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

Percentage Accurate: 78.5% → 87.5%

Time: 22.1s

Alternatives: 17

Speedup: 0.8×

• 37.2% 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: 78.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \mathsf{fma}\left(\frac{x}{z}, \frac{9}{\frac{c}{y}}, \frac{\frac{b}{z}}{c}\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-89}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - b\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.5e-57)
   (fma (/ (* a t) c) -4.0 (fma (/ x z) (/ 9.0 (/ c y)) (/ (/ b z) c)))
   (if (<= z 7e-89)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (/ (/ (- (* x (* 9.0 y)) (- (* (* z 4.0) (* a t)) b)) z) c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.5e-57) {
		tmp = fma(((a * t) / c), -4.0, fma((x / z), (9.0 / (c / y)), ((b / z) / c)));
	} else if (z <= 7e-89) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * (a * t)) - b)) / z) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.5e-57)
		tmp = fma(Float64(Float64(a * t) / c), -4.0, fma(Float64(x / z), Float64(9.0 / Float64(c / y)), Float64(Float64(b / z) / c)));
	elseif (z <= 7e-89)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(Float64(z * 4.0) * Float64(a * t)) - b)) / z) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.5e-57], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0 + N[(N[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-89], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e-57

   1. Initial program 66.5%

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

      1. associate-+l- 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in x around 0 84.7%

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

      1. cancel-sign-sub-inv 84.7%

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

      2. metadata-eval 84.7%

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

      3. +-commutative 84.7%

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

      4. *-commutative 84.7%

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

      5. fma-def 84.7%

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

      6. associate-*r/ 84.8%

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

      7. associate-*r* 84.8%

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

      8. *-commutative 84.8%

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

      9. associate-*r* 84.8%

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

      10. *-commutative 84.8%

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

      11. times-frac 89.8%

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

      12. fma-def 91.1%

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

      13. associate-/l* 91.0%

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

      14. *-commutative 91.0%

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

      15. associate-/r* 93.5%

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

   6. Simplified 93.5%

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

   if -1.5e-57 < z < 6.9999999999999994e-89

   1. Initial program 97.9%

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

   if 6.9999999999999994e-89 < z

   1. Initial program 73.6%

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

      1. associate-+l- 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 74.9%

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

      4. *-commutative 74.9%

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

      5. associate-+l- 74.9%

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

   3. Simplified 82.3%

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

      1. associate-/r* 87.5%

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

      2. div-inv 87.4%

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

      3. associate-+l- 87.4%

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

      4. associate-*r* 76.4%

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

      5. associate-+l- 76.4%

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

      6. associate-*l* 76.4%

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

      7. associate-*r* 87.4%

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

   5. Applied egg-rr 87.4%

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

      1. un-div-inv 87.5%

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

      2. associate-+l- 87.5%

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

   7. Applied egg-rr 87.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \mathsf{fma}\left(\frac{x}{z}, \frac{9}{\frac{c}{y}}, \frac{\frac{b}{z}}{c}\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-89}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - b\right)}{z}}{c}\\ \end{array} \]

Alternative 2: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{-10} \lor \neg \left(c \leq 7.8 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - b\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -2.6e-10) (not (<= c 7.8e-42)))
   (fma -4.0 (/ a (/ c t)) (/ (+ (* 9.0 (/ (* x y) c)) (/ b c)) z))
   (/ (/ (- (* x (* 9.0 y)) (- (* (* z 4.0) (* a t)) b)) z) c)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -2.6e-10) || !(c <= 7.8e-42)) {
		tmp = fma(-4.0, (a / (c / t)), (((9.0 * ((x * y) / c)) + (b / c)) / z));
	} else {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * (a * t)) - b)) / z) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -2.6e-10) || !(c <= 7.8e-42))
		tmp = fma(-4.0, Float64(a / Float64(c / t)), Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) / z));
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(Float64(z * 4.0) * Float64(a * t)) - b)) / z) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -2.6e-10], N[Not[LessEqual[c, 7.8e-42]], $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], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.59999999999999981e-10 or 7.8000000000000003e-42 < c

