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

Percentage Accurate: 79.2% → 89.2%

Time: 12.5s

Alternatives: 16

Speedup: 0.3×

• 37.8% 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: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ \mathbf{if}\;z \leq -15:\\ \;\;\;\;\mathsf{fma}\left(\frac{9 \cdot x}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, t\_1\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+151}:\\ \;\;\;\;{z}^{-1} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z))))
   (if (<= z -15.0)
     (fma (/ (* 9.0 x) z) (/ y c) (fma (/ (* t a) c) -4.0 t_1))
     (if (<= z 1.5e+151)
       (* (pow z -1.0) (/ (fma (* (* -4.0 z) a) t (fma (* x y) 9.0 b)) c))
       (fma (* (/ x (* c z)) 9.0) y (fma (/ (* a t) c) -4.0 t_1))))))

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 (z <= -15.0) {
		tmp = fma(((9.0 * x) / z), (y / c), fma(((t * a) / c), -4.0, t_1));
	} else if (z <= 1.5e+151) {
		tmp = pow(z, -1.0) * (fma(((-4.0 * z) * a), t, fma((x * y), 9.0, b)) / c);
	} else {
		tmp = fma(((x / (c * z)) * 9.0), y, fma(((a * t) / c), -4.0, t_1));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	tmp = 0.0
	if (z <= -15.0)
		tmp = fma(Float64(Float64(9.0 * x) / z), Float64(y / c), fma(Float64(Float64(t * a) / c), -4.0, t_1));
	elseif (z <= 1.5e+151)
		tmp = Float64((z ^ -1.0) * Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(x * y), 9.0, b)) / c));
	else
		tmp = fma(Float64(Float64(x / Float64(c * z)) * 9.0), y, fma(Float64(Float64(a * t) / c), -4.0, 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -15.0], N[(N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0 + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+151], N[(N[Power[z, -1.0], $MachinePrecision] * N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -15

   1. Initial program 59.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 19.4

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

   5. Applied rewrites 19.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. 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. *-commutative N/A

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

      5. times-frac N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lower-/.f64 N/A

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

      19. lower-*.f64 94.0

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

   8. Applied rewrites 94.0%

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

   if -15 < z < 1.5e151

   1. Initial program 91.4%

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

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

      3. neg-mul-1 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 93.0%

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

   if 1.5e151 < z

   1. Initial program 58.1%

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

   3. Taylor expanded in 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 96.7

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

   5. Applied rewrites 96.7%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15:\\ \;\;\;\;\mathsf{fma}\left(\frac{9 \cdot x}{z}, \frac{y}{c}, \mathsf{fma}\left(\frac{t \cdot a}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+151}:\\ \;\;\;\;{z}^{-1} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4 \cdot z, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -1e-299)
     (/ (fma (* a t) (* -4.0 z) (fma (* x y) 9.0 b)) (* z c))
     (if (<= t_1 0.0)
       (/ (fma (* -4.0 t) a (* (/ (* y x) z) 9.0)) c)
       (if (<= t_1 INFINITY) t_1 (* (* (/ t c) a) -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -1e-299) {
		tmp = fma((a * t), (-4.0 * z), fma((x * y), 9.0, b)) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = fma((-4.0 * t), a, (((y * x) / z) * 9.0)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = ((t / c) * a) * -4.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-299)
		tmp = Float64(fma(Float64(a * t), Float64(-4.0 * z), fma(Float64(x * y), 9.0, b)) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-299], N[(N[(N[(a * t), $MachinePrecision] * N[(-4.0 * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $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)) < -9.99999999999999992e-300

   1. Initial program 90.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. 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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. associate-*r* N/A

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

   4. Applied rewrites 89.3%

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

   if -9.99999999999999992e-300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 28.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 28.3

