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

Percentage Accurate: 79.3% → 93.9%

Time: 17.5s

Alternatives: 18

Speedup: 0.7×

• 37.3% 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: 79.3% 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: 93.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} - \mathsf{fma}\left(x, \frac{y \cdot -9}{z}, a \cdot \left(t \cdot 4\right)\right)}{c}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (- (/ b z) (fma x (/ (* y -9.0) z) (* a (* t 4.0)))) c)))
   (if (<= z -4.6e-39)
     t_1
     (if (<= z 8.5e+49)
       (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
       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 / z) - fma(x, ((y * -9.0) / z), (a * (t * 4.0)))) / c;
	double tmp;
	if (z <= -4.6e-39) {
		tmp = t_1;
	} else if (z <= 8.5e+49) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) - fma(x, Float64(Float64(y * -9.0) / z), Float64(a * Float64(t * 4.0)))) / c)
	tmp = 0.0
	if (z <= -4.6e-39)
		tmp = t_1;
	elseif (z <= 8.5e+49)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] - N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -4.6e-39], t$95$1, If[LessEqual[z, 8.5e+49], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000016e-39 or 8.4999999999999996e49 < z

   1. Initial program 63.0%

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

   3. Taylor expanded in 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. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 77.4%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

   8. Simplified 93.6%

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

   if -4.60000000000000016e-39 < z < 8.4999999999999996e49

   1. Initial program 96.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

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

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

      11. *-lowering-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 97.5

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

   4. Applied egg-rr 97.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{b}{z} - \mathsf{fma}\left(x, \frac{y \cdot -9}{z}, a \cdot \left(t \cdot 4\right)\right)}{c}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - \mathsf{fma}\left(x, \frac{y \cdot -9}{z}, a \cdot \left(t \cdot 4\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-187}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, t\_2\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, t\_2\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \end{array} \]

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 (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (fma (* a t) (* z -4.0) b)))
   (if (<= t_1 -5e-187)
     (/ (fma (* x 9.0) y t_2) (* z c))
     (if (<= t_1 2e+190)
       (/ (/ (fma x (* y 9.0) t_2) c) z)
       (if (<= t_1 INFINITY)
         (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
         (* a (/ t (* c -0.25))))))))

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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = fma((a * t), (z * -4.0), b);
	double tmp;
	if (t_1 <= -5e-187) {
		tmp = fma((x * 9.0), y, t_2) / (z * c);
	} else if (t_1 <= 2e+190) {
		tmp = (fma(x, (y * 9.0), t_2) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else {
		tmp = a * (t / (c * -0.25));
	}
	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(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = fma(Float64(a * t), Float64(z * -4.0), b)
	tmp = 0.0
	if (t_1 <= -5e-187)
		tmp = Float64(fma(Float64(x * 9.0), y, t_2) / Float64(z * c));
	elseif (t_1 <= 2e+190)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), t_2) / c) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	else
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	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[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-187], N[(N[(N[(x * 9.0), $MachinePrecision] * y + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+190], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999996e-187

   1. Initial program 92.3%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot 9, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      6. associate-+l- N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot 9, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

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

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 91.5

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

   4. Applied egg-rr 91.5%

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

   if -4.9999999999999996e-187 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 2.0000000000000001e190

   1. Initial program 73.9%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 97.9%

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

   if 2.0000000000000001e190 < (/.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 88.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

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

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

      11. *-lowering-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 91.2

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

   4. Applied egg-rr 91.2%

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

   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

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 4.7

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

   5. Simplified 4.7%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 5.6

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

   7. Applied egg-rr 5.6%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-*l/ N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 83.5

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

   9. Applied egg-rr 83.5%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-187}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 2 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \end{array} \]

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 (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (/ (fma (* x 9.0) y (fma (* a t) (* z -4.0) b)) (* z c))))
   (if (<= t_1 -5e-187)
     t_2
     (if (<= t_1 0.0)
       (/ (/ (fma x (* y 9.0) b) z) c)
       (if (<= t_1 INFINITY) t_2 (* a (/ t (* c -0.25))))))))