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 72.4%

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

      4. *-commutative 72.4%

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

      5. associate-+l- 72.4%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in x around 0 85.8%

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

      1. cancel-sign-sub-inv 85.8%

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

      2. metadata-eval 85.8%

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

      3. +-commutative 85.8%

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

      4. fma-def 85.8%

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

      5. associate-/l* 89.5%

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

      6. fma-def 89.5%

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

      7. times-frac 84.3%

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

      8. *-commutative 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in z around 0 90.8%

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

   if -2.59999999999999981e-10 < c < 7.8000000000000003e-42

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. *-commutative 92.1%

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

      3. associate-*r* 94.7%

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

      4. *-commutative 94.7%

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

      5. associate-+l- 94.7%

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

   3. Simplified 94.6%

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

      1. associate-/r* 95.4%

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

      2. div-inv 95.3%

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

      3. associate-+l- 95.3%

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

      4. associate-*r* 92.9%

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

      5. associate-+l- 92.9%

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

      6. associate-*l* 92.9%

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

      7. associate-*r* 95.3%

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

   5. Applied egg-rr 95.3%

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

      1. un-div-inv 95.4%

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

      2. associate-+l- 95.4%

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

   7. Applied egg-rr 95.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{-10} \lor \neg \left(c \leq 7.8 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - b\right)}{z}}{c}\\ \end{array} \]

Alternative 3: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{b + \left(t_1 - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_3 := \frac{b + \left(t_1 - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(a \cdot t\right)\right)\right)}{c}}{z}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0)))
        (t_2 (/ (+ b (- t_1 (* a (* t (* z 4.0))))) (* z c)))
        (t_3 (/ (+ b (- t_1 (* (* z 4.0) (* a t)))) (* z c))))
   (if (<= t_2 -4e-262)
     t_3
     (if (<= t_2 0.0)
       (/ (/ (+ b (- (* x (* 9.0 y)) (* z (* 4.0 (* a t))))) c) z)
       (if (<= t_2 INFINITY) t_3 (* -4.0 (/ a (/ c t))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	double t_3 = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	double tmp;
	if (t_2 <= -4e-262) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = ((b + ((x * (9.0 * y)) - (z * (4.0 * (a * t))))) / c) / z;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	double t_3 = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	double tmp;
	if (t_2 <= -4e-262) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = ((b + ((x * (9.0 * y)) - (z * (4.0 * (a * t))))) / c) / z;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c)
	t_3 = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c)
	tmp = 0
	if t_2 <= -4e-262:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = ((b + ((x * (9.0 * y)) - (z * (4.0 * (a * t))))) / c) / z
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_3 = Float64(Float64(b + Float64(t_1 - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -4e-262)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(a * t))))) / c) / z);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	t_3 = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	tmp = 0.0;
	if (t_2 <= -4e-262)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = ((b + ((x * (9.0 * y)) - (z * (4.0 * (a * t))))) / c) / z;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(t$95$1 - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b + N[(t$95$1 - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-262], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(-4.0 * N[(a / N[(c / t), $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)) < -4.00000000000000005e-262 or 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 89.3%

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

      1. associate-+l- 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 90.5%

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

      4. *-commutative 90.5%

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

      5. associate-+l- 90.5%

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

   3. Simplified 92.1%

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

   if -4.00000000000000005e-262 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 54.7%

