c}} \]

   if 1.14999999999999998e-82 < t

   1. Initial program 76.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 76.2

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 39.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 39.3%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.5%

       \[\leadsto \left(\frac{-4}{c} \cdot a\right) \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-223}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot x\right) \cdot 9\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-223}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= t -1.12e+39)
   (* (* (/ t c) a) -4.0)
   (if (<= t 6.2e-223)
     (* (* (/ y (* c z)) 9.0) x)
     (if (<= t 1.15e-82) (/ (/ b z) c) (* (* (/ -4.0 c) a) t)))))

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 (t <= -1.12e+39) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 6.2e-223) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (t <= 1.15e-82) {
		tmp = (b / z) / c;
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.12d+39)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t <= 6.2d-223) then
        tmp = ((y / (c * z)) * 9.0d0) * x
    else if (t <= 1.15d-82) then
        tmp = (b / z) / c
    else
        tmp = (((-4.0d0) / c) * a) * t
    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 tmp;
	if (t <= -1.12e+39) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 6.2e-223) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (t <= 1.15e-82) {
		tmp = (b / z) / c;
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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):
	tmp = 0
	if t <= -1.12e+39:
		tmp = ((t / c) * a) * -4.0
	elif t <= 6.2e-223:
		tmp = ((y / (c * z)) * 9.0) * x
	elif t <= 1.15e-82:
		tmp = (b / z) / c
	else:
		tmp = ((-4.0 / c) * a) * t
	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 (t <= -1.12e+39)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 6.2e-223)
		tmp = Float64(Float64(Float64(y / Float64(c * z)) * 9.0) * x);
	elseif (t <= 1.15e-82)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(Float64(-4.0 / c) * a) * t);
	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)
	tmp = 0.0;
	if (t <= -1.12e+39)
		tmp = ((t / c) * a) * -4.0;
	elseif (t <= 6.2e-223)
		tmp = ((y / (c * z)) * 9.0) * x;
	elseif (t <= 1.15e-82)
		tmp = (b / z) / c;
	else
		tmp = ((-4.0 / c) * a) * t;
	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_] := If[LessEqual[t, -1.12e+39], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 6.2e-223], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.15e-82], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(-4.0 / c), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.12e39

   1. Initial program 77.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 79.6

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 82.5%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 59.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 59.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 67.7%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -1.12e39 < t < 6.20000000000000036e-223

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 84.2

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac N/A

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{9}{z}} \cdot \frac{x \cdot y}{c} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\frac{x \cdot y}{c}} \]

      7. *-commutative N/A

         \[\leadsto \frac{9}{z} \cdot \frac{\color{blue}{y \cdot x}}{c} \]

      8. lower-*.f64 45.6

         \[\leadsto \frac{9}{z} \cdot \frac{\color{blue}{y \cdot x}}{c} \]

   7. Applied rewrites 45.6%

      \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]
   8. Step-by-step derivation

   9. Applied rewrites 47.8%

      \[\leadsto -9 \cdot \color{blue}{\frac{\left(-y\right) \cdot x}{c \cdot z}} \]
   10. Step-by-step derivation

   11. Applied rewrites 48.0%

       \[\leadsto \left(\frac{y}{c \cdot z} \cdot 9\right) \cdot \color{blue}{x} \]

   if 6.20000000000000036e-223 < t < 1.14999999999999998e-82

   1. Initial program 78.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 53.6

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 59.6%

      \[\leadsto \frac{\frac{b}{z}}{\color{blue}{c}} \]

   if 1.14999999999999998e-82 < t

   1. Initial program 76.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 76.2

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 39.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 39.3%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.5%

       \[\leadsto \left(\frac{-4}{c} \cdot a\right) \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-223}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{y}{c \cdot z} \cdot \left(x \cdot 9\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= t -1.12e+39)
   (* (* (/ t c) a) -4.0)
   (if (<= t 6.2e-223)
     (* (/ y (* c z)) (* x 9.0))
     (if (<= t 1.15e-82) (/ (/ b z) c) (* (* (/ -4.0 c) a) t)))))