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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = fma((x * 9.0), y, fma((a * t), (z * -4.0), b)) / (z * c);
	double tmp;
	if (t_1 <= -5e-187) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = (fma(x, (y * 9.0), b) / z) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = a * (t / (c * -0.25));
	}
	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(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = Float64(fma(Float64(x * 9.0), y, fma(Float64(a * t), Float64(z * -4.0), b)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-187)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), b) / z) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	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[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-187], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999996e-187 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 92.2%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot 9, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      6. associate-+l- N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot 9, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

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

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 92.7

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

   4. Applied egg-rr 92.7%

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

   if -4.9999999999999996e-187 < (/.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 38.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 87.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 4.7

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

   5. Simplified 4.7%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 5.6

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

   7. Applied egg-rr 5.6%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-*l/ N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 83.5

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

   9. Applied egg-rr 83.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-187}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot y\right)\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), t\_1\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 10^{-20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+251}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, t\_1\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* x y))) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -1e+135)
     (/ (fma a (* -4.0 (* z t)) t_1) (* z c))
     (if (<= t_2 1e-20)
       (/ (fma a (* t -4.0) (/ b z)) c)
       (if (<= t_2 5e+251)
         (/ (fma (* a (* z -4.0)) t t_1) (* z c))
         (/ (* 9.0 (* x (/ y z))) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (x * y);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1e+135) {
		tmp = fma(a, (-4.0 * (z * t)), t_1) / (z * c);
	} else if (t_2 <= 1e-20) {
		tmp = fma(a, (t * -4.0), (b / z)) / c;
	} else if (t_2 <= 5e+251) {
		tmp = fma((a * (z * -4.0)), t, t_1) / (z * c);
	} else {
		tmp = (9.0 * (x * (y / z))) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(x * y))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -1e+135)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), t_1) / Float64(z * c));
	elseif (t_2 <= 1e-20)
		tmp = Float64(fma(a, Float64(t * -4.0), Float64(b / z)) / c);
	elseif (t_2 <= 5e+251)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, t_1) / Float64(z * c));
	else
		tmp = Float64(Float64(9.0 * Float64(x * Float64(y / z))) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+135], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-20], N[(N[(a * N[(t * -4.0), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 5e+251], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999962e134

   1. Initial program 86.1%

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

   3. Taylor expanded in b around 0

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

      1. 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

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 80.7

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

   5. Simplified 80.7%

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

   if -9.99999999999999962e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999945e-21

   1. Initial program 79.7%

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

      1. associate-+l- N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. neg-lowering-neg.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 88.4

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

   7. Simplified 88.4%

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

   if 9.99999999999999945e-21 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000005e251

   1. Initial program 83.2%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

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

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

      11. *-lowering-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 80.5

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 68.8

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

   7. Simplified 68.8%

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

   if 5.0000000000000005e251 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 51.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 65.3%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 60.9

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

   7. Simplified 60.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. associate-*l* N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 82.3

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

   9. Applied egg-rr 82.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+251}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+82}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -1e+135)
     (/ (fma a (* -4.0 (* z t)) (* 9.0 (* x y))) (* z c))
     (if (<= t_1 2e+82)
       (/ (fma a (* t -4.0) (/ b z)) c)
       (* (/ (* x 9.0) z) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+135) {
		tmp = fma(a, (-4.0 * (z * t)), (9.0 * (x * y))) / (z * c);
	} else if (t_1 <= 2e+82) {
		tmp = fma(a, (t * -4.0), (b / z)) / c;
	} else {
		tmp = ((x * 9.0) / z) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+135)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (t_1 <= 2e+82)
		tmp = Float64(fma(a, Float64(t * -4.0), Float64(b / z)) / c);
	else
		tmp = Float64(Float64(Float64(x * 9.0) / z) * Float64(y / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+135], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+82], N[(N[(a * N[(t * -4.0), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999962e134

