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

Percentage Accurate: 78.9% → 88.0%

Time: 22.0s

Alternatives: 19

Speedup: 0.7×

• 36.7% 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: 78.9% 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: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{1}{\frac{c}{a \cdot t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, t\_1\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 c))))
   (if (<= z -2.3e+72)
     (fma -4.0 (/ 1.0 (/ c (* a t))) (fma 9.0 (* (/ x c) (/ y z)) t_1))
     (if (<= z 2.5e-74)
       (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) c))
       (fma (* t (/ a c)) -4.0 (fma 9.0 (/ (* x y) (* z c)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (z <= -2.3e+72) {
		tmp = fma(-4.0, (1.0 / (c / (a * t))), fma(9.0, ((x / c) * (y / z)), t_1));
	} else if (z <= 2.5e-74) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / c);
	} else {
		tmp = fma((t * (a / c)), -4.0, fma(9.0, ((x * y) / (z * c)), t_1));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (z <= -2.3e+72)
		tmp = fma(-4.0, Float64(1.0 / Float64(c / Float64(a * t))), fma(9.0, Float64(Float64(x / c) * Float64(y / z)), t_1));
	elseif (z <= 2.5e-74)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / c));
	else
		tmp = fma(Float64(t * Float64(a / c)), -4.0, fma(9.0, Float64(Float64(x * y) / Float64(z * c)), t_1));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+72], N[(-4.0 * N[(1.0 / N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-74], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e72

   1. Initial program 60.0%

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

      1. associate-+l- 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*r* 65.3%

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

      4. *-commutative 65.3%

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

      5. associate-+l- 65.3%

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

      6. *-commutative 65.3%

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

      7. associate-*r* 60.0%

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

      8. *-commutative 60.0%

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

      9. associate-*l* 60.0%

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

      10. associate-*l* 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in x around 0 78.9%

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

      1. cancel-sign-sub-inv 78.9%

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

      2. metadata-eval 78.9%

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

      3. +-commutative 78.9%

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

      4. fma-def 78.9%

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

      5. associate-/l* 80.2%

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

      6. fma-def 80.3%

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

      7. times-frac 92.0%

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

      8. *-commutative 92.0%

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

   7. Simplified 92.0%

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

      1. clear-num 91.8%

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

      2. inv-pow 91.8%

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

   9. Applied egg-rr 91.8%

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

       1. unpow-1 91.8%

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

       2. associate-/l/ 90.6%

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

   11. Simplified 90.6%

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

   if -2.3e72 < z < 2.49999999999999999e-74

   1. Initial program 96.2%

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

      1. associate-+l- 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*r* 95.6%

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

      4. *-commutative 95.6%

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

      5. associate-+l- 95.6%

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

      6. *-commutative 95.6%

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

      7. associate-*r* 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   6. Applied egg-rr 98.3%

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

   if 2.49999999999999999e-74 < z

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 76.8%

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

      4. *-commutative 76.8%

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

      5. associate-+l- 76.8%

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

      6. *-commutative 76.8%

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

      7. associate-*r* 72.5%

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

      8. *-commutative 72.5%

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

      9. associate-*l* 72.5%

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

      10. associate-*l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in x around 0 88.5%

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

      1. cancel-sign-sub-inv 88.5%

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

      2. metadata-eval 88.5%

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

      3. +-commutative 88.5%

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

      4. *-commutative 88.5%

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

      5. fma-def 88.5%

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

      6. associate-/l* 85.2%

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

      7. associate-/r/ 86.1%

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

      8. fma-def 86.1%

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

      9. *-commutative 86.1%

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

      10. *-commutative 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{1}{\frac{c}{a \cdot t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{z \cdot c}\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, t\_1\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 c))))
   (if (<= z -1.25e+72)
     (fma -4.0 (/ a (/ c t)) (fma 9.0 (* (/ x c) (/ y z)) t_1))
     (if (<= z 3.1e-74)
       (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) c))
       (fma (* t (/ a c)) -4.0 (fma 9.0 (/ (* x y) (* z c)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (z <= -1.25e+72) {
		tmp = fma(-4.0, (a / (c / t)), fma(9.0, ((x / c) * (y / z)), t_1));
	} else if (z <= 3.1e-74) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / c);
	} else {
		tmp = fma((t * (a / c)), -4.0, fma(9.0, ((x * y) / (z * c)), t_1));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (z <= -1.25e+72)
		tmp = fma(-4.0, Float64(a / Float64(c / t)), fma(9.0, Float64(Float64(x / c) * Float64(y / z)), t_1));
	elseif (z <= 3.1e-74)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / c));
	else
		tmp = fma(Float64(t * Float64(a / c)), -4.0, fma(9.0, Float64(Float64(x * y) / Float64(z * c)), t_1));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+72], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-74], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999998e72

   1. Initial program 60.0%

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

      1. associate-+l- 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*r* 65.3%

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

      4. *-commutative 65.3%

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

      5. associate-+l- 65.3%

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

      6. *-commutative 65.3%

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

      7. associate-*r* 60.0%

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

      8. *-commutative 60.0%

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

      9. associate-*l* 60.0%

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

      10. associate-*l* 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in x around 0 78.9%

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

      1. cancel-sign-sub-inv 78.9%

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

      2. metadata-eval 78.9%

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

      3. +-commutative 78.9%

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

      4. fma-def 78.9%

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

      5. associate-/l* 80.2%

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

      6. fma-def 80.3%

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

      7. times-frac 92.0%

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

      8. *-commutative 92.0%

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

   7. Simplified 92.0%

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

   if -1.24999999999999998e72 < z < 3.1000000000000002e-74

   1. Initial program 96.2%

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

      1. associate-+l- 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*r* 95.6%

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

      4. *-commutative 95.6%

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

      5. associate-+l- 95.6%

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

      6. *-commutative 95.6%

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

      7. associate-*r* 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   6. Applied egg-rr 98.3%

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

   if 3.1000000000000002e-74 < z

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 76.8%

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

      4. *-commutative 76.8%

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

      5. associate-+l- 76.8%

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

      6. *-commutative 76.8%

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

      7. associate-*r* 72.5%

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

      8. *-commutative 72.5%

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

      9. associate-*l* 72.5%

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

      10. associate-*l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in x around 0 88.5%

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

      1. cancel-sign-sub-inv 88.5%

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

      2. metadata-eval 88.5%

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

      3. +-commutative 88.5%

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

      4. *-commutative 88.5%

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

      5. fma-def 88.5%

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

      6. associate-/l* 85.2%

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

      7. associate-/r/ 86.1%

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

      8. fma-def 86.1%

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

      9. *-commutative 86.1%

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

      10. *-commutative 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{z \cdot c}\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_3 := a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\left(b + \mathsf{fma}\left(z \cdot a, -4 \cdot t, t\_1\right)\right) \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+120}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, t\_3\right)}{c}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(b + \left(t\_3 + t\_1\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* 9.0 y)))
        (t_2 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c)))
        (t_3 (* a (* z (* -4.0 t)))))
   (if (<= t_2 -2e+49)
     (* (+ b (fma (* z a) (* -4.0 t) t_1)) (/ (/ 1.0 z) c))
     (if (<= t_2 5e+120)
       (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) t_3)) c))
       (if (<= t_2 INFINITY)
         (* (+ b (+ t_3 t_1)) (/ 1.0 (* z c)))
         (* -4.0 (* t (/ a c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double t_2 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_3 = a * (z * (-4.0 * t));
	double tmp;
	if (t_2 <= -2e+49) {
		tmp = (b + fma((z * a), (-4.0 * t), t_1)) * ((1.0 / z) / c);
	} else if (t_2 <= 5e+120) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), t_3)) / c);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (b + (t_3 + t_1)) * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(9.0 * y))
	t_2 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_3 = Float64(a * Float64(z * Float64(-4.0 * t)))
	tmp = 0.0
	if (t_2 <= -2e+49)
		tmp = Float64(Float64(b + fma(Float64(z * a), Float64(-4.0 * t), t_1)) * Float64(Float64(1.0 / z) / c));
	elseif (t_2 <= 5e+120)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), t_3)) / c));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(b + Float64(t_3 + t_1)) * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+49], N[(N[(b + N[(N[(z * a), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+120], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(b + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.99999999999999989e49

   1. Initial program 87.9%

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

      1. associate-+l- 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*r* 92.8%

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

      4. *-commutative 92.8%

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

      5. associate-+l- 92.8%

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

      6. *-commutative 92.8%

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

      7. associate-*r* 87.9%

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

      8. *-commutative 87.9%

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

      9. associate-*l* 87.9%

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

      10. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

      1. div-inv 91.4%

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

      2. associate-*r* 87.8%

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

      3. cancel-sign-sub-inv 87.8%

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

      4. fma-def 87.8%

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

      5. distribute-lft-neg-in 87.8%

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

      6. *-commutative 87.8%

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

      7. distribute-rgt-neg-in 87.8%

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

      8. distribute-lft-neg-in 87.8%

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

      9. distribute-rgt-neg-in 87.8%

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

      10. metadata-eval 87.8%

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

      11. associate-*r* 87.8%

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

      12. *-commutative 87.8%

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

   6. Applied egg-rr 87.8%

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

      1. fma-udef 87.8%

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

   8. Applied egg-rr 87.8%

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

   9. Taylor expanded in z around 0 87.8%

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

       1. *-commutative 87.8%

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

       2. associate-/r* 87.8%

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

   11. Simplified 87.8%

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

       1. +-commutative 87.8%

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

       2. associate-*r* 92.7%

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

       3. fma-def 92.7%

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

   13. Applied egg-rr 92.7%

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

   if -1.99999999999999989e49 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5.00000000000000019e120