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

   5. Applied rewrites 28.3%

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

   6. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 98.6

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

   8. Applied rewrites 98.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 98.8%

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

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

   1. Initial program 89.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 70.3

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

   5. Applied rewrites 70.3%

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

   7. Applied rewrites 75.9%

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

Alternative 3: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(a \cdot t, -4 \cdot z, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_2 (/ (fma (* a t) (* -4.0 z) (fma (* x y) 9.0 b)) (* z c))))
   (if (<= t_1 -1e-299)
     t_2
     (if (<= t_1 0.0)
       (/ (fma (* -4.0 t) a (* (/ (* y x) z) 9.0)) c)
       (if (<= t_1 INFINITY) t_2 (* (* (/ t c) a) -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = fma((a * t), (-4.0 * z), fma((x * y), 9.0, b)) / (z * c);
	double tmp;
	if (t_1 <= -1e-299) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = fma((-4.0 * t), a, (((y * x) / z) * 9.0)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = ((t / c) * a) * -4.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = Float64(fma(Float64(a * t), Float64(-4.0 * z), fma(Float64(x * y), 9.0, b)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-299)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a * t), $MachinePrecision] * N[(-4.0 * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-299], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -9.99999999999999992e-300 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.9%

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

      1. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. associate-*r* N/A

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

   4. Applied rewrites 89.1%

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

   if -9.99999999999999992e-300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 28.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 28.3

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

   5. Applied rewrites 28.3%

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

   6. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 98.6

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

   8. Applied rewrites 98.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 98.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 70.3

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

   5. Applied rewrites 70.3%

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

   7. Applied rewrites 75.9%

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

Alternative 4: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-47} \lor \neg \left(z \leq 1.5 \cdot 10^{+151}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{z}^{-1} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.5e-47) (not (<= z 1.5e+151)))
   (fma (* (/ x (* c z)) 9.0) y (fma (/ (* a t) c) -4.0 (/ b (* c z))))
   (* (pow z -1.0) (/ (fma (* (* -4.0 z) a) t (fma (* x y) 9.0 b)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.5e-47) || !(z <= 1.5e+151)) {
		tmp = fma(((x / (c * z)) * 9.0), y, fma(((a * t) / c), -4.0, (b / (c * z))));
	} else {
		tmp = pow(z, -1.0) * (fma(((-4.0 * z) * a), t, fma((x * y), 9.0, b)) / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.5e-47) || !(z <= 1.5e+151))
		tmp = fma(Float64(Float64(x / Float64(c * z)) * 9.0), y, fma(Float64(Float64(a * t) / c), -4.0, Float64(b / Float64(c * z))));
	else
		tmp = Float64((z ^ -1.0) * Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(x * y), 9.0, b)) / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.5e-47], N[Not[LessEqual[z, 1.5e+151]], $MachinePrecision]], N[(N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0 + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[z, -1.0], $MachinePrecision] * N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000008e-47 or 1.5e151 < z

   1. Initial program 62.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 92.9

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

   5. Applied rewrites 92.9%

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

   if -1.50000000000000008e-47 < z < 1.5e151

   1. Initial program 91.3%

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

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

      3. neg-mul-1 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 93.0%

      \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{-c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-47} \lor \neg \left(z \leq 1.5 \cdot 10^{+151}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c \cdot z} \cdot 9, y, \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{z}^{-1} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+133}:\\ \;\;\;\;{z}^{-1} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{t \cdot a}{y}, -4, \frac{x}{z} \cdot 9\right) \cdot y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.7e+151)
   (/ (fma (* -4.0 t) a (* (/ (* y x) z) 9.0)) c)
   (if (<= z 2.15e+133)
     (* (pow z -1.0) (/ (fma (* (* -4.0 z) a) t (fma (* x y) 9.0 b)) c))
     (/ (* (fma (/ (* t a) y) -4.0 (* (/ x z) 9.0)) y) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.7e+151) {
		tmp = fma((-4.0 * t), a, (((y * x) / z) * 9.0)) / c;
	} else if (z <= 2.15e+133) {
		tmp = pow(z, -1.0) * (fma(((-4.0 * z) * a), t, fma((x * y), 9.0, b)) / c);
	} else {
		tmp = (fma(((t * a) / y), -4.0, ((x / z) * 9.0)) * y) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.7e+151)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	elseif (z <= 2.15e+133)
		tmp = Float64((z ^ -1.0) * Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(x * y), 9.0, b)) / c));
	else
		tmp = Float64(Float64(fma(Float64(Float64(t * a) / y), -4.0, Float64(Float64(x / z) * 9.0)) * 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.7e+151], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.15e+133], N[(N[Power[z, -1.0], $MachinePrecision] * N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision] * -4.0 + N[(N[(x / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e151