   1. Initial program 86.1%

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

   3. Taylor expanded in b around 0

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

      1. 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

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 80.7

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

   5. Simplified 80.7%

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

   if -9.99999999999999962e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e82

   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. Step-by-step derivation

      1. associate-+l- N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. neg-lowering-neg.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 72.9%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 85.8

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

   7. Simplified 85.8%

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

   if 1.9999999999999999e82 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 65.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 68.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 57.0

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

   7. Simplified 57.0%

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

      1. associate-/r* N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 65.6

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

   9. Applied egg-rr 65.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+82}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+82}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -1e+135)
     (/ (/ (fma x (* y 9.0) b) z) c)
     (if (<= t_1 2e+82)
       (/ (fma a (* t -4.0) (/ b z)) c)
       (* (/ (* x 9.0) z) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+135) {
		tmp = (fma(x, (y * 9.0), b) / z) / c;
	} else if (t_1 <= 2e+82) {
		tmp = fma(a, (t * -4.0), (b / z)) / c;
	} else {
		tmp = ((x * 9.0) / z) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+135)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), b) / z) / c);
	elseif (t_1 <= 2e+82)
		tmp = Float64(fma(a, Float64(t * -4.0), Float64(b / z)) / c);
	else
		tmp = Float64(Float64(Float64(x * 9.0) / z) * Float64(y / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+135], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+82], N[(N[(a * N[(t * -4.0), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999962e134

   1. Initial program 86.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 78.3%

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

   if -9.99999999999999962e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e82

   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. Step-by-step derivation

      1. associate-+l- N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. neg-lowering-neg.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 72.9%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 85.8

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

   7. Simplified 85.8%

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

   if 1.9999999999999999e82 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 65.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 68.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 57.0

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

   7. Simplified 57.0%

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

      1. associate-/r* N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 65.6

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

   9. Applied egg-rr 65.6%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+82}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t \cdot -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -1e+113)
     (/ (/ (fma x (* y 9.0) b) z) c)
     (if (<= t_1 4e+49)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (* (/ (* x 9.0) z) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+113) {
		tmp = (fma(x, (y * 9.0), b) / z) / c;
	} else if (t_1 <= 4e+49) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = ((x * 9.0) / z) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+113)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), b) / z) / c);
	elseif (t_1 <= 4e+49)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(x * 9.0) / z) * Float64(y / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+113], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 4e+49], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e113

   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. Step-by-step derivation

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 79.5%

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

   if -1e113 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999979e49

   1. Initial program 80.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 75.2

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

   5. Simplified 75.2%

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

   if 3.99999999999999979e49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 67.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 69.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 56.3

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

   7. Simplified 56.3%

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

      1. associate-/r* N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 63.9

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

   9. Applied egg-rr 63.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -1e+135)
     (/ (/ t_1 c) z)
     (if (<= t_1 4e+49)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (* (/ (* x 9.0) z) (/ 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+135) {
		tmp = (t_1 / c) / z;
	} else if (t_1 <= 4e+49) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = ((x * 9.0) / z) * (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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+135)
		tmp = Float64(Float64(t_1 / c) / z);
	elseif (t_1 <= 4e+49)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(x * 9.0) / z) * Float64(y / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+135], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4e+49], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999962e134

   1. Initial program 86.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 70.1

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

   7. Simplified 70.1%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r/ N/A

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

      6. /-lowering-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. /-lowering-/.f64 N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-lowering-*.f64 78.2

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

   9. Applied egg-rr 78.2%

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

   if -9.99999999999999962e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999979e49

   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 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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 75.0

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

   5. Simplified 75.0%

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

   if 3.99999999999999979e49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 67.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 69.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 56.3