   1. Initial program 87.4%

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

      1. associate-+l- 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-*r* 85.7%

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

      4. *-commutative 85.7%

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

      5. associate-+l- 85.7%

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

      6. *-commutative 85.7%

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

      7. associate-*r* 87.4%

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

      8. *-commutative 87.4%

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

      9. associate-*l* 87.5%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   6. Applied egg-rr 98.0%

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

   if 5.00000000000000019e120 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 88.5%

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

      1. associate-+l- 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 89.5%

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

      4. *-commutative 89.5%

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

      5. associate-+l- 89.5%

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

      6. *-commutative 89.5%

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

      7. associate-*r* 88.5%

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

      8. *-commutative 88.5%

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

      9. associate-*l* 88.5%

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

      10. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

      1. div-inv 88.4%

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

      2. associate-*r* 88.5%

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

      3. cancel-sign-sub-inv 88.5%

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

      4. fma-def 88.5%

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

      5. distribute-lft-neg-in 88.5%

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

      6. *-commutative 88.5%

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

      7. distribute-rgt-neg-in 88.5%

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

      8. distribute-lft-neg-in 88.5%

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

      9. distribute-rgt-neg-in 88.5%

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

      10. metadata-eval 88.5%

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

      11. associate-*r* 88.5%

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

      12. *-commutative 88.5%

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

   6. Applied egg-rr 88.5%

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

      1. fma-udef 88.5%

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

   8. Applied egg-rr 88.5%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) 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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 6.7%

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

      4. *-commutative 6.7%

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

      5. associate-+l- 6.7%

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

      6. *-commutative 6.7%

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

      7. associate-*r* 0.0%

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

      8. *-commutative 0.0%

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

      9. associate-*l* 0.0%

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

      10. associate-*l* 6.7%

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

   3. Simplified 6.7%

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

      1. div-inv 6.7%

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

      2. associate-*r* 0.0%

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

      3. cancel-sign-sub-inv 0.0%

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

      4. fma-def 0.0%

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

      5. distribute-lft-neg-in 0.0%

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

      6. *-commutative 0.0%

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

      7. distribute-rgt-neg-in 0.0%

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

      8. distribute-lft-neg-in 0.0%

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

      9. distribute-rgt-neg-in 0.0%

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

      10. metadata-eval 0.0%

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

      11. associate-*r* 0.0%

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

      12. *-commutative 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in a around inf 55.1%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\left(b + \mathsf{fma}\left(z \cdot a, -4 \cdot t, x \cdot \left(9 \cdot y\right)\right)\right) \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 5 \cdot 10^{+120}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\left(b + \left(a \cdot \left(z \cdot \left(-4 \cdot t\right)\right) + x \cdot \left(9 \cdot y\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := \frac{\frac{1}{z}}{c}\\ t_3 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(b + \mathsf{fma}\left(z \cdot a, -4 \cdot t, t\_1\right)\right) \cdot t\_2\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2 \cdot \left(b + \left(a \cdot \left(z \cdot \left(-4 \cdot t\right)\right) + t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* 9.0 y)))
        (t_2 (/ (/ 1.0 z) c))
        (t_3 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_3 (- INFINITY))
     (* (+ b (fma (* z a) (* -4.0 t) t_1)) t_2)
     (if (<= t_3 INFINITY)
       (* t_2 (+ b (+ (* a (* z (* -4.0 t))) t_1)))
       (* -4.0 (* t (/ a c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double t_2 = (1.0 / z) / c;
	double t_3 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (b + fma((z * a), (-4.0 * t), t_1)) * t_2;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2 * (b + ((a * (z * (-4.0 * t))) + t_1));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(9.0 * y))
	t_2 = Float64(Float64(1.0 / z) / c)
	t_3 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(b + fma(Float64(z * a), Float64(-4.0 * t), t_1)) * t_2);
	elseif (t_3 <= Inf)
		tmp = Float64(t_2 * Float64(b + Float64(Float64(a * Float64(z * Float64(-4.0 * t))) + t_1)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(b + N[(N[(z * a), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$2 * N[(b + N[(N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 81.8%

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

      1. associate-+l- 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r* 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-+l- 91.0%

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

      6. *-commutative 91.0%

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

      7. associate-*r* 81.8%

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

      8. *-commutative 81.8%

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

      9. associate-*l* 81.8%

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

      10. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

      1. div-inv 89.0%

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

      2. associate-*r* 81.8%

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

      3. cancel-sign-sub-inv 81.8%

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

      4. fma-def 81.8%

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

      5. distribute-lft-neg-in 81.8%

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

      6. *-commutative 81.8%

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

      7. distribute-rgt-neg-in 81.8%

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

      8. distribute-lft-neg-in 81.8%

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

      9. distribute-rgt-neg-in 81.8%

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

      10. metadata-eval 81.8%

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

      11. associate-*r* 81.8%

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

      12. *-commutative 81.8%

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

   6. Applied egg-rr 81.8%

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

      1. fma-udef 81.8%

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

   8. Applied egg-rr 81.8%

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

   9. Taylor expanded in z around 0 81.8%

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

       1. *-commutative 81.8%

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

       2. associate-/r* 81.8%

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

   11. Simplified 81.8%

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

       1. +-commutative 81.8%

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

       2. associate-*r* 91.0%

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

       3. fma-def 91.0%

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

   13. Applied egg-rr 91.0%

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

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

   1. Initial program 89.7%

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

      1. associate-+l- 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-*r* 89.2%

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

      4. *-commutative 89.2%

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

      5. associate-+l- 89.2%

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

      6. *-commutative 89.2%

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

      7. associate-*r* 89.7%

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

      8. *-commutative 89.7%

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

      9. associate-*l* 89.7%

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

      10. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

      1. div-inv 88.4%

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

      2. associate-*r* 89.7%

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

      3. cancel-sign-sub-inv 89.7%

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

      4. fma-def 89.7%

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

      5. distribute-lft-neg-in 89.7%

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

      6. *-commutative 89.7%

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

      7. distribute-rgt-neg-in 89.7%

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

      8. distribute-lft-neg-in 89.7%

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

      9. distribute-rgt-neg-in 89.7%

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

      10. metadata-eval 89.7%

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

      11. associate-*r* 89.7%

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

      12. *-commutative 89.7%

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

   6. Applied egg-rr 89.7%

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

      1. fma-udef 89.7%

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

   8. Applied egg-rr 89.7%

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

   9. Taylor expanded in z around 0 89.7%

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

       1. *-commutative 89.7%

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

       2. associate-/r* 90.0%

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

   11. Simplified 90.0%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) 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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 6.7%

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

      4. *-commutative 6.7%

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

      5. associate-+l- 6.7%

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

      6. *-commutative 6.7%

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

      7. associate-*r* 0.0%

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

      8. *-commutative 0.0%

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

      9. associate-*l* 0.0%

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

      10. associate-*l* 6.7%

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

   3. Simplified 6.7%

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

      1. div-inv 6.7%

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

      2. associate-*r* 0.0%

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

      3. cancel-sign-sub-inv 0.0%

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

      4. fma-def 0.0%

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

      5. distribute-lft-neg-in 0.0%

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

      6. *-commutative 0.0%

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

      7. distribute-rgt-neg-in 0.0%

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

      8. distribute-lft-neg-in 0.0%

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

      9. distribute-rgt-neg-in 0.0%

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

      10. metadata-eval 0.0%

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

      11. associate-*r* 0.0%

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

      12. *-commutative 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in a around inf 55.1%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 88.6%

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

Alternative 5: 84.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 1.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.65e-50)
   (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* z c))
   (fma -4.0 (/ a (/ c t)) (/ (+ (* 9.0 (/ (* x y) c)) (/ b c)) z))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.65e-50) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = fma(-4.0, (a / (c / t)), (((9.0 * ((x * y) / c)) + (b / c)) / z));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.65e-50)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	else
		tmp = fma(-4.0, Float64(a / Float64(c / t)), Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.65e-50], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.6499999999999999e-50

   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. Step-by-step derivation

      1. associate-+l- 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*r* 86.5%

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

      4. *-commutative 86.5%

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

      5. associate-+l- 86.5%

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

      6. *-commutative 86.5%

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

      7. associate-*r* 84.3%

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

      8. *-commutative 84.3%

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

      9. associate-*l* 84.3%

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

      10. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

   if 1.6499999999999999e-50 < c

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*r* 78.8%

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

      8. *-commutative 78.8%

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

      9. associate-*l* 78.8%

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

      10. associate-*l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around 0 83.1%