   1. Initial program 38.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 12.7

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

   5. Applied rewrites 12.7%

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

   6. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 51.6

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

   8. Applied rewrites 51.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 86.8%

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

   if -1.7e151 < z < 2.14999999999999997e133

   1. Initial program 88.9%

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

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

      3. neg-mul-1 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 93.1%

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

   if 2.14999999999999997e133 < z

   1. Initial program 61.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 25.7

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

   5. Applied rewrites 25.7%

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

   6. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 62.2

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

   8. Applied rewrites 62.2%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 81.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+133}:\\ \;\;\;\;{z}^{-1} \cdot \frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{t \cdot a}{y}, -4, \frac{x}{z} \cdot 9\right) \cdot y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (fma (* -4.0 t) a (* (/ (* y x) z) 9.0)) c)))
   (if (<= t_1 -5e-93)
     t_2
     (if (<= t_1 5e+38)
       (/ (/ (fma -4.0 (* (* t z) a) b) z) c)
       (if (<= t_1 4e+184) t_2 (* (/ (* 9.0 x) c) (/ y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = fma((-4.0 * t), a, (((y * x) / z) * 9.0)) / c;
	double tmp;
	if (t_1 <= -5e-93) {
		tmp = t_2;
	} else if (t_1 <= 5e+38) {
		tmp = (fma(-4.0, ((t * z) * a), b) / z) / c;
	} else if (t_1 <= 4e+184) {
		tmp = t_2;
	} else {
		tmp = ((9.0 * x) / c) * (y / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(fma(Float64(-4.0 * t), a, Float64(Float64(Float64(y * x) / z) * 9.0)) / c)
	tmp = 0.0
	if (t_1 <= -5e-93)
		tmp = t_2;
	elseif (t_1 <= 5e+38)
		tmp = Float64(Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / z) / c);
	elseif (t_1 <= 4e+184)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-93], t$95$2, If[LessEqual[t$95$1, 5e+38], N[(N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 4e+184], t$95$2, N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999994e-93 or 4.9999999999999997e38 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000007e184

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 24.7

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

   5. Applied rewrites 24.7%

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

   6. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 69.1

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 77.9%

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

   if -4.99999999999999994e-93 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e38

   1. Initial program 83.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if 4.00000000000000007e184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 58.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      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 87.2

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

   5. Applied rewrites 87.2%

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

   7. Applied rewrites 92.6%

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

Alternative 7: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(t \cdot z\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-4, t\_2, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+212}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, t\_2 \cdot -4\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* t z) a)))
   (if (<= t_1 -50000000000.0)
     (/ (/ (fma (* y x) 9.0 b) z) c)
     (if (<= t_1 5e+38)
       (/ (/ (fma -4.0 t_2 b) z) c)
       (if (<= t_1 5e+212)
         (/ (fma (* y x) 9.0 (* t_2 -4.0)) (* z c))
         (* (* (/ y c) 9.0) (/ x z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = (t * z) * a;
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	} else if (t_1 <= 5e+38) {
		tmp = (fma(-4.0, t_2, b) / z) / c;
	} else if (t_1 <= 5e+212) {
		tmp = fma((y * x), 9.0, (t_2 * -4.0)) / (z * c);
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(t * z) * a)
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	elseif (t_1 <= 5e+38)
		tmp = Float64(Float64(fma(-4.0, t_2, b) / z) / c);
	elseif (t_1 <= 5e+212)
		tmp = Float64(fma(Float64(y * x), 9.0, Float64(t_2 * -4.0)) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+38], N[(N[(N[(-4.0 * t$95$2 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+212], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(t$95$2 * -4.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e10