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 (t <= -1.12e+39) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 6.2e-223) {
		tmp = (y / (c * z)) * (x * 9.0);
	} else if (t <= 1.15e-82) {
		tmp = (b / z) / c;
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.12d+39)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t <= 6.2d-223) then
        tmp = (y / (c * z)) * (x * 9.0d0)
    else if (t <= 1.15d-82) then
        tmp = (b / z) / c
    else
        tmp = (((-4.0d0) / c) * a) * t
    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 tmp;
	if (t <= -1.12e+39) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 6.2e-223) {
		tmp = (y / (c * z)) * (x * 9.0);
	} else if (t <= 1.15e-82) {
		tmp = (b / z) / c;
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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):
	tmp = 0
	if t <= -1.12e+39:
		tmp = ((t / c) * a) * -4.0
	elif t <= 6.2e-223:
		tmp = (y / (c * z)) * (x * 9.0)
	elif t <= 1.15e-82:
		tmp = (b / z) / c
	else:
		tmp = ((-4.0 / c) * a) * t
	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 (t <= -1.12e+39)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 6.2e-223)
		tmp = Float64(Float64(y / Float64(c * z)) * Float64(x * 9.0));
	elseif (t <= 1.15e-82)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(Float64(-4.0 / c) * a) * t);
	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)
	tmp = 0.0;
	if (t <= -1.12e+39)
		tmp = ((t / c) * a) * -4.0;
	elseif (t <= 6.2e-223)
		tmp = (y / (c * z)) * (x * 9.0);
	elseif (t <= 1.15e-82)
		tmp = (b / z) / c;
	else
		tmp = ((-4.0 / c) * a) * t;
	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_] := If[LessEqual[t, -1.12e+39], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 6.2e-223], N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(x * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-82], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(-4.0 / c), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.12e39

   1. Initial program 77.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 79.6

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 82.5%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 59.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 59.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 67.7%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -1.12e39 < t < 6.20000000000000036e-223

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 84.2

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac N/A

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{9}{z}} \cdot \frac{x \cdot y}{c} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\frac{x \cdot y}{c}} \]

      7. *-commutative N/A

         \[\leadsto \frac{9}{z} \cdot \frac{\color{blue}{y \cdot x}}{c} \]

      8. lower-*.f64 45.6

         \[\leadsto \frac{9}{z} \cdot \frac{\color{blue}{y \cdot x}}{c} \]

   7. Applied rewrites 45.6%

      \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]
   8. Step-by-step derivation

   9. Applied rewrites 48.0%

      \[\leadsto \left(9 \cdot x\right) \cdot \color{blue}{\frac{y}{c \cdot z}} \]

   if 6.20000000000000036e-223 < t < 1.14999999999999998e-82

   1. Initial program 78.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 53.6

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 59.6%

      \[\leadsto \frac{\frac{b}{z}}{\color{blue}{c}} \]

   if 1.14999999999999998e-82 < t

   1. Initial program 76.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 76.2

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 82.7%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 39.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 39.3%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.5%

       \[\leadsto \left(\frac{-4}{c} \cdot a\right) \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{y}{c \cdot z} \cdot \left(x \cdot 9\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+86}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= t -1.5e+86)
   (* (* (/ t c) a) -4.0)
   (if (<= t 2.45e-26)
     (/ (fma (* y x) 9.0 b) (* c z))
     (* (* (/ -4.0 c) a) t))))

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 (t <= -1.5e+86) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 2.45e-26) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = ((-4.0 / c) * a) * t;
	}
	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 (t <= -1.5e+86)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 2.45e-26)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 / c) * a) * t);
	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[t, -1.5e+86], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 2.45e-26], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 / c), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.49999999999999988e86

   1. Initial program 76.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 78.1

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 81.4%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 60.0

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 60.0%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 69.4%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -1.49999999999999988e86 < t < 2.45e-26

   1. Initial program 82.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 67.9

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 67.9%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if 2.45e-26 < t

   1. Initial program 76.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 73.3

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 81.4%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 39.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 39.2%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.7%

       \[\leadsto \left(\frac{-4}{c} \cdot a\right) \cdot \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+86}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+25}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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
 (if (<= b -7.5e+62)
   (/ b (* c z))
   (if (<= b 5.9e+25) (* (* (/ t c) a) -4.0) (/ (/ b c) 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 tmp;
	if (b <= -7.5e+62) {
		tmp = b / (c * z);
	} else if (b <= 5.9e+25) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = (b / c) / z;
	}
	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.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-7.5d+62)) then
        tmp = b / (c * z)
    else if (b <= 5.9d+25) then
        tmp = ((t / c) * a) * (-4.0d0)
    else
        tmp = (b / c) / z
    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 tmp;
	if (b <= -7.5e+62) {
		tmp = b / (c * z);
	} else if (b <= 5.9e+25) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = (b / c) / z;
	}
	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):
	tmp = 0
	if b <= -7.5e+62:
		tmp = b / (c * z)
	elif b <= 5.9e+25:
		tmp = ((t / c) * a) * -4.0
	else:
		tmp = (b / c) / 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)
	tmp = 0.0
	if (b <= -7.5e+62)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= 5.9e+25)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	else
		tmp = Float64(Float64(b / c) / z);
	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)
	tmp = 0.0;
	if (b <= -7.5e+62)
		tmp = b / (c * z);
	elseif (b <= 5.9e+25)
		tmp = ((t / c) * a) * -4.0;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[b, -7.5e+62], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e+25], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.49999999999999998e62