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

      1. cancel-sign-sub-inv 83.1%

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

      2. metadata-eval 83.1%

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

      3. +-commutative 83.1%

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

      4. fma-def 83.1%

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

      5. associate-/l* 83.1%

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

      6. fma-def 83.1%

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

      7. times-frac 81.5%

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

      8. *-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in z around 0 88.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-204}:\\ \;\;\;\;\frac{b + \left(t\_2 - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(b + \left(a \cdot \left(z \cdot \left(-4 \cdot t\right)\right) + t\_2\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (* x (* 9.0 y))))
   (if (<= t_1 -1e-204)
     (/ (+ b (- t_2 (* (* z 4.0) (* a t)))) (* z c))
     (if (<= t_1 0.0)
       (/ (+ (* 9.0 (/ (* x y) c)) (/ b c)) z)
       (if (<= t_1 INFINITY)
         (* (+ b (+ (* a (* z (* -4.0 t))) t_2)) (/ 1.0 (* z c)))
         (* -4.0 (* t (/ a c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = x * (9.0 * y);
	double tmp;
	if (t_1 <= -1e-204) {
		tmp = (b + (t_2 - ((z * 4.0) * (a * t)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((a * (z * (-4.0 * t))) + t_2)) * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = x * (9.0 * y);
	double tmp;
	if (t_1 <= -1e-204) {
		tmp = (b + (t_2 - ((z * 4.0) * (a * t)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b + ((a * (z * (-4.0 * t))) + t_2)) * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	t_2 = x * (9.0 * y)
	tmp = 0
	if t_1 <= -1e-204:
		tmp = (b + (t_2 - ((z * 4.0) * (a * t)))) / (z * c)
	elif t_1 <= 0.0:
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z
	elif t_1 <= math.inf:
		tmp = (b + ((a * (z * (-4.0 * t))) + t_2)) * (1.0 / (z * c))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = Float64(x * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= -1e-204)
		tmp = Float64(Float64(b + Float64(t_2 - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(a * Float64(z * Float64(-4.0 * t))) + t_2)) * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	t_2 = x * (9.0 * y);
	tmp = 0.0;
	if (t_1 <= -1e-204)
		tmp = (b + (t_2 - ((z * 4.0) * (a * t)))) / (z * c);
	elseif (t_1 <= 0.0)
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	elseif (t_1 <= Inf)
		tmp = (b + ((a * (z * (-4.0 * t))) + t_2)) * (1.0 / (z * c));
	else
		tmp = -4.0 * (t * (a / 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.
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[(9.0 * x), $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[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-204], N[(N[(b + N[(t$95$2 - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1e-204

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-+l- 93.0%

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

      6. *-commutative 93.0%

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

      7. associate-*r* 90.0%

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

      8. *-commutative 90.0%

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

      9. associate-*l* 90.0%

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

      10. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   if -1e-204 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 60.3%

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

      1. associate-+l- 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-*r* 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-+l- 59.8%

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

      6. *-commutative 59.8%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-*l* 60.3%

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

      10. associate-*l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in x around inf 55.6%

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

      1. associate-*r* 55.6%

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

      2. *-commutative 55.6%

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

      3. associate-*r* 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in x around 0 55.6%

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

   9. Taylor expanded in z around 0 85.2%

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

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

   1. Initial program 90.6%

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

      1. associate-+l- 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+l- 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*r* 90.6%

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

      8. *-commutative 90.6%

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

      9. associate-*l* 90.7%

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

      10. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. div-inv 89.8%

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

      2. associate-*r* 90.6%

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

      3. cancel-sign-sub-inv 90.6%

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

      4. fma-def 90.6%

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

      5. distribute-lft-neg-in 90.6%

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

      6. *-commutative 90.6%

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

      7. distribute-rgt-neg-in 90.6%

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

      8. distribute-lft-neg-in 90.6%

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

      9. distribute-rgt-neg-in 90.6%

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

      10. metadata-eval 90.6%

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

      11. associate-*r* 90.6%

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

      12. *-commutative 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. fma-udef 90.6%

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

   8. Applied egg-rr 90.6%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) 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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 6.7%

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

      4. *-commutative 6.7%

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

      5. associate-+l- 6.7%

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

      6. *-commutative 6.7%

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

      7. associate-*r* 0.0%

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

      8. *-commutative 0.0%

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

      9. associate-*l* 0.0%

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

      10. associate-*l* 6.7%

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

   3. Simplified 6.7%

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

      1. div-inv 6.7%

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

      2. associate-*r* 0.0%

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

      3. cancel-sign-sub-inv 0.0%

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

      4. fma-def 0.0%

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

      5. distribute-lft-neg-in 0.0%

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

      6. *-commutative 0.0%

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

      7. distribute-rgt-neg-in 0.0%

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

      8. distribute-lft-neg-in 0.0%

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

      9. distribute-rgt-neg-in 0.0%

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

      10. metadata-eval 0.0%

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

      11. associate-*r* 0.0%

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

      12. *-commutative 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in a around inf 55.1%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -1 \cdot 10^{-204}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\left(b + \left(a \cdot \left(z \cdot \left(-4 \cdot t\right)\right) + x \cdot \left(9 \cdot y\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-204}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -1e-204)
     (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* z c))
     (if (<= t_1 0.0)
       (/ (+ (* 9.0 (/ (* x y) c)) (/ b c)) z)
       (if (<= t_1 INFINITY) t_1 (* -4.0 (* t (/ a c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-204) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-204) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -1e-204:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c)
	elif t_1 <= 0.0:
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-204)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -1e-204)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	elseif (t_1 <= 0.0)
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = -4.0 * (t * (a / 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.
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[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-204], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1e-204

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-+l- 93.0%

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

      6. *-commutative 93.0%

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

      7. associate-*r* 90.0%

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

      8. *-commutative 90.0%

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

      9. associate-*l* 90.0%

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

      10. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   if -1e-204 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 60.3%

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

      1. associate-+l- 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-*r* 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-+l- 59.8%

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

      6. *-commutative 59.8%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-*l* 60.3%

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

      10. associate-*l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in x around inf 55.6%

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

      1. associate-*r* 55.6%

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

      2. *-commutative 55.6%

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

      3. associate-*r* 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in x around 0 55.6%

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

   9. Taylor expanded in z around 0 85.2%

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

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

   1. Initial program 90.6%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) 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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 6.7%

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

      4. *-commutative 6.7%

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

      5. associate-+l- 6.7%

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

      6. *-commutative 6.7%

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

      7. associate-*r* 0.0%

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

      8. *-commutative 0.0%

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

      9. associate-*l* 0.0%

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

      10. associate-*l* 6.7%

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

   3. Simplified 6.7%

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

      1. div-inv 6.7%

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

      2. associate-*r* 0.0%

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

      3. cancel-sign-sub-inv 0.0%

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

      4. fma-def 0.0%

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

      5. distribute-lft-neg-in 0.0%

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

      6. *-commutative 0.0%

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

      7. distribute-rgt-neg-in 0.0%

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

      8. distribute-lft-neg-in 0.0%

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

      9. distribute-rgt-neg-in 0.0%

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

      10. metadata-eval 0.0%

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

      11. associate-*r* 0.0%

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

      12. *-commutative 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in a around inf 55.1%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -1 \cdot 10^{-204}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -135:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 3500000:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 y) (/ x (* z c)))))
   (if (<= z -2.35e+145)
     (* -4.0 (* t (/ a c)))
     (if (<= z -4.5e+104)
       t_1
       (if (<= z -135.0)
         (/ (/ b z) c)
         (if (<= z -3.2e-298)
           t_1
           (if (<= z 2.02e-227)
             (* b (/ 1.0 (* z c)))
             (if (<= z 3500000.0)
               (* 9.0 (/ y (* c (/ z x))))
               (/ (* a (* -4.0 t)) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * y) * (x / (z * c));
	double tmp;
	if (z <= -2.35e+145) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -4.5e+104) {
		tmp = t_1;
	} else if (z <= -135.0) {
		tmp = (b / z) / c;
	} else if (z <= -3.2e-298) {
		tmp = t_1;
	} else if (z <= 2.02e-227) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 3500000.0) {
		tmp = 9.0 * (y / (c * (z / x)));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (9.0d0 * y) * (x / (z * c))
    if (z <= (-2.35d+145)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-4.5d+104)) then
        tmp = t_1
    else if (z <= (-135.0d0)) then
        tmp = (b / z) / c
    else if (z <= (-3.2d-298)) then
        tmp = t_1
    else if (z <= 2.02d-227) then
        tmp = b * (1.0d0 / (z * c))
    else if (z <= 3500000.0d0) then
        tmp = 9.0d0 * (y / (c * (z / x)))
    else
        tmp = (a * ((-4.0d0) * t)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * y) * (x / (z * c));
	double tmp;
	if (z <= -2.35e+145) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -4.5e+104) {
		tmp = t_1;
	} else if (z <= -135.0) {
		tmp = (b / z) / c;
	} else if (z <= -3.2e-298) {
		tmp = t_1;
	} else if (z <= 2.02e-227) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 3500000.0) {
		tmp = 9.0 * (y / (c * (z / x)));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 * y) * (x / (z * c))
	tmp = 0
	if z <= -2.35e+145:
		tmp = -4.0 * (t * (a / c))
	elif z <= -4.5e+104:
		tmp = t_1
	elif z <= -135.0:
		tmp = (b / z) / c
	elif z <= -3.2e-298:
		tmp = t_1
	elif z <= 2.02e-227:
		tmp = b * (1.0 / (z * c))
	elif z <= 3500000.0:
		tmp = 9.0 * (y / (c * (z / x)))
	else:
		tmp = (a * (-4.0 * t)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * y) * Float64(x / Float64(z * c)))
	tmp = 0.0
	if (z <= -2.35e+145)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -4.5e+104)
		tmp = t_1;
	elseif (z <= -135.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (z <= -3.2e-298)
		tmp = t_1;
	elseif (z <= 2.02e-227)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (z <= 3500000.0)
		tmp = Float64(9.0 * Float64(y / Float64(c * Float64(z / x))));
	else
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * y) * (x / (z * c));
	tmp = 0.0;
	if (z <= -2.35e+145)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -4.5e+104)
		tmp = t_1;
	elseif (z <= -135.0)
		tmp = (b / z) / c;
	elseif (z <= -3.2e-298)
		tmp = t_1;
	elseif (z <= 2.02e-227)
		tmp = b * (1.0 / (z * c));
	elseif (z <= 3500000.0)
		tmp = 9.0 * (y / (c * (z / x)));
	else
		tmp = (a * (-4.0 * t)) / 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.
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[(9.0 * y), $MachinePrecision] * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+145], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e+104], t$95$1, If[LessEqual[z, -135.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -3.2e-298], t$95$1, If[LessEqual[z, 2.02e-227], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3500000.0], N[(9.0 * N[(y / N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.3500000000000001e145