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

   7. Simplified 56.3%

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

      1. associate-/r* N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 63.9

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

   9. Applied egg-rr 63.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z} \cdot \frac{y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+100}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-156}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.3e+100)
   (* (/ b c) (/ 1.0 z))
   (if (<= b -2.9e-156)
     (* (* x 9.0) (/ y (* z c)))
     (if (<= b 1.8e+147) (* t (/ a (* c -0.25))) (/ (/ 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 (b <= -4.3e+100) {
		tmp = (b / c) * (1.0 / z);
	} else if (b <= -2.9e-156) {
		tmp = (x * 9.0) * (y / (z * c));
	} else if (b <= 1.8e+147) {
		tmp = t * (a / (c * -0.25));
	} 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 (b <= (-4.3d+100)) then
        tmp = (b / c) * (1.0d0 / z)
    else if (b <= (-2.9d-156)) then
        tmp = (x * 9.0d0) * (y / (z * c))
    else if (b <= 1.8d+147) then
        tmp = t * (a / (c * (-0.25d0)))
    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 (b <= -4.3e+100) {
		tmp = (b / c) * (1.0 / z);
	} else if (b <= -2.9e-156) {
		tmp = (x * 9.0) * (y / (z * c));
	} else if (b <= 1.8e+147) {
		tmp = t * (a / (c * -0.25));
	} 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 b <= -4.3e+100:
		tmp = (b / c) * (1.0 / z)
	elif b <= -2.9e-156:
		tmp = (x * 9.0) * (y / (z * c))
	elif b <= 1.8e+147:
		tmp = t * (a / (c * -0.25))
	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 (b <= -4.3e+100)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	elseif (b <= -2.9e-156)
		tmp = Float64(Float64(x * 9.0) * Float64(y / Float64(z * c)));
	elseif (b <= 1.8e+147)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4.3e+100)
		tmp = (b / c) * (1.0 / z);
	elseif (b <= -2.9e-156)
		tmp = (x * 9.0) * (y / (z * c));
	elseif (b <= 1.8e+147)
		tmp = t * (a / (c * -0.25));
	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[LessEqual[b, -4.3e+100], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e-156], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+147], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.29999999999999993e100

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 59.6%

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

      1. div-inv N/A

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{b \cdot 1}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{c \cdot z}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c}} \cdot \frac{1}{z} \]

      7. /-lowering-/.f64 65.1

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

   7. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   if -4.29999999999999993e100 < b < -2.90000000000000021e-156

   1. Initial program 86.8%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 53.5

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

   7. Simplified 53.5%

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

      1. associate-/r* N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 59.1

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

   9. Applied egg-rr 59.1%

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

   if -2.90000000000000021e-156 < b < 1.8000000000000001e147

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.8

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

   5. Simplified 47.8%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.8

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

   7. Applied egg-rr 50.8%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 58.0

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

   9. Applied egg-rr 58.0%

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

   if 1.8000000000000001e147 < b

   1. Initial program 65.5%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 51.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 66.0

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

   7. Applied egg-rr 66.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+100}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-156}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -1.18 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-154}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -1.18e+97)
     t_1
     (if (<= b -1.1e-154)
       (* (* x 9.0) (/ y (* z c)))
       (if (<= b 1.02e+147) (* t (/ a (* c -0.25))) 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 (b <= -1.18e+97) {
		tmp = t_1;
	} else if (b <= -1.1e-154) {
		tmp = (x * 9.0) * (y / (z * c));
	} else if (b <= 1.02e+147) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-1.18d+97)) then
        tmp = t_1
    else if (b <= (-1.1d-154)) then
        tmp = (x * 9.0d0) * (y / (z * c))
    else if (b <= 1.02d+147) then
        tmp = t * (a / (c * (-0.25d0)))
    else
        tmp = t_1
    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 = (b / c) / z;
	double tmp;
	if (b <= -1.18e+97) {
		tmp = t_1;
	} else if (b <= -1.1e-154) {
		tmp = (x * 9.0) * (y / (z * c));
	} else if (b <= 1.02e+147) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_1;
	}
	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 = (b / c) / z
	tmp = 0
	if b <= -1.18e+97:
		tmp = t_1
	elif b <= -1.1e-154:
		tmp = (x * 9.0) * (y / (z * c))
	elif b <= 1.02e+147:
		tmp = t * (a / (c * -0.25))
	else:
		tmp = 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(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -1.18e+97)
		tmp = t_1;
	elseif (b <= -1.1e-154)
		tmp = Float64(Float64(x * 9.0) * Float64(y / Float64(z * c)));
	elseif (b <= 1.02e+147)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -1.18e+97)
		tmp = t_1;
	elseif (b <= -1.1e-154)
		tmp = (x * 9.0) * (y / (z * c));
	elseif (b <= 1.02e+147)
		tmp = t * (a / (c * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -1.18e+97], t$95$1, If[LessEqual[b, -1.1e-154], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e+147], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.18000000000000006e97 or 1.0199999999999999e147 < b