   1. Initial program 78.2%

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

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

      3. neg-mul-1 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 82.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 72.3

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

   7. Applied rewrites 72.3%

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

   if -5e10 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999997e38

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if 4.9999999999999997e38 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999992e212

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 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 50.6

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 78.6

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

   8. Applied rewrites 78.6%

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

   if 4.99999999999999992e212 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 50.1%

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

   3. Taylor expanded in 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 92.1

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

   5. Applied rewrites 92.1%

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

Alternative 8: 68.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+184}:\\ \;\;\;\;\left(\frac{-4}{c} \cdot t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -50000000000.0)
     (/ (/ (fma (* y x) 9.0 b) z) c)
     (if (<= t_1 5e+69)
       (/ (/ (fma -4.0 (* (* t z) a) b) z) c)
       (if (<= t_1 4e+184)
         (* (* (/ -4.0 c) t) a)
         (* (/ (* 9.0 x) c) (/ y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	} else if (t_1 <= 5e+69) {
		tmp = (fma(-4.0, ((t * z) * a), b) / z) / c;
	} else if (t_1 <= 4e+184) {
		tmp = ((-4.0 / c) * t) * a;
	} else {
		tmp = ((9.0 * x) / c) * (y / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	elseif (t_1 <= 5e+69)
		tmp = Float64(Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / z) / c);
	elseif (t_1 <= 4e+184)
		tmp = Float64(Float64(Float64(-4.0 / c) * t) * a);
	else
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+69], N[(N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 4e+184], N[(N[(N[(-4.0 / c), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e10

   1. Initial program 78.2%

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

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

      3. neg-mul-1 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 82.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 72.3

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

   7. Applied rewrites 72.3%

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

   if -5e10 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000036e69

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 78.4

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

   5. Applied rewrites 78.4%

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

   if 5.00000000000000036e69 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000007e184

   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 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 59.0

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

   5. Applied rewrites 59.0%

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

   7. Applied rewrites 59.0%

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

   9. Applied rewrites 59.9%

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

   if 4.00000000000000007e184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 58.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      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 87.2

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

   5. Applied rewrites 87.2%

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

   7. Applied rewrites 92.6%

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

Alternative 9: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -50000000000.0)
     (/ (/ (fma (* y x) 9.0 b) z) c)
     (if (<= t_1 2e+157)
       (/ (fma -4.0 (* (* t z) a) b) (* z c))
       (* (/ (* 9.0 x) c) (/ y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	} else if (t_1 <= 2e+157) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else {
		tmp = ((9.0 * x) / c) * (y / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	elseif (t_1 <= 2e+157)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+157], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e10

   1. Initial program 78.2%

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

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

      3. neg-mul-1 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. times-frac N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 82.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 72.3

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

   7. Applied rewrites 72.3%

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

   if -5e10 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999997e157

   1. Initial program 83.8%

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

   3. 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 75.2

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

   5. Applied rewrites 75.2%

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

   if 1.99999999999999997e157 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 57.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      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 82.1

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

   5. Applied rewrites 82.1%

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

   7. Applied rewrites 87.2%

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

Alternative 10: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -50000000000.0)
     (/ (fma (* y x) 9.0 b) (* z c))
     (if (<= t_1 2e+157)
       (/ (fma -4.0 (* (* t z) a) b) (* z c))
       (* (/ (* 9.0 x) c) (/ y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 2e+157) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else {
		tmp = ((9.0 * x) / c) * (y / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 2e+157)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+157], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e10

   1. Initial program 78.2%

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

   3. Taylor expanded in z around 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 72.2

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

   5. Applied rewrites 72.2%

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

   if -5e10 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999997e157

   1. Initial program 83.8%

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

   3. 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 75.2

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

   5. Applied rewrites 75.2%

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

   if 1.99999999999999997e157 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 57.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      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 82.1