   1. Initial program 49.6%

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

      1. associate-+l- 49.6%

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

      2. *-commutative 49.6%

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

      3. associate-*r* 49.8%

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

      4. *-commutative 49.8%

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

      5. associate-+l- 49.8%

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

      6. *-commutative 49.8%

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

      7. associate-*r* 49.6%

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

      8. *-commutative 49.6%

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

      9. associate-*l* 49.6%

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

      10. associate-*l* 53.4%

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

   3. Simplified 53.4%

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

      1. div-inv 53.4%

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

      2. associate-*r* 49.5%

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

      3. cancel-sign-sub-inv 49.5%

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

      4. fma-def 49.5%

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

      5. distribute-lft-neg-in 49.5%

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

      6. *-commutative 49.5%

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

      7. distribute-rgt-neg-in 49.5%

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

      8. distribute-lft-neg-in 49.5%

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

      9. distribute-rgt-neg-in 49.5%

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

      10. metadata-eval 49.5%

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

      11. associate-*r* 49.5%

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

      12. *-commutative 49.5%

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

   6. Applied egg-rr 49.5%

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

   7. Taylor expanded in a around inf 65.5%

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

      1. associate-*l/ 65.7%

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

      2. *-commutative 65.7%

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

   9. Simplified 65.7%

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

   if -2.3500000000000001e145 < z < -4.4999999999999998e104 or -135 < z < -3.19999999999999997e-298

   1. Initial program 95.5%

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

      1. associate-+l- 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 95.5%

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

      4. *-commutative 95.5%

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

      5. associate-+l- 95.5%

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

      6. *-commutative 95.5%

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

      7. associate-*r* 95.5%

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

      8. *-commutative 95.5%

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

      9. associate-*l* 95.5%

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

      10. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

      1. div-inv 93.1%

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

      2. associate-*r* 95.5%

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

      3. cancel-sign-sub-inv 95.5%

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

      4. fma-def 95.5%

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

      5. distribute-lft-neg-in 95.5%

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

      6. *-commutative 95.5%

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

      7. distribute-rgt-neg-in 95.5%

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

      8. distribute-lft-neg-in 95.5%

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

      9. distribute-rgt-neg-in 95.5%

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

      10. metadata-eval 95.5%

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

      11. associate-*r* 95.5%

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

      12. *-commutative 95.5%

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

   6. Applied egg-rr 95.5%

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

      1. fma-udef 95.5%

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

   8. Applied egg-rr 95.5%

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

   9. Taylor expanded in x around inf 62.1%

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

       1. associate-*r/ 62.1%

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

       2. associate-*r* 62.2%

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

       3. *-commutative 62.2%

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

       4. associate-*r* 62.2%

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

       5. *-commutative 62.2%

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

       6. associate-/l* 70.9%

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

       7. associate-/r/ 66.2%

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

   11. Simplified 66.2%

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

   if -4.4999999999999998e104 < z < -135

   1. Initial program 83.1%

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

      1. associate-+l- 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-*r* 87.7%

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

      4. *-commutative 87.7%

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

      5. associate-+l- 87.7%

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

      6. *-commutative 87.7%

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

      7. associate-*r* 83.1%

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

      8. *-commutative 83.1%

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

      9. associate-*l* 83.1%

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

      10. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. div-inv 92.0%

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

      2. associate-*r* 83.3%

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

      3. cancel-sign-sub-inv 83.3%

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

      4. fma-def 83.3%

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

      5. distribute-lft-neg-in 83.3%

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

      6. *-commutative 83.3%

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

      7. distribute-rgt-neg-in 83.3%

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

      8. distribute-lft-neg-in 83.3%

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

      9. distribute-rgt-neg-in 83.3%

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

      10. metadata-eval 83.3%

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

      11. associate-*r* 83.3%

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

      12. *-commutative 83.3%

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

   6. Applied egg-rr 83.3%

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

   7. Taylor expanded in b around inf 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-/r* 71.0%

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

   9. Simplified 71.0%

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

   if -3.19999999999999997e-298 < z < 2.0200000000000001e-227

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-+l- 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-*r* 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

      1. div-inv 72.2%

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

   9. Applied egg-rr 72.2%

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

   if 2.0200000000000001e-227 < z < 3.5e6

   1. Initial program 93.4%

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

      1. associate-+l- 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*r* 93.5%

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

      4. *-commutative 93.5%

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

      5. associate-+l- 93.5%

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

      6. *-commutative 93.5%

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

      7. associate-*r* 93.4%

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

      8. *-commutative 93.4%

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

      9. associate-*l* 93.4%

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

      10. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 52.8%

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

      4. *-commutative 52.8%

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

      5. times-frac 50.7%

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

   7. Simplified 50.7%

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

      1. associate-*l/ 52.8%

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

   9. Applied egg-rr 52.8%

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

       1. associate-/l* 52.8%

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

   11. Simplified 52.8%

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

       1. *-un-lft-identity 52.8%

          \[\leadsto \frac{9 \cdot y}{\color{blue}{1 \cdot \frac{z}{\frac{x}{c}}}} \]

       2. times-frac 52.8%

          \[\leadsto \color{blue}{\frac{9}{1} \cdot \frac{y}{\frac{z}{\frac{x}{c}}}} \]

       3. metadata-eval 52.8%

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

       4. associate-/r/ 52.8%

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

   13. Applied egg-rr 52.8%

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

   if 3.5e6 < z

   1. Initial program 68.4%

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

      1. associate-+l- 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

      6. *-commutative 73.8%

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

      7. associate-*r* 68.4%

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

      8. *-commutative 68.4%

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

      9. associate-*l* 68.5%

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

      10. associate-*l* 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*l/ 58.9%

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

      4. *-commutative 58.9%

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

      5. associate-*r* 58.9%

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

      6. *-commutative 58.9%

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

      7. *-commutative 58.9%

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

   7. Simplified 58.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+104}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq -135:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-298}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 3500000:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq -350:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-298}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 300000:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.35e+145)
   (* -4.0 (* t (/ a c)))
   (if (<= z -1.1e+107)
     (/ 9.0 (* (/ z y) (/ c x)))
     (if (<= z -350.0)
       (/ (/ b z) c)
       (if (<= z -8.6e-298)
         (* (* 9.0 y) (/ x (* z c)))
         (if (<= z 1.02e-224)
           (* b (/ 1.0 (* z c)))
           (if (<= z 300000.0)
             (* 9.0 (/ y (* c (/ z x))))
             (/ (* a (* -4.0 t)) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.35e+145) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -1.1e+107) {
		tmp = 9.0 / ((z / y) * (c / x));
	} else if (z <= -350.0) {
		tmp = (b / z) / c;
	} else if (z <= -8.6e-298) {
		tmp = (9.0 * y) * (x / (z * c));
	} else if (z <= 1.02e-224) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 300000.0) {
		tmp = 9.0 * (y / (c * (z / x)));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-2.35d+145)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-1.1d+107)) then
        tmp = 9.0d0 / ((z / y) * (c / x))
    else if (z <= (-350.0d0)) then
        tmp = (b / z) / c
    else if (z <= (-8.6d-298)) then
        tmp = (9.0d0 * y) * (x / (z * c))
    else if (z <= 1.02d-224) then
        tmp = b * (1.0d0 / (z * c))
    else if (z <= 300000.0d0) then
        tmp = 9.0d0 * (y / (c * (z / x)))
    else
        tmp = (a * ((-4.0d0) * t)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.35e+145) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -1.1e+107) {
		tmp = 9.0 / ((z / y) * (c / x));
	} else if (z <= -350.0) {
		tmp = (b / z) / c;
	} else if (z <= -8.6e-298) {
		tmp = (9.0 * y) * (x / (z * c));
	} else if (z <= 1.02e-224) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 300000.0) {
		tmp = 9.0 * (y / (c * (z / x)));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -2.35e+145:
		tmp = -4.0 * (t * (a / c))
	elif z <= -1.1e+107:
		tmp = 9.0 / ((z / y) * (c / x))
	elif z <= -350.0:
		tmp = (b / z) / c
	elif z <= -8.6e-298:
		tmp = (9.0 * y) * (x / (z * c))
	elif z <= 1.02e-224:
		tmp = b * (1.0 / (z * c))
	elif z <= 300000.0:
		tmp = 9.0 * (y / (c * (z / x)))
	else:
		tmp = (a * (-4.0 * t)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.35e+145)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -1.1e+107)
		tmp = Float64(9.0 / Float64(Float64(z / y) * Float64(c / x)));
	elseif (z <= -350.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (z <= -8.6e-298)
		tmp = Float64(Float64(9.0 * y) * Float64(x / Float64(z * c)));
	elseif (z <= 1.02e-224)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (z <= 300000.0)
		tmp = Float64(9.0 * Float64(y / Float64(c * Float64(z / x))));
	else
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -2.35e+145)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -1.1e+107)
		tmp = 9.0 / ((z / y) * (c / x));
	elseif (z <= -350.0)
		tmp = (b / z) / c;
	elseif (z <= -8.6e-298)
		tmp = (9.0 * y) * (x / (z * c));
	elseif (z <= 1.02e-224)
		tmp = b * (1.0 / (z * c));
	elseif (z <= 300000.0)
		tmp = 9.0 * (y / (c * (z / x)));
	else
		tmp = (a * (-4.0 * t)) / 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.
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, -2.35e+145], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e+107], N[(9.0 / N[(N[(z / y), $MachinePrecision] * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -350.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -8.6e-298], N[(N[(9.0 * y), $MachinePrecision] * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-224], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 300000.0], N[(9.0 * N[(y / N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.3500000000000001e145