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

      1. associate-+l- 54.7%

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

      2. *-commutative 54.7%

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

      3. associate-*r* 44.3%

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

      4. *-commutative 44.3%

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

      5. associate-+l- 44.3%

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

   3. Simplified 54.7%

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

      1. *-un-lft-identity 54.7%

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

      2. times-frac 99.7%

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

      3. associate-+l- 99.7%

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

      4. associate-*r* 99.7%

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

      5. associate-+l- 99.7%

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

      6. associate-*l* 99.5%

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

      7. associate-*r* 99.5%

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

   5. Applied egg-rr 99.5%

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

      1. associate-*l/ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-*l* 100.0%

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

   7. Applied egg-rr 100.0%

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

   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* 6.2%

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

      4. *-commutative 6.2%

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

      5. associate-+l- 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 37.6%

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

      1. *-commutative 37.6%

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

      2. associate-/l* 51.5%

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

   6. Simplified 51.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -4 \cdot 10^{-262}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(a \cdot t\right)\right)\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 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 87.8%

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

      1. associate-+l- 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-*r* 88.5%

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

      4. *-commutative 88.5%

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

      5. associate-+l- 88.5%

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

   3. Simplified 90.6%

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

   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* 6.2%

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

      4. *-commutative 6.2%

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

      5. associate-+l- 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 37.6%

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

      1. *-commutative 37.6%

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

      2. associate-/l* 51.5%

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

   6. Simplified 51.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 5: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+62}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-37}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - t_1}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+232}:\\ \;\;\;\;\frac{\frac{b - t_1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 4.0 (* a (* z t)))))
   (if (<= z -1.1e+256)
     (/ b (* z c))
     (if (<= z -1.15e+62)
       (* (/ (* a t) c) -4.0)
       (if (<= z -5e-37)
         (/ (- (* 9.0 (* x y)) t_1) (* z c))
         (if (<= z 1.4e+69)
           (/ (+ b (* x (* 9.0 y))) (* z c))
           (if (<= z 1.2e+232)
             (/ (/ (- b t_1) z) c)
             (* t (* -4.0 (/ a c))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 4.0 * (a * (z * t));
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -1.15e+62) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= -5e-37) {
		tmp = ((9.0 * (x * y)) - t_1) / (z * c);
	} else if (z <= 1.4e+69) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (z <= 1.2e+232) {
		tmp = ((b - t_1) / z) / c;
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 * (a * (z * t))
    if (z <= (-1.1d+256)) then
        tmp = b / (z * c)
    else if (z <= (-1.15d+62)) then
        tmp = ((a * t) / c) * (-4.0d0)
    else if (z <= (-5d-37)) then
        tmp = ((9.0d0 * (x * y)) - t_1) / (z * c)
    else if (z <= 1.4d+69) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else if (z <= 1.2d+232) then
        tmp = ((b - t_1) / z) / c
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 4.0 * (a * (z * t));
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -1.15e+62) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= -5e-37) {
		tmp = ((9.0 * (x * y)) - t_1) / (z * c);
	} else if (z <= 1.4e+69) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (z <= 1.2e+232) {
		tmp = ((b - t_1) / z) / c;
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = 4.0 * (a * (z * t))
	tmp = 0
	if z <= -1.1e+256:
		tmp = b / (z * c)
	elif z <= -1.15e+62:
		tmp = ((a * t) / c) * -4.0
	elif z <= -5e-37:
		tmp = ((9.0 * (x * y)) - t_1) / (z * c)
	elif z <= 1.4e+69:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	elif z <= 1.2e+232:
		tmp = ((b - t_1) / z) / c
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(4.0 * Float64(a * Float64(z * t)))
	tmp = 0.0
	if (z <= -1.1e+256)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= -1.15e+62)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (z <= -5e-37)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) - t_1) / Float64(z * c));
	elseif (z <= 1.4e+69)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	elseif (z <= 1.2e+232)
		tmp = Float64(Float64(Float64(b - t_1) / z) / c);
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 4.0 * (a * (z * t));
	tmp = 0.0;
	if (z <= -1.1e+256)
		tmp = b / (z * c);
	elseif (z <= -1.15e+62)
		tmp = ((a * t) / c) * -4.0;
	elseif (z <= -5e-37)
		tmp = ((9.0 * (x * y)) - t_1) / (z * c);
	elseif (z <= 1.4e+69)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	elseif (z <= 1.2e+232)
		tmp = ((b - t_1) / z) / c;
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+256], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e+62], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, -5e-37], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+69], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+232], N[(N[(N[(b - t$95$1), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.1e256