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 56.5%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 65.4

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

   7. Applied egg-rr 65.4%

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

   if -1.18000000000000006e97 < b < -1.10000000000000004e-154

   1. Initial program 86.8%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 53.5

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

   7. Simplified 53.5%

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

      1. associate-/r* N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 59.1

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

   9. Applied egg-rr 59.1%

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

   if -1.10000000000000004e-154 < b < 1.0199999999999999e147

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.8

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

   5. Simplified 47.8%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.8

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

   7. Applied egg-rr 50.8%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 58.0

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

   9. Applied egg-rr 58.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.18 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-154}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-155}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -5.4e+88)
     t_1
     (if (<= b -2.1e-155)
       (* 9.0 (/ (* x y) (* z c)))
       (if (<= b 1.7e+147) (* t (/ a (* c -0.25))) 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 (b <= -5.4e+88) {
		tmp = t_1;
	} else if (b <= -2.1e-155) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 1.7e+147) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-5.4d+88)) then
        tmp = t_1
    else if (b <= (-2.1d-155)) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 1.7d+147) then
        tmp = t * (a / (c * (-0.25d0)))
    else
        tmp = t_1
    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 = (b / c) / z;
	double tmp;
	if (b <= -5.4e+88) {
		tmp = t_1;
	} else if (b <= -2.1e-155) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 1.7e+147) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_1;
	}
	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 = (b / c) / z
	tmp = 0
	if b <= -5.4e+88:
		tmp = t_1
	elif b <= -2.1e-155:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 1.7e+147:
		tmp = t * (a / (c * -0.25))
	else:
		tmp = 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(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -5.4e+88)
		tmp = t_1;
	elseif (b <= -2.1e-155)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 1.7e+147)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -5.4e+88)
		tmp = t_1;
	elseif (b <= -2.1e-155)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 1.7e+147)
		tmp = t * (a / (c * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -5.4e+88], t$95$1, If[LessEqual[b, -2.1e-155], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+147], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.40000000000000031e88 or 1.7e147 < b

   1. Initial program 69.5%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 55.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 64.4

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

   7. Applied egg-rr 64.4%

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

   if -5.40000000000000031e88 < b < -2.1000000000000002e-155

   1. Initial program 89.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 55.9

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

   7. Simplified 55.9%

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

      1. associate-/r* N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 57.2

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

   9. Applied egg-rr 57.2%

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

   if -2.1000000000000002e-155 < b < 1.7e147

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.8

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

   5. Simplified 47.8%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.8

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

   7. Applied egg-rr 50.8%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 58.0

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

   9. Applied egg-rr 58.0%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-155}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \end{array} \]

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 -3.2e+80)
   (/ (* -4.0 (* a t)) c)
   (if (<= z 8e+53) (/ (fma 9.0 (* x y) b) (* z c)) (* a (/ t (* c -0.25))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.2e+80) {
		tmp = (-4.0 * (a * t)) / c;
	} else if (z <= 8e+53) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = a * (t / (c * -0.25));
	}
	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 <= -3.2e+80)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) / c);
	elseif (z <= 8e+53)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	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, -3.2e+80], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 8e+53], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1999999999999999e80

   1. Initial program 62.6%

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

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 54.7

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

   5. Simplified 54.7%

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

   if -3.1999999999999999e80 < z < 7.9999999999999999e53

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 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. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 77.8