   1. Initial program 49.6%

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

      1. associate-+l- 49.6%

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

      2. *-commutative 49.6%

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

      3. associate-*r* 49.8%

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

      4. *-commutative 49.8%

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

      5. associate-+l- 49.8%

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

      6. *-commutative 49.8%

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

      7. associate-*r* 49.6%

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

      8. *-commutative 49.6%

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

      9. associate-*l* 49.6%

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

      10. associate-*l* 53.4%

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

   3. Simplified 53.4%

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

      1. div-inv 53.4%

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

      2. associate-*r* 49.5%

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

      3. cancel-sign-sub-inv 49.5%

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

      4. fma-def 49.5%

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

      5. distribute-lft-neg-in 49.5%

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

      6. *-commutative 49.5%

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

      7. distribute-rgt-neg-in 49.5%

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

      8. distribute-lft-neg-in 49.5%

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

      9. distribute-rgt-neg-in 49.5%

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

      10. metadata-eval 49.5%

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

      11. associate-*r* 49.5%

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

      12. *-commutative 49.5%

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

   6. Applied egg-rr 49.5%

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

   7. Taylor expanded in a around inf 65.5%

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

      1. associate-*l/ 65.7%

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

      2. *-commutative 65.7%

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

   9. Simplified 65.7%

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

   if -2.3500000000000001e145 < z < -1.1e107

   1. Initial program 81.2%

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

      1. associate-+l- 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*r* 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-+l- 81.2%

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

      6. *-commutative 81.2%

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

      7. associate-*r* 81.2%

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

      8. *-commutative 81.2%

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

      9. associate-*l* 81.2%

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

      10. associate-*l* 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in x around inf 71.3%

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

      1. associate-*r/ 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*r* 71.1%

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

      4. *-commutative 71.1%

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

      5. times-frac 86.5%

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

   7. Simplified 86.5%

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

      1. associate-/l* 86.2%

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

      2. clear-num 69.6%

         \[\leadsto \frac{9}{\frac{z}{y}} \cdot \color{blue}{\frac{1}{\frac{c}{x}}} \]

      3. frac-times 70.5%

         \[\leadsto \color{blue}{\frac{9 \cdot 1}{\frac{z}{y} \cdot \frac{c}{x}}} \]

      4. metadata-eval 70.5%

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

   9. Applied egg-rr 70.5%

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

   if -1.1e107 < z < -350

   1. Initial program 83.1%

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

      1. associate-+l- 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-*r* 87.7%

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

      4. *-commutative 87.7%

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

      5. associate-+l- 87.7%

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

      6. *-commutative 87.7%

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

      7. associate-*r* 83.1%

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

      8. *-commutative 83.1%

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

      9. associate-*l* 83.1%

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

      10. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. div-inv 92.0%

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

      2. associate-*r* 83.3%

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

      3. cancel-sign-sub-inv 83.3%

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

      4. fma-def 83.3%

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

      5. distribute-lft-neg-in 83.3%

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

      6. *-commutative 83.3%

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

      7. distribute-rgt-neg-in 83.3%

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

      8. distribute-lft-neg-in 83.3%

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

      9. distribute-rgt-neg-in 83.3%

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

      10. metadata-eval 83.3%

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

      11. associate-*r* 83.3%

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

      12. *-commutative 83.3%

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

   6. Applied egg-rr 83.3%

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

   7. Taylor expanded in b around inf 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-/r* 71.0%

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

   9. Simplified 71.0%

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

   if -350 < z < -8.600000000000001e-298

   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. Step-by-step derivation

      1. associate-+l- 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*r* 96.7%

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

      4. *-commutative 96.7%

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

      5. associate-+l- 96.7%

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

      6. *-commutative 96.7%

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

      7. associate-*r* 96.7%

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

      8. *-commutative 96.7%

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

      9. associate-*l* 96.7%

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

      10. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

      1. div-inv 94.9%

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

      2. associate-*r* 96.6%

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

      3. cancel-sign-sub-inv 96.6%

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

      4. fma-def 96.6%

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

      5. distribute-lft-neg-in 96.6%

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

      6. *-commutative 96.6%

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

      7. distribute-rgt-neg-in 96.6%

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

      8. distribute-lft-neg-in 96.6%

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

      9. distribute-rgt-neg-in 96.6%

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

      10. metadata-eval 96.6%

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

      11. associate-*r* 96.6%

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

      12. *-commutative 96.6%

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

   6. Applied egg-rr 96.6%

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

      1. fma-udef 96.6%

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

   8. Applied egg-rr 96.6%

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

   9. Taylor expanded in x around inf 61.3%

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

       1. associate-*r/ 61.4%

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

       2. associate-*r* 61.4%

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

       3. *-commutative 61.4%

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

       4. associate-*r* 61.4%

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

       5. *-commutative 61.4%

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

       6. associate-/l* 69.4%

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

       7. associate-/r/ 65.8%

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

   11. Simplified 65.8%

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

   if -8.600000000000001e-298 < z < 1.02e-224

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-+l- 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-*r* 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

      1. div-inv 72.2%

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

   9. Applied egg-rr 72.2%

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

   if 1.02e-224 < z < 3e5

   1. Initial program 93.4%

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

      1. associate-+l- 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*r* 93.5%

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

      4. *-commutative 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 93.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 93.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 93.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 93.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.8%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 52.8%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 52.8%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 52.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 52.8%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 50.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 52.8%

         \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]

   9. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]
   10. Step-by-step derivation

       1. associate-/l* 52.8%

          \[\leadsto \color{blue}{\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}} \]

   11. Simplified 52.8%

       \[\leadsto \color{blue}{\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 52.8%

          \[\leadsto \frac{9 \cdot y}{\color{blue}{1 \cdot \frac{z}{\frac{x}{c}}}} \]

       2. times-frac 52.8%

          \[\leadsto \color{blue}{\frac{9}{1} \cdot \frac{y}{\frac{z}{\frac{x}{c}}}} \]

       3. metadata-eval 52.8%

          \[\leadsto \color{blue}{9} \cdot \frac{y}{\frac{z}{\frac{x}{c}}} \]

       4. associate-/r/ 52.8%

          \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z}{x} \cdot c}} \]

   13. Applied egg-rr 52.8%

       \[\leadsto \color{blue}{9 \cdot \frac{y}{\frac{z}{x} \cdot c}} \]

   if 3e5 < z

   1. Initial program 68.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 73.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 68.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-*l/ 58.9%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

      4. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(t \cdot a\right)}}{c} \]

      5. associate-*r* 58.9%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot t\right) \cdot a}}{c} \]

      6. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{\left(t \cdot -4\right)} \cdot a}{c} \]

      7. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)}}{c} \]

   7. Simplified 58.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq -350:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-298}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 300000:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+143}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq -230:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-297}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 16500000:\\ \;\;\;\;\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.5e+143)
   (* -4.0 (* t (/ a c)))
   (if (<= z -2.1e+102)
     (/ 9.0 (* (/ z y) (/ c x)))
     (if (<= z -230.0)
       (/ (/ b z) c)
       (if (<= z -1.06e-297)
         (* (* 9.0 y) (/ x (* z c)))
         (if (<= z 1.4e-222)
           (* b (/ 1.0 (* z c)))
           (if (<= z 16500000.0)
             (/ (* 9.0 y) (/ z (/ x c)))
             (/ (* a (* -4.0 t)) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.5e+143) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.1e+102) {
		tmp = 9.0 / ((z / y) * (c / x));
	} else if (z <= -230.0) {
		tmp = (b / z) / c;
	} else if (z <= -1.06e-297) {
		tmp = (9.0 * y) * (x / (z * c));
	} else if (z <= 1.4e-222) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 16500000.0) {
		tmp = (9.0 * y) / (z / (x / c));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-7.5d+143)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-2.1d+102)) then
        tmp = 9.0d0 / ((z / y) * (c / x))
    else if (z <= (-230.0d0)) then
        tmp = (b / z) / c
    else if (z <= (-1.06d-297)) then
        tmp = (9.0d0 * y) * (x / (z * c))
    else if (z <= 1.4d-222) then
        tmp = b * (1.0d0 / (z * c))
    else if (z <= 16500000.0d0) then
        tmp = (9.0d0 * y) / (z / (x / c))
    else
        tmp = (a * ((-4.0d0) * t)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.5e+143) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.1e+102) {
		tmp = 9.0 / ((z / y) * (c / x));
	} else if (z <= -230.0) {
		tmp = (b / z) / c;
	} else if (z <= -1.06e-297) {
		tmp = (9.0 * y) * (x / (z * c));
	} else if (z <= 1.4e-222) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 16500000.0) {
		tmp = (9.0 * y) / (z / (x / c));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7.5e+143:
		tmp = -4.0 * (t * (a / c))
	elif z <= -2.1e+102:
		tmp = 9.0 / ((z / y) * (c / x))
	elif z <= -230.0:
		tmp = (b / z) / c
	elif z <= -1.06e-297:
		tmp = (9.0 * y) * (x / (z * c))
	elif z <= 1.4e-222:
		tmp = b * (1.0 / (z * c))
	elif z <= 16500000.0:
		tmp = (9.0 * y) / (z / (x / c))
	else:
		tmp = (a * (-4.0 * t)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.5e+143)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -2.1e+102)
		tmp = Float64(9.0 / Float64(Float64(z / y) * Float64(c / x)));
	elseif (z <= -230.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (z <= -1.06e-297)
		tmp = Float64(Float64(9.0 * y) * Float64(x / Float64(z * c)));
	elseif (z <= 1.4e-222)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (z <= 16500000.0)
		tmp = Float64(Float64(9.0 * y) / Float64(z / Float64(x / c)));
	else
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7.5e+143)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -2.1e+102)
		tmp = 9.0 / ((z / y) * (c / x));
	elseif (z <= -230.0)
		tmp = (b / z) / c;
	elseif (z <= -1.06e-297)
		tmp = (9.0 * y) * (x / (z * c));
	elseif (z <= 1.4e-222)
		tmp = b * (1.0 / (z * c));
	elseif (z <= 16500000.0)
		tmp = (9.0 * y) / (z / (x / c));
	else
		tmp = (a * (-4.0 * t)) / 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.
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, -7.5e+143], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e+102], N[(9.0 / N[(N[(z / y), $MachinePrecision] * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -230.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -1.06e-297], N[(N[(9.0 * y), $MachinePrecision] * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-222], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 16500000.0], N[(N[(9.0 * y), $MachinePrecision] / N[(z / N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -7.49999999999999974e143