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -1.1e256 < z < -1.14999999999999992e62

   1. Initial program 49.4%

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

      1. associate-+l- 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*r* 57.8%

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

      4. *-commutative 57.8%

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

      5. associate-+l- 57.8%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in z around inf 72.5%

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

      1. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   if -1.14999999999999992e62 < z < -4.9999999999999997e-37

   1. Initial program 88.0%

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

      1. associate-+l- 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-*r* 88.0%

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

      4. *-commutative 88.0%

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

      5. associate-+l- 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in b around 0 76.4%

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

   if -4.9999999999999997e-37 < z < 1.39999999999999991e69

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. *-commutative 97.0%

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

      3. associate-*r* 96.3%

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

      4. *-commutative 96.3%

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

      5. associate-+l- 96.3%

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

   3. Simplified 95.5%

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

      1. div-inv 95.6%

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

      2. associate-+l- 95.6%

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

      3. associate-*r* 97.1%

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

      4. associate-+l- 97.1%

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

      5. associate-*l* 97.0%

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

      6. associate-*r* 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in z around 0 87.8%

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

      1. associate-*r* 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*r* 87.9%

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

      4. *-commutative 87.9%

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

   8. Simplified 87.9%

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

   if 1.39999999999999991e69 < z < 1.2000000000000001e232

   1. Initial program 69.8%

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

      1. associate-+l- 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-+l- 76.0%

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

   3. Simplified 82.1%

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

      1. associate-/r* 91.0%

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

      2. div-inv 90.8%

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

      3. associate-+l- 90.8%

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

      4. associate-*r* 72.8%

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

      5. associate-+l- 72.8%

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

      6. associate-*l* 72.9%

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

      7. associate-*r* 90.8%

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

   5. Applied egg-rr 90.8%

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

      1. un-div-inv 91.0%

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

      2. associate-+l- 91.0%

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

   7. Applied egg-rr 91.0%

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

   8. Taylor expanded in x around 0 64.4%

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

   if 1.2000000000000001e232 < z

   1. Initial program 40.8%

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

      1. associate-+l- 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*r* 28.0%

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

      4. *-commutative 28.0%

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

      5. associate-+l- 28.0%

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

   3. Simplified 47.2%

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

      1. div-inv 47.2%

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

      2. associate-+l- 47.2%

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

      3. associate-*r* 40.8%

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

      4. associate-+l- 40.8%

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

      5. associate-*l* 40.8%

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

      6. associate-*r* 47.2%

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

   5. Applied egg-rr 47.2%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-*l/ 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. associate-*l* 68.1%

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

   8. Simplified 68.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+62}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-37}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+232}:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 6: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-65} \lor \neg \left(z \leq 8.6 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.9e-65) (not (<= z 8.6e-89)))
   (/ (/ (- (* x (* 9.0 y)) (- (* (* z 4.0) (* a t)) b)) z) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.9e-65) || !(z <= 8.6e-89)) {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * (a * t)) - b)) / z) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.9d-65)) .or. (.not. (z <= 8.6d-89))) then
        tmp = (((x * (9.0d0 * y)) - (((z * 4.0d0) * (a * t)) - b)) / z) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.9e-65) || !(z <= 8.6e-89)) {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * (a * t)) - b)) / z) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.9e-65) or not (z <= 8.6e-89):
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * (a * t)) - b)) / z) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.9e-65) || !(z <= 8.6e-89))
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(Float64(z * 4.0) * Float64(a * t)) - b)) / z) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.9e-65) || ~((z <= 8.6e-89)))
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * (a * t)) - b)) / z) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.9e-65], N[Not[LessEqual[z, 8.6e-89]], $MachinePrecision]], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e-65 or 8.59999999999999974e-89 < z