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

   5. Simplified 77.8%

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

   if 7.9999999999999999e53 < z

   1. Initial program 48.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 35.1

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

   5. Simplified 35.1%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 37.1

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

   7. Applied egg-rr 37.1%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-*l/ N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 58.6

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

   9. Applied egg-rr 58.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{if}\;t \leq -1.28 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.07:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ a (* c -0.25)))))
   (if (<= t -1.28e+17) t_1 (if (<= t 0.07) (/ (/ b c) z) 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 = t * (a / (c * -0.25));
	double tmp;
	if (t <= -1.28e+17) {
		tmp = t_1;
	} else if (t <= 0.07) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a / (c * (-0.25d0)))
    if (t <= (-1.28d+17)) then
        tmp = t_1
    else if (t <= 0.07d0) then
        tmp = (b / c) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a / (c * -0.25));
	double tmp;
	if (t <= -1.28e+17) {
		tmp = t_1;
	} else if (t <= 0.07) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a / (c * -0.25))
	tmp = 0
	if t <= -1.28e+17:
		tmp = t_1
	elif t <= 0.07:
		tmp = (b / c) / z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a / Float64(c * -0.25)))
	tmp = 0.0
	if (t <= -1.28e+17)
		tmp = t_1;
	elseif (t <= 0.07)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a / (c * -0.25));
	tmp = 0.0;
	if (t <= -1.28e+17)
		tmp = t_1;
	elseif (t <= 0.07)
		tmp = (b / c) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.28e+17], t$95$1, If[LessEqual[t, 0.07], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.28e17 or 0.070000000000000007 < t

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.2

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

   5. Simplified 47.2%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.4

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

   7. Applied egg-rr 49.4%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 64.7

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

   9. Applied egg-rr 64.7%

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

   if -1.28e17 < t < 0.070000000000000007

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 40.9%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 46.3

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

   7. Applied egg-rr 46.3%

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

Alternative 14: 46.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-198}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \end{array} \]

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 (<= t -1.1e+17)
   (* t (/ a (* c -0.25)))
   (if (<= t 3.2e-198) (/ b (* z c)) (* a (/ t (* c -0.25))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.1e+17) {
		tmp = t * (a / (c * -0.25));
	} else if (t <= 3.2e-198) {
		tmp = b / (z * c);
	} else {
		tmp = a * (t / (c * -0.25));
	}
	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 (t <= (-1.1d+17)) then
        tmp = t * (a / (c * (-0.25d0)))
    else if (t <= 3.2d-198) then
        tmp = b / (z * c)
    else
        tmp = a * (t / (c * (-0.25d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.1e+17) {
		tmp = t * (a / (c * -0.25));
	} else if (t <= 3.2e-198) {
		tmp = b / (z * c);
	} else {
		tmp = a * (t / (c * -0.25));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.1e+17:
		tmp = t * (a / (c * -0.25))
	elif t <= 3.2e-198:
		tmp = b / (z * c)
	else:
		tmp = a * (t / (c * -0.25))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.1e+17)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	elseif (t <= 3.2e-198)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.1e+17)
		tmp = t * (a / (c * -0.25));
	elseif (t <= 3.2e-198)
		tmp = b / (z * c);
	else
		tmp = a * (t / (c * -0.25));
	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[t, -1.1e+17], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-198], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e17

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 48.0

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

   5. Simplified 48.0%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.9

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

   7. Applied egg-rr 49.9%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 64.4

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

   9. Applied egg-rr 64.4%

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

   if -1.1e17 < t < 3.19999999999999994e-198

   1. Initial program 84.0%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 42.7%

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

   if 3.19999999999999994e-198 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 39.5

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

   5. Simplified 39.5%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 41.0

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

   7. Applied egg-rr 41.0%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-*l/ N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 51.5