   1. Initial program 49.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 49.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 49.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 49.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 49.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 49.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 49.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 49.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 49.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 49.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 53.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 53.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 49.5%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 49.5%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 49.5%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 49.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 49.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 49.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 49.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 65.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 65.7%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 65.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 65.7%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -7.49999999999999974e143 < z < -2.10000000000000001e102

   1. Initial program 81.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 71.1%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 71.1%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 71.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 71.1%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 86.5%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]
   8. Step-by-step derivation

      1. associate-/l* 86.2%

         \[\leadsto \color{blue}{\frac{9}{\frac{z}{y}}} \cdot \frac{x}{c} \]

      2. clear-num 69.6%

         \[\leadsto \frac{9}{\frac{z}{y}} \cdot \color{blue}{\frac{1}{\frac{c}{x}}} \]

      3. frac-times 70.5%

         \[\leadsto \color{blue}{\frac{9 \cdot 1}{\frac{z}{y} \cdot \frac{c}{x}}} \]

      4. metadata-eval 70.5%

         \[\leadsto \frac{\color{blue}{9}}{\frac{z}{y} \cdot \frac{c}{x}} \]

   9. Applied egg-rr 70.5%

      \[\leadsto \color{blue}{\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}} \]

   if -2.10000000000000001e102 < z < -230

   1. Initial program 83.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 87.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 83.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 83.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 92.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 83.3%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 83.3%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 83.3%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 83.3%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 83.3%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 83.3%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in b around inf 70.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 70.8%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 71.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if -230 < z < -1.06e-297

   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. Step-by-step derivation

      1. associate-+l- 96.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 96.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 96.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 96.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 96.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 95.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 94.9%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 96.6%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 96.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 96.6%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 96.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 96.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 96.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. fma-udef 96.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   8. Applied egg-rr 96.6%

      \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   9. Taylor expanded in x around inf 61.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 61.4%

          \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

       2. associate-*r* 61.4%

          \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

       3. *-commutative 61.4%

          \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y}{c \cdot z} \]

       4. associate-*r* 61.4%

          \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{c \cdot z} \]

       5. *-commutative 61.4%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{z \cdot c}} \]

       6. associate-/l* 69.4%

          \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot c}{9 \cdot y}}} \]

       7. associate-/r/ 65.8%

          \[\leadsto \color{blue}{\frac{x}{z \cdot c} \cdot \left(9 \cdot y\right)} \]

   11. Simplified 65.8%

       \[\leadsto \color{blue}{\frac{x}{z \cdot c} \cdot \left(9 \cdot y\right)} \]

   if -1.06e-297 < z < 1.40000000000000004e-222

   1. Initial program 99.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 99.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 99.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 99.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 99.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 99.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 99.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 69.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 69.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 72.2%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 72.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   if 1.40000000000000004e-222 < z < 1.65e7

   1. Initial program 93.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 93.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 93.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 93.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 93.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 93.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 93.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.8%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 52.8%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 52.8%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 52.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 52.8%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 50.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 52.8%

         \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]

   9. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]
   10. Step-by-step derivation

       1. associate-/l* 52.8%

          \[\leadsto \color{blue}{\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}} \]

   11. Simplified 52.8%

       \[\leadsto \color{blue}{\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}} \]

   if 1.65e7 < z

   1. Initial program 68.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 73.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 68.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-*l/ 58.9%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

      4. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(t \cdot a\right)}}{c} \]

      5. associate-*r* 58.9%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot t\right) \cdot a}}{c} \]

      6. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{\left(t \cdot -4\right)} \cdot a}{c} \]

      7. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)}}{c} \]

   7. Simplified 58.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+143}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq -230:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-297}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 16500000:\\ \;\;\;\;\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+100}:\\ \;\;\;\;\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq -370:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-298}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;\frac{\frac{x}{c} \cdot \left(9 \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5.6e+144)
   (* -4.0 (* t (/ a c)))
   (if (<= z -1.25e+100)
     (/ 9.0 (* (/ z y) (/ c x)))
     (if (<= z -370.0)
       (/ (/ b z) c)
       (if (<= z -2.5e-298)
         (* (* 9.0 y) (/ x (* z c)))
         (if (<= z 1.15e-226)
           (* b (/ 1.0 (* z c)))
           (if (<= z 46000000.0)
             (/ (* (/ x c) (* 9.0 y)) z)
             (/ (* a (* -4.0 t)) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.6e+144) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -1.25e+100) {
		tmp = 9.0 / ((z / y) * (c / x));
	} else if (z <= -370.0) {
		tmp = (b / z) / c;
	} else if (z <= -2.5e-298) {
		tmp = (9.0 * y) * (x / (z * c));
	} else if (z <= 1.15e-226) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 46000000.0) {
		tmp = ((x / c) * (9.0 * y)) / z;
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-5.6d+144)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-1.25d+100)) then
        tmp = 9.0d0 / ((z / y) * (c / x))
    else if (z <= (-370.0d0)) then
        tmp = (b / z) / c
    else if (z <= (-2.5d-298)) then
        tmp = (9.0d0 * y) * (x / (z * c))
    else if (z <= 1.15d-226) then
        tmp = b * (1.0d0 / (z * c))
    else if (z <= 46000000.0d0) then
        tmp = ((x / c) * (9.0d0 * y)) / z
    else
        tmp = (a * ((-4.0d0) * t)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.6e+144) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -1.25e+100) {
		tmp = 9.0 / ((z / y) * (c / x));
	} else if (z <= -370.0) {
		tmp = (b / z) / c;
	} else if (z <= -2.5e-298) {
		tmp = (9.0 * y) * (x / (z * c));
	} else if (z <= 1.15e-226) {
		tmp = b * (1.0 / (z * c));
	} else if (z <= 46000000.0) {
		tmp = ((x / c) * (9.0 * y)) / z;
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -5.6e+144:
		tmp = -4.0 * (t * (a / c))
	elif z <= -1.25e+100:
		tmp = 9.0 / ((z / y) * (c / x))
	elif z <= -370.0:
		tmp = (b / z) / c
	elif z <= -2.5e-298:
		tmp = (9.0 * y) * (x / (z * c))
	elif z <= 1.15e-226:
		tmp = b * (1.0 / (z * c))
	elif z <= 46000000.0:
		tmp = ((x / c) * (9.0 * y)) / z
	else:
		tmp = (a * (-4.0 * t)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.6e+144)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -1.25e+100)
		tmp = Float64(9.0 / Float64(Float64(z / y) * Float64(c / x)));
	elseif (z <= -370.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (z <= -2.5e-298)
		tmp = Float64(Float64(9.0 * y) * Float64(x / Float64(z * c)));
	elseif (z <= 1.15e-226)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (z <= 46000000.0)
		tmp = Float64(Float64(Float64(x / c) * Float64(9.0 * y)) / z);
	else
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -5.6e+144)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -1.25e+100)
		tmp = 9.0 / ((z / y) * (c / x));
	elseif (z <= -370.0)
		tmp = (b / z) / c;
	elseif (z <= -2.5e-298)
		tmp = (9.0 * y) * (x / (z * c));
	elseif (z <= 1.15e-226)
		tmp = b * (1.0 / (z * c));
	elseif (z <= 46000000.0)
		tmp = ((x / c) * (9.0 * y)) / z;
	else
		tmp = (a * (-4.0 * t)) / 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.
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, -5.6e+144], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e+100], N[(9.0 / N[(N[(z / y), $MachinePrecision] * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -370.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -2.5e-298], N[(N[(9.0 * y), $MachinePrecision] * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-226], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 46000000.0], N[(N[(N[(x / c), $MachinePrecision] * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -5.60000000000000013e144

   1. Initial program 49.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 49.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 49.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 49.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 49.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 49.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 49.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 49.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 49.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 49.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 53.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 53.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 49.5%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 49.5%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 49.5%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 49.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 49.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 49.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 49.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 49.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 65.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 65.7%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 65.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 65.7%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -5.60000000000000013e144 < z < -1.25e100

   1. Initial program 81.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 71.1%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 71.1%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 71.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 71.1%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 86.5%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]
   8. Step-by-step derivation

      1. associate-/l* 86.2%

         \[\leadsto \color{blue}{\frac{9}{\frac{z}{y}}} \cdot \frac{x}{c} \]

      2. clear-num 69.6%

         \[\leadsto \frac{9}{\frac{z}{y}} \cdot \color{blue}{\frac{1}{\frac{c}{x}}} \]

      3. frac-times 70.5%

         \[\leadsto \color{blue}{\frac{9 \cdot 1}{\frac{z}{y} \cdot \frac{c}{x}}} \]

      4. metadata-eval 70.5%

         \[\leadsto \frac{\color{blue}{9}}{\frac{z}{y} \cdot \frac{c}{x}} \]