   1. Initial program 70.0%

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

      1. associate-+l- 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 73.2%

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

      4. *-commutative 73.2%

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

      5. associate-+l- 73.2%

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

   3. Simplified 77.6%

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

      1. associate-/r* 83.3%

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

      2. div-inv 83.2%

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

      3. associate-+l- 83.2%

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

      4. associate-*r* 74.0%

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

      5. associate-+l- 74.0%

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

      6. associate-*l* 74.0%

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

      7. associate-*r* 83.2%

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

   5. Applied egg-rr 83.2%

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

      1. un-div-inv 83.3%

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

      2. associate-+l- 83.3%

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

   7. Applied egg-rr 83.3%

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

   if -1.9000000000000001e-65 < z < 8.59999999999999974e-89

   1. Initial program 97.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-65} \lor \neg \left(z \leq 8.6 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+73}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+228}:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.1e+256)
   (/ b (* z c))
   (if (<= z -1.4e+40)
     (* (/ (* a t) c) -4.0)
     (if (<= z 2.3e+73)
       (/ (+ b (* x (* 9.0 y))) (* z c))
       (if (<= z 3e+228)
         (/ (/ (- b (* 4.0 (* a (* z t)))) z) c)
         (* t (* -4.0 (/ a c))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -1.4e+40) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= 2.3e+73) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (z <= 3e+228) {
		tmp = ((b - (4.0 * (a * (z * t)))) / z) / c;
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.1d+256)) then
        tmp = b / (z * c)
    else if (z <= (-1.4d+40)) then
        tmp = ((a * t) / c) * (-4.0d0)
    else if (z <= 2.3d+73) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else if (z <= 3d+228) then
        tmp = ((b - (4.0d0 * (a * (z * t)))) / z) / c
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -1.4e+40) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= 2.3e+73) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (z <= 3e+228) {
		tmp = ((b - (4.0 * (a * (z * t)))) / z) / c;
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.1e+256:
		tmp = b / (z * c)
	elif z <= -1.4e+40:
		tmp = ((a * t) / c) * -4.0
	elif z <= 2.3e+73:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	elif z <= 3e+228:
		tmp = ((b - (4.0 * (a * (z * t)))) / z) / c
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.1e+256)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= -1.4e+40)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (z <= 2.3e+73)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	elseif (z <= 3e+228)
		tmp = Float64(Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / z) / c);
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.1e+256)
		tmp = b / (z * c);
	elseif (z <= -1.4e+40)
		tmp = ((a * t) / c) * -4.0;
	elseif (z <= 2.3e+73)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	elseif (z <= 3e+228)
		tmp = ((b - (4.0 * (a * (z * t)))) / z) / c;
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.1e+256], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e+40], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 2.3e+73], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+228], N[(N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1e256

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -1.1e256 < z < -1.4000000000000001e40

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 58.3%

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

      4. *-commutative 58.3%

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

      5. associate-+l- 58.3%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   if -1.4000000000000001e40 < z < 2.3e73

   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* 96.1%

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

      4. *-commutative 96.1%

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

      5. associate-+l- 96.1%

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

   3. Simplified 95.4%

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

      1. div-inv 95.5%

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

      2. associate-+l- 95.5%

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

      3. associate-*r* 96.8%

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

      4. associate-+l- 96.8%

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

      5. associate-*l* 96.8%

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

      6. associate-*r* 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in z around 0 84.0%