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

   9. Applied egg-rr 51.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-198}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.000105:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ a (* c -0.25)))))
   (if (<= t -2.8e+17) t_1 (if (<= t 0.000105) (* b (/ 1.0 (* z c))) 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 = t * (a / (c * -0.25));
	double tmp;
	if (t <= -2.8e+17) {
		tmp = t_1;
	} else if (t <= 0.000105) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a / (c * (-0.25d0)))
    if (t <= (-2.8d+17)) then
        tmp = t_1
    else if (t <= 0.000105d0) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a / (c * -0.25));
	double tmp;
	if (t <= -2.8e+17) {
		tmp = t_1;
	} else if (t <= 0.000105) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_1;
	}
	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 = t * (a / (c * -0.25))
	tmp = 0
	if t <= -2.8e+17:
		tmp = t_1
	elif t <= 0.000105:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = 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(t * Float64(a / Float64(c * -0.25)))
	tmp = 0.0
	if (t <= -2.8e+17)
		tmp = t_1;
	elseif (t <= 0.000105)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a / (c * -0.25));
	tmp = 0.0;
	if (t <= -2.8e+17)
		tmp = t_1;
	elseif (t <= 0.000105)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+17], t$95$1, If[LessEqual[t, 0.000105], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e17 or 1.05e-4 < t

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.2

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

   5. Simplified 47.2%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.4

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

   7. Applied egg-rr 49.4%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 64.7

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

   9. Applied egg-rr 64.7%

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

   if -2.8e17 < t < 1.05e-4

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 40.9%

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

      1. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{b}}} \]

      2. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{z \cdot c} \cdot b} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{z \cdot c} \cdot b} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{z \cdot c}} \cdot b \]

      5. *-lowering-*.f64 41.5

         \[\leadsto \frac{1}{\color{blue}{z \cdot c}} \cdot b \]

   7. Applied egg-rr 41.5%

      \[\leadsto \color{blue}{\frac{1}{z \cdot c} \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 0.000105:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-198}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \end{array} \end{array} \]

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 (<= t -8.5e+16)
   (* t (/ a (* c -0.25)))
   (if (<= t 3e-198) (/ b (* z c)) (* (* a t) (/ -4.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.5e+16) {
		tmp = t * (a / (c * -0.25));
	} else if (t <= 3e-198) {
		tmp = b / (z * c);
	} else {
		tmp = (a * t) * (-4.0 / c);
	}
	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 (t <= (-8.5d+16)) then
        tmp = t * (a / (c * (-0.25d0)))
    else if (t <= 3d-198) then
        tmp = b / (z * c)
    else
        tmp = (a * t) * ((-4.0d0) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.5e+16) {
		tmp = t * (a / (c * -0.25));
	} else if (t <= 3e-198) {
		tmp = b / (z * c);
	} else {
		tmp = (a * t) * (-4.0 / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8.5e+16:
		tmp = t * (a / (c * -0.25))
	elif t <= 3e-198:
		tmp = b / (z * c)
	else:
		tmp = (a * t) * (-4.0 / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8.5e+16)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	elseif (t <= 3e-198)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -8.5e+16)
		tmp = t * (a / (c * -0.25));
	elseif (t <= 3e-198)
		tmp = b / (z * c);
	else
		tmp = (a * t) * (-4.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8.5e+16], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-198], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5e16

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 48.0

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

   5. Simplified 48.0%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.9

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

   7. Applied egg-rr 49.9%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. div-inv N/A

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

      10. associate-/l* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 64.4

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

   9. Applied egg-rr 64.4%

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

   if -8.5e16 < t < 3.0000000000000001e-198

   1. Initial program 84.0%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 42.7%

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

   if 3.0000000000000001e-198 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 39.5

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

   5. Simplified 39.5%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 41.0

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

   7. Applied egg-rr 41.0%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. times-frac N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. div-inv N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-/r* N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 49.8