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 56.7

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 56.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -7.49999999999999998e62 < b < 5.9e25

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 79.9

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 81.2%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 47.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.8%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if 5.9e25 < b

   1. Initial program 85.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 64.3

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 64.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 67.8%

      \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+25}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+25}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ b (* c z))))
   (if (<= b -7.5e+62) t_1 (if (<= b 5.9e+25) (* (* (/ t c) a) -4.0) 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 = b / (c * z);
	double tmp;
	if (b <= -7.5e+62) {
		tmp = t_1;
	} else if (b <= 5.9e+25) {
		tmp = ((t / c) * a) * -4.0;
	} 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.
real(8) function code(x, y, z, t, a, b, c)
    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 = b / (c * z)
    if (b <= (-7.5d+62)) then
        tmp = t_1
    else if (b <= 5.9d+25) then
        tmp = ((t / c) * a) * (-4.0d0)
    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 = b / (c * z);
	double tmp;
	if (b <= -7.5e+62) {
		tmp = t_1;
	} else if (b <= 5.9e+25) {
		tmp = ((t / c) * a) * -4.0;
	} 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 = b / (c * z)
	tmp = 0
	if b <= -7.5e+62:
		tmp = t_1
	elif b <= 5.9e+25:
		tmp = ((t / c) * a) * -4.0
	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(b / Float64(c * z))
	tmp = 0.0
	if (b <= -7.5e+62)
		tmp = t_1;
	elseif (b <= 5.9e+25)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	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 = b / (c * z);
	tmp = 0.0;
	if (b <= -7.5e+62)
		tmp = t_1;
	elseif (b <= 5.9e+25)
		tmp = ((t / c) * a) * -4.0;
	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[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+62], t$95$1, If[LessEqual[b, 5.9e+25], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.49999999999999998e62 or 5.9e25 < b

   1. Initial program 82.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 60.7

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 60.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -7.49999999999999998e62 < b < 5.9e25

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      4. associate-/l* N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      5. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      7. inv-pow N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      8. lower-pow.f64 N/A

         \[\leadsto \frac{\color{blue}{{z}^{-1}}}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}} \]

      9. lower-/.f64 79.9

         \[\leadsto \frac{{z}^{-1}}{\color{blue}{\frac{c}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}} \]

      12. sub-neg N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right)} + b}} \]

      13. +-commutative N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right)} + b}} \]

      14. associate-+l+ N/A

          \[\leadsto \frac{{z}^{-1}}{\frac{c}{\color{blue}{\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)}}} \]

   4. Applied rewrites 81.2%

      \[\leadsto \color{blue}{\frac{{z}^{-1}}{\frac{c}{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 47.6

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   7. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.8%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+25}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{c} \cdot -4\\ \mathbf{if}\;z \leq -470000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (/ (* t a) c) -4.0)))
   (if (<= z -470000.0) t_1 (if (<= z 4.2e-47) (/ 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 = ((t * a) / c) * -4.0;
	double tmp;
	if (z <= -470000.0) {
		tmp = t_1;
	} else if (z <= 4.2e-47) {
		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.
real(8) function code(x, y, z, t, a, b, c)
    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 = ((t * a) / c) * (-4.0d0)
    if (z <= (-470000.0d0)) then
        tmp = t_1
    else if (z <= 4.2d-47) 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 = ((t * a) / c) * -4.0;
	double tmp;
	if (z <= -470000.0) {
		tmp = t_1;
	} else if (z <= 4.2e-47) {
		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 = ((t * a) / c) * -4.0
	tmp = 0
	if z <= -470000.0:
		tmp = t_1
	elif z <= 4.2e-47:
		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(t * a) / c) * -4.0)
	tmp = 0.0
	if (z <= -470000.0)
		tmp = t_1;
	elseif (z <= 4.2e-47)
		tmp = Float64(b / Float64(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 = ((t * a) / c) * -4.0;
	tmp = 0.0;
	if (z <= -470000.0)
		tmp = t_1;
	elseif (z <= 4.2e-47)
		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[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -470000.0], t$95$1, If[LessEqual[z, 4.2e-47], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7e5 or 4.2000000000000001e-47 < z

   1. Initial program 67.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. lower-*.f64 55.4

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c} \cdot -4 \]

   5. Applied rewrites 55.4%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

   if -4.7e5 < z < 4.2000000000000001e-47

   1. Initial program 92.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 50.5

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 50.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -470000:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

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 (* c 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) {
	return b / (c * z);
}

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.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (c * z)
end function

Java

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 / (c * z);
}

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 / (c * z)

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(c * z))
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 / (c * z);
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[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   2. lower-*.f64 35.9

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 35.9%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.3% 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

real(8) function code(x, y, z, t, a, b, c)
    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 2024295 
(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)))