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

      1. associate-*r* 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

   8. Simplified 84.1%

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

   if 2.3e73 < z < 3.0000000000000001e228

   1. Initial program 69.8%

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

      1. associate-+l- 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-+l- 76.0%

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

   3. Simplified 82.1%

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

      1. associate-/r* 91.0%

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

      2. div-inv 90.8%

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

      3. associate-+l- 90.8%

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

      4. associate-*r* 72.8%

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

      5. associate-+l- 72.8%

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

      6. associate-*l* 72.9%

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

      7. associate-*r* 90.8%

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

   5. Applied egg-rr 90.8%

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

      1. un-div-inv 91.0%

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

      2. associate-+l- 91.0%

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

   7. Applied egg-rr 91.0%

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

   8. Taylor expanded in x around 0 64.4%

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

   if 3.0000000000000001e228 < z

   1. Initial program 40.8%

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

      1. associate-+l- 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*r* 28.0%

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

      4. *-commutative 28.0%

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

      5. associate-+l- 28.0%

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

   3. Simplified 47.2%

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

      1. div-inv 47.2%

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

      2. associate-+l- 47.2%

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

      3. associate-*r* 40.8%

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

      4. associate-+l- 40.8%

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

      5. associate-*l* 40.8%

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

      6. associate-*r* 47.2%

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

   5. Applied egg-rr 47.2%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-*l/ 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. associate-*l* 68.1%

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

   8. Simplified 68.1%

      \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+73}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+228}:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 8: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-37}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-309}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 -1.1e+256)
     t_1
     (if (<= z -6e-37)
       (* (/ (* a t) c) -4.0)
       (if (<= z -1.85e-214)
         (* b (/ (/ 1.0 c) z))
         (if (<= z -9e-309)
           (* 9.0 (* (/ x c) (/ y z)))
           (if (<= z 2.6e+36) t_1 (* t (* -4.0 (/ a c))))))))))

C

assert(x < y);
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 <= -1.1e+256) {
		tmp = t_1;
	} else if (z <= -6e-37) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= -1.85e-214) {
		tmp = b * ((1.0 / c) / z);
	} else if (z <= -9e-309) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (z <= 2.6e+36) {
		tmp = t_1;
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b / (z * c)
    if (z <= (-1.1d+256)) then
        tmp = t_1
    else if (z <= (-6d-37)) then
        tmp = ((a * t) / c) * (-4.0d0)
    else if (z <= (-1.85d-214)) then
        tmp = b * ((1.0d0 / c) / z)
    else if (z <= (-9d-309)) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (z <= 2.6d+36) then
        tmp = t_1
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static 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 <= -1.1e+256) {
		tmp = t_1;
	} else if (z <= -6e-37) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= -1.85e-214) {
		tmp = b * ((1.0 / c) / z);
	} else if (z <= -9e-309) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (z <= 2.6e+36) {
		tmp = t_1;
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if z <= -1.1e+256:
		tmp = t_1
	elif z <= -6e-37:
		tmp = ((a * t) / c) * -4.0
	elif z <= -1.85e-214:
		tmp = b * ((1.0 / c) / z)
	elif z <= -9e-309:
		tmp = 9.0 * ((x / c) * (y / z))
	elif z <= 2.6e+36:
		tmp = t_1
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (z <= -1.1e+256)
		tmp = t_1;
	elseif (z <= -6e-37)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (z <= -1.85e-214)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (z <= -9e-309)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (z <= 2.6e+36)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (z <= -1.1e+256)
		tmp = t_1;
	elseif (z <= -6e-37)
		tmp = ((a * t) / c) * -4.0;
	elseif (z <= -1.85e-214)
		tmp = b * ((1.0 / c) / z);
	elseif (z <= -9e-309)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (z <= 2.6e+36)
		tmp = t_1;
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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, -1.1e+256], t$95$1, If[LessEqual[z, -6e-37], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, -1.85e-214], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-309], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+36], t$95$1, N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1e256 or -9.0000000000000021e-309 < z < 2.6000000000000001e36

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-*r* 91.2%

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

      4. *-commutative 91.2%

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

      5. associate-+l- 91.2%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in b around inf 56.7%

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

      1. *-commutative 56.7%

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

   6. Simplified 56.7%

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

   if -1.1e256 < z < -6e-37

   1. Initial program 65.7%

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

      1. associate-+l- 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-+l- 70.6%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