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

   9. Applied egg-rr 49.8%

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

Alternative 17: 48.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-9}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ a (* c -0.25)))))
   (if (<= t -1e+17) t_1 (if (<= t 7.3e-9) (/ b (* z c)) 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 = t * (a / (c * -0.25));
	double tmp;
	if (t <= -1e+17) {
		tmp = t_1;
	} else if (t <= 7.3e-9) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a / (c * (-0.25d0)))
    if (t <= (-1d+17)) then
        tmp = t_1
    else if (t <= 7.3d-9) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a / (c * -0.25));
	double tmp;
	if (t <= -1e+17) {
		tmp = t_1;
	} else if (t <= 7.3e-9) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a / (c * -0.25))
	tmp = 0
	if t <= -1e+17:
		tmp = t_1
	elif t <= 7.3e-9:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a / Float64(c * -0.25)))
	tmp = 0.0
	if (t <= -1e+17)
		tmp = t_1;
	elseif (t <= 7.3e-9)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a / (c * -0.25));
	tmp = 0.0;
	if (t <= -1e+17)
		tmp = t_1;
	elseif (t <= 7.3e-9)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+17], t$95$1, If[LessEqual[t, 7.3e-9], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1e17 or 7.30000000000000002e-9 < t

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.2

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

   5. Simplified 47.2%

      \[\leadsto \frac{\color{blue}{\left(a \cdot \left(t \cdot z\right)\right) \cdot -4}}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(\left(a \cdot t\right) \cdot z\right)} \cdot -4}{z \cdot c} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(a \cdot t\right) \cdot z\right)} \cdot -4}{z \cdot c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\color{blue}{\left(t \cdot a\right)} \cdot z\right) \cdot -4}{z \cdot c} \]

      4. *-lowering-*.f64 49.4

         \[\leadsto \frac{\left(\color{blue}{\left(t \cdot a\right)} \cdot z\right) \cdot -4}{z \cdot c} \]

   7. Applied egg-rr 49.4%

      \[\leadsto \frac{\color{blue}{\left(\left(t \cdot a\right) \cdot z\right)} \cdot -4}{z \cdot c} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \frac{\color{blue}{\left(t \cdot a\right) \cdot \left(z \cdot -4\right)}}{z \cdot c} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot \frac{z \cdot -4}{z \cdot c}} \]

      3. times-frac N/A

         \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\left(\frac{z}{z} \cdot \frac{-4}{c}\right)} \]

      4. *-inverses N/A

         \[\leadsto \left(t \cdot a\right) \cdot \left(\color{blue}{1} \cdot \frac{-4}{c}\right) \]

      5. metadata-eval N/A

         \[\leadsto \left(t \cdot a\right) \cdot \left(1 \cdot \frac{\color{blue}{\frac{1}{\frac{-1}{4}}}}{c}\right) \]

      6. associate-/r* N/A

         \[\leadsto \left(t \cdot a\right) \cdot \left(1 \cdot \color{blue}{\frac{1}{\frac{-1}{4} \cdot c}}\right) \]

      7. *-commutative N/A

         \[\leadsto \left(t \cdot a\right) \cdot \left(1 \cdot \frac{1}{\color{blue}{c \cdot \frac{-1}{4}}}\right) \]

      8. div-inv N/A

         \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\frac{1}{c \cdot \frac{-1}{4}}} \]

      9. div-inv N/A

         \[\leadsto \color{blue}{\frac{t \cdot a}{c \cdot \frac{-1}{4}}} \]

      10. associate-/l* N/A

          \[\leadsto \color{blue}{t \cdot \frac{a}{c \cdot \frac{-1}{4}}} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{t \cdot \frac{a}{c \cdot \frac{-1}{4}}} \]

      12. /-lowering-/.f64 N/A

          \[\leadsto t \cdot \color{blue}{\frac{a}{c \cdot \frac{-1}{4}}} \]

      13. *-lowering-*.f64 64.7

          \[\leadsto t \cdot \frac{a}{\color{blue}{c \cdot -0.25}} \]

   9. Applied egg-rr 64.7%

      \[\leadsto \color{blue}{t \cdot \frac{a}{c \cdot -0.25}} \]

   if -1e17 < t < 7.30000000000000002e-9

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   4. Step-by-step derivation

   5. Simplified 40.9%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 35.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
4. Step-by-step derivation

5. Simplified 34.4%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
6. Add Preprocessing

Developer Target 1: 80.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

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 2024205 
(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)))