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

   5. Applied rewrites 82.1%

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

   7. Applied rewrites 87.2%

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

Alternative 11: 53.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+33} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+184}\right):\\ \;\;\;\;\left(9 \cdot \frac{x}{z \cdot c}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (or (<= t_1 -1e+33) (not (<= t_1 4e+184)))
     (* (* 9.0 (/ x (* z c))) y)
     (* (/ (* a t) c) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -1e+33) || !(t_1 <= 4e+184)) {
		tmp = (9.0 * (x / (z * c))) * y;
	} else {
		tmp = ((a * t) / c) * -4.0;
	}
	return tmp;
}

Fortran

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 = (x * 9.0d0) * y
    if ((t_1 <= (-1d+33)) .or. (.not. (t_1 <= 4d+184))) then
        tmp = (9.0d0 * (x / (z * c))) * y
    else
        tmp = ((a * t) / c) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -1e+33) || !(t_1 <= 4e+184)) {
		tmp = (9.0 * (x / (z * c))) * y;
	} else {
		tmp = ((a * t) / c) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if (t_1 <= -1e+33) or not (t_1 <= 4e+184):
		tmp = (9.0 * (x / (z * c))) * y
	else:
		tmp = ((a * t) / c) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if ((t_1 <= -1e+33) || !(t_1 <= 4e+184))
		tmp = Float64(Float64(9.0 * Float64(x / Float64(z * c))) * y);
	else
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if ((t_1 <= -1e+33) || ~((t_1 <= 4e+184)))
		tmp = (9.0 * (x / (z * c))) * y;
	else
		tmp = ((a * t) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+33], N[Not[LessEqual[t$95$1, 4e+184]], $MachinePrecision]], N[(N[(9.0 * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999995e32 or 4.00000000000000007e184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 71.4%

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

   3. Taylor expanded in 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 70.2

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

   5. Applied rewrites 70.2%

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

   7. Applied rewrites 67.1%

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

   if -9.9999999999999995e32 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000007e184

   1. Initial program 83.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 54.8

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

   5. Applied rewrites 54.8%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -1 \cdot 10^{+33} \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 4 \cdot 10^{+184}\right):\\ \;\;\;\;\left(9 \cdot \frac{x}{z \cdot c}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -6.6e-49)
   (* (/ (* a t) c) -4.0)
   (if (<= a 4.2e+66) (/ (fma (* y x) 9.0 b) (* z c)) (* (* t (/ a c)) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6.6e-49) {
		tmp = ((a * t) / c) * -4.0;
	} else if (a <= 4.2e+66) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -6.6e-49)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (a <= 4.2e+66)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -6.6e-49], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 4.2e+66], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.6e-49

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 56.7

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

   5. Applied rewrites 56.7%

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

   if -6.6e-49 < a < 4.20000000000000011e66

   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 71.1

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

   5. Applied rewrites 71.1%

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

   if 4.20000000000000011e66 < a

   1. Initial program 72.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 68.2

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

   5. Applied rewrites 68.2%

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

   7. Applied rewrites 76.4%

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

Alternative 13: 46.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-183} \lor \neg \left(a \leq 15000000000\right):\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -6e-183) (not (<= a 15000000000.0)))
   (* (* t a) (/ -4.0 c))
   (/ b (* c z))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -6e-183) || !(a <= 15000000000.0)) {
		tmp = (t * a) * (-4.0 / c);
	} 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.
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 ((a <= (-6d-183)) .or. (.not. (a <= 15000000000.0d0))) then
        tmp = (t * a) * ((-4.0d0) / c)
    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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -6e-183) || !(a <= 15000000000.0)) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -6e-183) or not (a <= 15000000000.0):
		tmp = (t * a) * (-4.0 / c)
	else:
		tmp = b / (c * z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -6e-183) || !(a <= 15000000000.0))
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -6e-183) || ~((a <= 15000000000.0)))
		tmp = (t * a) * (-4.0 / c);
	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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -6e-183], N[Not[LessEqual[a, 15000000000.0]], $MachinePrecision]], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.9999999999999996e-183 or 1.5e10 < a