   6. Simplified 61.0%

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

   if -6e-37 < z < -1.8500000000000001e-214

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

      1. div-inv 65.2%

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

      2. associate-/r* 65.2%

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

   8. Applied egg-rr 65.2%

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

   9. Taylor expanded in z around 0 65.2%

      \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 65.2%

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

   11. Simplified 65.2%

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

   if -1.8500000000000001e-214 < z < -9.0000000000000021e-309

   1. Initial program 96.5%

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

      1. associate-+l- 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*r* 93.2%

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

      4. *-commutative 93.2%

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

      5. associate-+l- 93.2%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in x around inf 63.4%

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

      1. frac-times 56.9%

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

   6. Applied egg-rr 56.9%

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

   if 2.6000000000000001e36 < z

   1. Initial program 61.0%

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

      1. associate-+l- 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-*r* 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-+l- 63.0%

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

   3. Simplified 72.6%

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

      1. div-inv 72.5%

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

      2. associate-+l- 72.5%

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

      3. associate-*r* 60.9%

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

      4. associate-+l- 60.9%

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

      5. associate-*l* 61.0%

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

      6. associate-*r* 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in z around inf 56.6%

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

      1. associate-*l/ 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. associate-*l* 59.6%

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

   8. Simplified 59.6%

      \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-37}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-309}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 9: 65.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.1e+256)
   (/ b (* z c))
   (if (<= z -1.4e+40)
     (* (/ (* a t) c) -4.0)
     (if (<= z 1.4e+72)
       (/ (+ b (* x (* 9.0 y))) (* z c))
       (* t (* -4.0 (/ a c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -1.4e+40) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= 1.4e+72) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.1d+256)) then
        tmp = b / (z * c)
    else if (z <= (-1.4d+40)) then
        tmp = ((a * t) / c) * (-4.0d0)
    else if (z <= 1.4d+72) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -1.4e+40) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= 1.4e+72) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.1e+256:
		tmp = b / (z * c)
	elif z <= -1.4e+40:
		tmp = ((a * t) / c) * -4.0
	elif z <= 1.4e+72:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.1e+256)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= -1.4e+40)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (z <= 1.4e+72)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.1e+256)
		tmp = b / (z * c);
	elseif (z <= -1.4e+40)
		tmp = ((a * t) / c) * -4.0;
	elseif (z <= 1.4e+72)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.1e+256], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e+40], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 1.4e+72], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e256

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -1.1e256 < z < -1.4000000000000001e40

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 58.3%

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

      4. *-commutative 58.3%

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

      5. associate-+l- 58.3%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   if -1.4000000000000001e40 < z < 1.4e72

   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* 96.1%

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

      4. *-commutative 96.1%

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

      5. associate-+l- 96.1%

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

   3. Simplified 95.4%

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

      1. div-inv 95.5%

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

      2. associate-+l- 95.5%

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

      3. associate-*r* 96.8%

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

      4. associate-+l- 96.8%

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

      5. associate-*l* 96.8%

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

      6. associate-*r* 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in z around 0 84.0%