   9. Applied egg-rr 70.5%

      \[\leadsto \color{blue}{\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}} \]

   if -1.25e100 < z < -370

   1. Initial program 83.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 87.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 83.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 83.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 92.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 83.3%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 83.3%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 83.3%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 83.3%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 83.3%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 83.3%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 83.3%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in b around inf 70.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 70.8%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 71.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if -370 < z < -2.5000000000000001e-298

   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. Step-by-step derivation

      1. associate-+l- 96.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 96.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 96.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 96.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 96.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 95.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 94.9%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 96.6%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 96.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 96.6%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 96.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 96.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 96.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 96.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. fma-udef 96.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   8. Applied egg-rr 96.6%

      \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   9. Taylor expanded in x around inf 61.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 61.4%

          \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

       2. associate-*r* 61.4%

          \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

       3. *-commutative 61.4%

          \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y}{c \cdot z} \]

       4. associate-*r* 61.4%

          \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{c \cdot z} \]

       5. *-commutative 61.4%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{z \cdot c}} \]

       6. associate-/l* 69.4%

          \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot c}{9 \cdot y}}} \]

       7. associate-/r/ 65.8%

          \[\leadsto \color{blue}{\frac{x}{z \cdot c} \cdot \left(9 \cdot y\right)} \]

   11. Simplified 65.8%

       \[\leadsto \color{blue}{\frac{x}{z \cdot c} \cdot \left(9 \cdot y\right)} \]

   if -2.5000000000000001e-298 < z < 1.15e-226

   1. Initial program 99.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 99.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 99.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 99.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 99.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 99.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 99.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 69.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 69.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 72.2%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 72.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   if 1.15e-226 < z < 4.6e7

   1. Initial program 93.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 93.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 93.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 93.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 93.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 93.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 93.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.8%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 52.8%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 52.8%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 52.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 52.8%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 50.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 52.8%

         \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]

   9. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]

   if 4.6e7 < z

   1. Initial program 68.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 73.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 68.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-*l/ 58.9%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

      4. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(t \cdot a\right)}}{c} \]

      5. associate-*r* 58.9%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot t\right) \cdot a}}{c} \]

      6. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{\left(t \cdot -4\right)} \cdot a}{c} \]

      7. *-commutative 58.9%

         \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)}}{c} \]

   7. Simplified 58.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+100}:\\ \;\;\;\;\frac{9}{\frac{z}{y} \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq -370:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-298}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;\frac{\frac{x}{c} \cdot \left(9 \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 47000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+83}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* x (* 9.0 y))) (* z c))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= z -4.5e+141)
     t_2
     (if (<= z 47000000000000.0)
       t_1
       (if (<= z 9e+83)
         (/ (* a (* -4.0 t)) c)
         (if (<= z 1.55e+111) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (x * (9.0 * y))) / (z * c);
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (z <= -4.5e+141) {
		tmp = t_2;
	} else if (z <= 47000000000000.0) {
		tmp = t_1;
	} else if (z <= 9e+83) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= 1.55e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = (b + (x * (9.0d0 * y))) / (z * c)
    t_2 = (-4.0d0) * (t * (a / c))
    if (z <= (-4.5d+141)) then
        tmp = t_2
    else if (z <= 47000000000000.0d0) then
        tmp = t_1
    else if (z <= 9d+83) then
        tmp = (a * ((-4.0d0) * t)) / c
    else if (z <= 1.55d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (x * (9.0 * y))) / (z * c);
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (z <= -4.5e+141) {
		tmp = t_2;
	} else if (z <= 47000000000000.0) {
		tmp = t_1;
	} else if (z <= 9e+83) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= 1.55e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (x * (9.0 * y))) / (z * c)
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if z <= -4.5e+141:
		tmp = t_2
	elif z <= 47000000000000.0:
		tmp = t_1
	elif z <= 9e+83:
		tmp = (a * (-4.0 * t)) / c
	elif z <= 1.55e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (z <= -4.5e+141)
		tmp = t_2;
	elseif (z <= 47000000000000.0)
		tmp = t_1;
	elseif (z <= 9e+83)
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	elseif (z <= 1.55e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 + (x * (9.0 * y))) / (z * c);
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (z <= -4.5e+141)
		tmp = t_2;
	elseif (z <= 47000000000000.0)
		tmp = t_1;
	elseif (z <= 9e+83)
		tmp = (a * (-4.0 * t)) / c;
	elseif (z <= 1.55e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+141], t$95$2, If[LessEqual[z, 47000000000000.0], t$95$1, If[LessEqual[z, 9e+83], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.55e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000002e141 or 1.55e111 < z

   1. Initial program 55.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 55.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 55.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 59.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 59.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 59.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 59.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 55.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 55.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 55.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 62.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 62.3%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 55.5%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 55.5%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 55.5%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 55.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 55.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 55.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 55.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 55.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 55.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 55.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 55.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 65.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 67.1%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 67.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 67.1%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -4.5000000000000002e141 < z < 4.7e13 or 8.9999999999999999e83 < z < 1.55e111

   1. Initial program 92.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 92.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 92.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 94.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 94.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 94.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 94.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 92.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 92.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 92.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 85.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 85.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 85.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 85.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 85.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 4.7e13 < z < 8.9999999999999999e83

   1. Initial program 99.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 99.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 92.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 92.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 92.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 92.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 99.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 99.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 70.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 70.6%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-*l/ 70.6%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

      4. *-commutative 70.6%

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(t \cdot a\right)}}{c} \]

      5. associate-*r* 70.6%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot t\right) \cdot a}}{c} \]

      6. *-commutative 70.6%

         \[\leadsto \frac{\color{blue}{\left(t \cdot -4\right)} \cdot a}{c} \]

      7. *-commutative 70.6%

         \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)}}{c} \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 47000000000000:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+83}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+183} \lor \neg \left(z \leq 3.1 \cdot 10^{+185}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.5e+183) (not (<= z 3.1e+185)))
   (* -4.0 (* t (/ a c)))
   (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.5e+183) || !(z <= 3.1e+185)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.5d+183)) .or. (.not. (z <= 3.1d+185))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (a * t)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.5e+183) || !(z <= 3.1e+185)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.5e+183) or not (z <= 3.1e+185):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.5e+183) || !(z <= 3.1e+185))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.5e+183) || ~((z <= 3.1e+185)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.5e+183], N[Not[LessEqual[z, 3.1e+185]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999987e183 or 3.1e185 < z

   1. Initial program 48.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 48.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 48.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 53.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 53.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 53.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 53.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 48.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 48.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 48.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 53.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 53.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 53.2%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 48.7%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 48.7%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 48.7%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 48.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 48.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 48.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 48.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 48.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 48.7%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 48.7%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 48.7%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 48.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 73.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 75.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 75.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -3.49999999999999987e183 < z < 3.1e185

   1. Initial program 89.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 89.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 89.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 91.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 89.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 89.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 90.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 90.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+183} \lor \neg \left(z \leq 3.1 \cdot 10^{+185}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5500000:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+169}:\\ \;\;\;\;\frac{b + z \cdot \left(a \cdot \left(-4 \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= z -7.2e+145)
     t_1
     (if (<= z 5500000.0)
       (/ (+ b (* x (* 9.0 y))) (* z c))
       (if (<= z 2.5e+169) (/ (+ b (* z (* a (* -4.0 t)))) (* z c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (z <= -7.2e+145) {
		tmp = t_1;
	} else if (z <= 5500000.0) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (z <= 2.5e+169) {
		tmp = (b + (z * (a * (-4.0 * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = (-4.0d0) * (t * (a / c))
    if (z <= (-7.2d+145)) then
        tmp = t_1
    else if (z <= 5500000.0d0) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else if (z <= 2.5d+169) then
        tmp = (b + (z * (a * ((-4.0d0) * t)))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (z <= -7.2e+145) {
		tmp = t_1;
	} else if (z <= 5500000.0) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (z <= 2.5e+169) {
		tmp = (b + (z * (a * (-4.0 * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if z <= -7.2e+145:
		tmp = t_1
	elif z <= 5500000.0:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	elif z <= 2.5e+169:
		tmp = (b + (z * (a * (-4.0 * t)))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (z <= -7.2e+145)
		tmp = t_1;
	elseif (z <= 5500000.0)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	elseif (z <= 2.5e+169)
		tmp = Float64(Float64(b + Float64(z * Float64(a * Float64(-4.0 * t)))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (z <= -7.2e+145)
		tmp = t_1;
	elseif (z <= 5500000.0)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	elseif (z <= 2.5e+169)
		tmp = (b + (z * (a * (-4.0 * t)))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+145], t$95$1, If[LessEqual[z, 5500000.0], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+169], N[(N[(b + N[(z * N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999948e145 or 2.50000000000000009e169 < z

   1. Initial program 52.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 52.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 52.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 55.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 55.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 55.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 55.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 52.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 52.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 52.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 57.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 57.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 57.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 52.1%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 52.1%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 52.1%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 52.1%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 52.1%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 52.1%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 52.1%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 52.1%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 52.1%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 52.1%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 52.1%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 70.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 72.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 72.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 72.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -7.19999999999999948e145 < z < 5.5e6

   1. Initial program 94.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 94.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 94.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 85.4%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 85.5%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 85.5%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 5.5e6 < z < 2.50000000000000009e169

   1. Initial program 78.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 78.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 78.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.2%

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative 66.2%

         \[\leadsto \frac{-4 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} + b}{z \cdot c} \]

      2. associate-*r* 66.2%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot \left(t \cdot z\right)\right) \cdot a} + b}{z \cdot c} \]

      3. associate-*l* 66.2%

         \[\leadsto \frac{\color{blue}{\left(\left(-4 \cdot t\right) \cdot z\right)} \cdot a + b}{z \cdot c} \]