   1. Initial program 75.9%

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

   3. Taylor expanded in z around 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 56.4

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

   5. Applied rewrites 56.4%

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

   7. Applied rewrites 56.3%

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

   if -5.9999999999999996e-183 < a < 1.5e10

   1. Initial program 84.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.8

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

   5. Applied rewrites 41.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-183} \lor \neg \left(a \leq 15000000000\right):\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-183}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;a \leq 14500000000:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -6e-183)
   (* (/ (* a t) c) -4.0)
   (if (<= a 14500000000.0) (/ b (* c z)) (* (* t (/ a c)) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6e-183) {
		tmp = ((a * t) / c) * -4.0;
	} else if (a <= 14500000000.0) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Fortran

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 (a <= (-6d-183)) then
        tmp = ((a * t) / c) * (-4.0d0)
    else if (a <= 14500000000.0d0) then
        tmp = b / (c * z)
    else
        tmp = (t * (a / c)) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6e-183) {
		tmp = ((a * t) / c) * -4.0;
	} else if (a <= 14500000000.0) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -6e-183:
		tmp = ((a * t) / c) * -4.0
	elif a <= 14500000000.0:
		tmp = b / (c * z)
	else:
		tmp = (t * (a / c)) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -6e-183)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (a <= 14500000000.0)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -6e-183)
		tmp = ((a * t) / c) * -4.0;
	elseif (a <= 14500000000.0)
		tmp = b / (c * z);
	else
		tmp = (t * (a / c)) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -6e-183], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 14500000000.0], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.9999999999999996e-183

   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. 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 51.0

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

   5. Applied rewrites 51.0%

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

   if -5.9999999999999996e-183 < a < 1.45e10

   1. Initial program 84.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.8

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

   5. Applied rewrites 41.8%

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

   if 1.45e10 < a

   1. Initial program 73.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 65.2

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

   5. Applied rewrites 65.2%

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

   7. Applied rewrites 71.6%

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

Alternative 15: 47.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-183}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 14500000000:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -6e-183)
   (* (* t a) (/ -4.0 c))
   (if (<= a 14500000000.0) (/ b (* c z)) (* (* t (/ a c)) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6e-183) {
		tmp = (t * a) * (-4.0 / c);
	} else if (a <= 14500000000.0) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Fortran

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 (a <= (-6d-183)) then
        tmp = (t * a) * ((-4.0d0) / c)
    else if (a <= 14500000000.0d0) then
        tmp = b / (c * z)
    else
        tmp = (t * (a / c)) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6e-183) {
		tmp = (t * a) * (-4.0 / c);
	} else if (a <= 14500000000.0) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -6e-183:
		tmp = (t * a) * (-4.0 / c)
	elif a <= 14500000000.0:
		tmp = b / (c * z)
	else:
		tmp = (t * (a / c)) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -6e-183)
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	elseif (a <= 14500000000.0)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -6e-183)
		tmp = (t * a) * (-4.0 / c);
	elseif (a <= 14500000000.0)
		tmp = b / (c * z);
	else
		tmp = (t * (a / c)) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -6e-183], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 14500000000.0], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.9999999999999996e-183

   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. 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 51.0

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

   5. Applied rewrites 51.0%

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

   7. Applied rewrites 50.9%

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

   if -5.9999999999999996e-183 < a < 1.45e10

   1. Initial program 84.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.8

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

   5. Applied rewrites 41.8%

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

   if 1.45e10 < a

   1. Initial program 73.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 65.2

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

   5. Applied rewrites 65.2%

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

   7. Applied rewrites 71.6%

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

Alternative 16: 35.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(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);
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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 31.8

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

5. Applied rewrites 31.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.7% 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 2024309 
(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)))