      4. *-commutative 66.2%

         \[\leadsto \frac{\left(\color{blue}{\left(t \cdot -4\right)} \cdot z\right) \cdot a + b}{z \cdot c} \]

      5. *-commutative 66.2%

         \[\leadsto \frac{\color{blue}{\left(z \cdot \left(t \cdot -4\right)\right)} \cdot a + b}{z \cdot c} \]

      6. associate-*l* 75.7%

         \[\leadsto \frac{\color{blue}{z \cdot \left(\left(t \cdot -4\right) \cdot a\right)} + b}{z \cdot c} \]

      7. *-commutative 75.7%

         \[\leadsto \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot -4\right)\right)} + b}{z \cdot c} \]

   7. Simplified 75.7%

      \[\leadsto \frac{\color{blue}{z \cdot \left(a \cdot \left(t \cdot -4\right)\right)} + b}{z \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 5500000:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+169}:\\ \;\;\;\;\frac{b + z \cdot \left(a \cdot \left(-4 \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= a -4.1e-76)
     t_1
     (if (<= a 1.2e-189)
       (* 9.0 (/ y (* c (/ z x))))
       (if (<= a 2.25e+67) (/ (/ b z) c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -4.1e-76) {
		tmp = t_1;
	} else if (a <= 1.2e-189) {
		tmp = 9.0 * (y / (c * (z / x)));
	} else if (a <= 2.25e+67) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = (-4.0d0) * (t * (a / c))
    if (a <= (-4.1d-76)) then
        tmp = t_1
    else if (a <= 1.2d-189) then
        tmp = 9.0d0 * (y / (c * (z / x)))
    else if (a <= 2.25d+67) then
        tmp = (b / z) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -4.1e-76) {
		tmp = t_1;
	} else if (a <= 1.2e-189) {
		tmp = 9.0 * (y / (c * (z / x)));
	} else if (a <= 2.25e+67) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -4.1e-76:
		tmp = t_1
	elif a <= 1.2e-189:
		tmp = 9.0 * (y / (c * (z / x)))
	elif a <= 2.25e+67:
		tmp = (b / z) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -4.1e-76)
		tmp = t_1;
	elseif (a <= 1.2e-189)
		tmp = Float64(9.0 * Float64(y / Float64(c * Float64(z / x))));
	elseif (a <= 2.25e+67)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -4.1e-76)
		tmp = t_1;
	elseif (a <= 1.2e-189)
		tmp = 9.0 * (y / (c * (z / x)));
	elseif (a <= 2.25e+67)
		tmp = (b / z) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e-76], t$95$1, If[LessEqual[a, 1.2e-189], N[(9.0 * N[(y / N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+67], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.0999999999999998e-76 or 2.2499999999999999e67 < a

   1. Initial program 82.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 82.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 82.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 79.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 82.6%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 82.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 82.6%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 82.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 82.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 82.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 82.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 82.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 82.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 82.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 82.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 82.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 42.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 44.8%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 44.8%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 44.8%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -4.0999999999999998e-76 < a < 1.1999999999999999e-189

   1. Initial program 80.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 86.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 86.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.9%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 56.9%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 56.9%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 56.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 56.9%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 54.1%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 56.8%

         \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]

   9. Applied egg-rr 56.8%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}} \]
   10. Step-by-step derivation

       1. associate-/l* 53.9%

          \[\leadsto \color{blue}{\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}} \]

   11. Simplified 53.9%

       \[\leadsto \color{blue}{\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 53.9%

          \[\leadsto \frac{9 \cdot y}{\color{blue}{1 \cdot \frac{z}{\frac{x}{c}}}} \]

       2. times-frac 55.2%

          \[\leadsto \color{blue}{\frac{9}{1} \cdot \frac{y}{\frac{z}{\frac{x}{c}}}} \]

       3. metadata-eval 55.2%

          \[\leadsto \color{blue}{9} \cdot \frac{y}{\frac{z}{\frac{x}{c}}} \]

       4. associate-/r/ 60.2%

          \[\leadsto 9 \cdot \frac{y}{\color{blue}{\frac{z}{x} \cdot c}} \]

   13. Applied egg-rr 60.2%

       \[\leadsto \color{blue}{9 \cdot \frac{y}{\frac{z}{x} \cdot c}} \]

   if 1.1999999999999999e-189 < a < 2.2499999999999999e67

   1. Initial program 87.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 91.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 87.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 87.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 91.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 87.6%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 87.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 87.6%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 87.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 87.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 87.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 87.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 87.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 87.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 87.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 87.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 87.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in b around inf 58.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 56.4%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-76}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+123} \lor \neg \left(z \leq 2500000000000\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9e+123) (not (<= z 2500000000000.0)))
   (* -4.0 (* t (/ a c)))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9e+123) || !(z <= 2500000000000.0)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 ((z <= (-9d+123)) .or. (.not. (z <= 2500000000000.0d0))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 ((z <= -9e+123) || !(z <= 2500000000000.0)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -9e+123) or not (z <= 2500000000000.0):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9e+123) || !(z <= 2500000000000.0))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 ((z <= -9e+123) || ~((z <= 2500000000000.0)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9e+123], N[Not[LessEqual[z, 2500000000000.0]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999965e123 or 2.5e12 < z

   1. Initial program 63.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 67.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 63.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 63.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 63.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 69.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 69.8%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 63.2%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 63.2%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 63.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 63.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 63.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 63.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 63.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 59.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 59.5%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 59.5%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 59.5%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -8.99999999999999965e123 < z < 2.5e12

   1. Initial program 94.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 95.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 95.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 92.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+123} \lor \neg \left(z \leq 2500000000000\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+122} \lor \neg \left(z \leq 6800000000\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -7e+122) (not (<= z 6800000000.0)))
   (* -4.0 (* t (/ a c)))
   (* b (/ 1.0 (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7e+122) || !(z <= 6800000000.0)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-7d+122)) .or. (.not. (z <= 6800000000.0d0))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b * (1.0d0 / (z * c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7e+122) || !(z <= 6800000000.0)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7e+122) or not (z <= 6800000000.0):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b * (1.0 / (z * c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7e+122) || !(z <= 6800000000.0))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -7e+122) || ~((z <= 6800000000.0)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b * (1.0 / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -7e+122], N[Not[LessEqual[z, 6800000000.0]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000028e122 or 6.8e9 < z

   1. Initial program 63.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 67.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 63.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 63.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 63.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 69.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 69.8%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 63.2%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 63.2%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 63.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 63.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 63.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 63.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 63.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 63.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 59.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 59.5%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 59.5%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 59.5%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -7.00000000000000028e122 < z < 6.8e9

   1. Initial program 94.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 95.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 95.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 92.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 51.5%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 51.5%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+122} \lor \neg \left(z \leq 6800000000\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 2900000000000:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.85e+127)
   (* -4.0 (* t (/ a c)))
   (if (<= z 2900000000000.0) (* b (/ 1.0 (* z c))) (/ (* a (* -4.0 t)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.85e+127) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 2900000000000.0) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.85d+127)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= 2900000000000.0d0) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = (a * ((-4.0d0) * t)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.85e+127) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 2900000000000.0) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (a * (-4.0 * t)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.85e+127:
		tmp = -4.0 * (t * (a / c))
	elif z <= 2900000000000.0:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = (a * (-4.0 * t)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.85e+127)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= 2900000000000.0)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.85e+127)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= 2900000000000.0)
		tmp = b * (1.0 / (z * c));
	else
		tmp = (a * (-4.0 * t)) / 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.85e+127], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2900000000000.0], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8499999999999999e127

   1. Initial program 51.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 51.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 51.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 51.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 51.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 51.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 51.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 51.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 51.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 51.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 53.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 53.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-*r* 51.8%

         \[\leadsto \left(\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      3. cancel-sign-sub-inv 51.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      4. fma-def 51.8%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \left(-\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

      5. distribute-lft-neg-in 51.8%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. *-commutative 51.8%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. distribute-rgt-neg-in 51.8%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      8. distribute-lft-neg-in 51.8%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(\left(-z \cdot 4\right) \cdot t\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      9. distribute-rgt-neg-in 51.8%

         \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      10. metadata-eval 51.8%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(z \cdot \color{blue}{-4}\right) \cdot t\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      11. associate-*r* 51.8%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \color{blue}{\left(z \cdot \left(-4 \cdot t\right)\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      12. *-commutative 51.8%

          \[\leadsto \left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \color{blue}{\left(t \cdot -4\right)}\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

   6. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   7. Taylor expanded in a around inf 58.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 59.3%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 59.3%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   9. Simplified 59.3%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.8499999999999999e127 < z < 2.9e12

   1. Initial program 94.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 95.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 95.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 92.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 51.5%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 51.5%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   if 2.9e12 < z

   1. Initial program 67.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 67.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 67.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 73.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 67.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 67.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 59.7%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-*l/ 59.7%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

      4. *-commutative 59.7%

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(t \cdot a\right)}}{c} \]

      5. associate-*r* 59.7%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot t\right) \cdot a}}{c} \]

      6. *-commutative 59.7%

         \[\leadsto \frac{\color{blue}{\left(t \cdot -4\right)} \cdot a}{c} \]

      7. *-commutative 59.7%

         \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)}}{c} \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 2900000000000:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.8%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 82.8%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 82.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 84.7%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 84.7%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 84.7%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 84.7%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 82.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 82.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 82.9%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 83.8%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 83.8%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 40.4%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 40.4%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 40.4%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 40.4%

   \[\leadsto \frac{b}{z \cdot c} \]
9. Add Preprocessing

Developer target: 80.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))