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

      1. associate-*r* 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

   8. Simplified 84.1%

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

   if 1.4e72 < z

   1. Initial program 60.5%

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

      1. associate-+l- 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.7%

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

      4. *-commutative 60.7%

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

      5. associate-+l- 60.7%

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

   3. Simplified 70.9%

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

      1. div-inv 70.7%

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

      2. associate-+l- 70.7%

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

      3. associate-*r* 60.4%

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

      4. associate-+l- 60.4%

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

      5. associate-*l* 60.5%

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

      6. associate-*r* 70.8%

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

   5. Applied egg-rr 70.8%

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

   6. Taylor expanded in z around inf 57.9%

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

      1. associate-*l/ 61.0%

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

      2. *-commutative 61.0%

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

      3. *-commutative 61.0%

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

      4. associate-*l* 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 10: 43.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.6 \cdot 10^{-261}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 3.6e-261)
   (* 9.0 (* (/ x c) (/ y z)))
   (if (<= a 7.2e-50)
     (/ b (* z c))
     (if (<= a 1.45e+74) (* 9.0 (* (/ x z) (/ y c))) (* t (* -4.0 (/ a c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.6e-261) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 7.2e-50) {
		tmp = b / (z * c);
	} else if (a <= 1.45e+74) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 3.6d-261) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (a <= 7.2d-50) then
        tmp = b / (z * c)
    else if (a <= 1.45d+74) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.6e-261) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 7.2e-50) {
		tmp = b / (z * c);
	} else if (a <= 1.45e+74) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 3.6e-261:
		tmp = 9.0 * ((x / c) * (y / z))
	elif a <= 7.2e-50:
		tmp = b / (z * c)
	elif a <= 1.45e+74:
		tmp = 9.0 * ((x / z) * (y / c))
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 3.6e-261)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (a <= 7.2e-50)
		tmp = Float64(b / Float64(z * c));
	elseif (a <= 1.45e+74)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 3.6e-261)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (a <= 7.2e-50)
		tmp = b / (z * c);
	elseif (a <= 1.45e+74)
		tmp = 9.0 * ((x / z) * (y / c));
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 3.6e-261], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-50], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+74], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 3.59999999999999999e-261

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-+l- 81.9%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in x around inf 42.4%

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

      1. frac-times 42.4%

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

   6. Applied egg-rr 42.4%

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

   if 3.59999999999999999e-261 < a < 7.19999999999999958e-50

   1. Initial program 83.4%

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

      1. associate-+l- 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in b around inf 57.6%

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

      1. *-commutative 57.6%

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

   6. Simplified 57.6%

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

   if 7.19999999999999958e-50 < a < 1.4500000000000001e74

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*r* 85.2%

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

      4. *-commutative 85.2%

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

      5. associate-+l- 85.2%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around inf 54.7%

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

      1. *-commutative 54.7%

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

      2. times-frac 50.6%

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

   6. Simplified 50.6%

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

   if 1.4500000000000001e74 < a

   1. Initial program 83.9%

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

      1. associate-+l- 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 74.9%

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

      4. *-commutative 74.9%

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

      5. associate-+l- 74.9%

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

   3. Simplified 79.4%

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

      1. div-inv 79.4%

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

      2. associate-+l- 79.4%

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

      3. associate-*r* 84.0%

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

      4. associate-+l- 84.0%

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

      5. associate-*l* 84.0%

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

      6. associate-*r* 79.5%

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

   5. Applied egg-rr 79.5%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate-*l/ 63.4%

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

      2. *-commutative 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*l* 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.6 \cdot 10^{-261}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 11: 42.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{-263}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 4.2e-263)
   (* 9.0 (* (/ x c) (/ y z)))
   (if (<= a 4e-50)
     (/ b (* z c))
     (if (<= a 1.08e+74) (* 9.0 (/ (* x y) (* z c))) (* t (* -4.0 (/ a c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.2e-263) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 4e-50) {
		tmp = b / (z * c);
	} else if (a <= 1.08e+74) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 4.2d-263) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (a <= 4d-50) then
        tmp = b / (z * c)
    else if (a <= 1.08d+74) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.2e-263) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 4e-50) {
		tmp = b / (z * c);
	} else if (a <= 1.08e+74) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 4.2e-263:
		tmp = 9.0 * ((x / c) * (y / z))
	elif a <= 4e-50:
		tmp = b / (z * c)
	elif a <= 1.08e+74:
		tmp = 9.0 * ((x * y) / (z * c))
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 4.2e-263)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (a <= 4e-50)
		tmp = Float64(b / Float64(z * c));
	elseif (a <= 1.08e+74)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 4.2e-263)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (a <= 4e-50)
		tmp = b / (z * c);
	elseif (a <= 1.08e+74)
		tmp = 9.0 * ((x * y) / (z * c));
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 4.2e-263], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-50], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e+74], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 4.20000000000000005e-263

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-+l- 81.9%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in x around inf 42.4%

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

      1. frac-times 42.4%

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

   6. Applied egg-rr 42.4%

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

   if 4.20000000000000005e-263 < a < 4.00000000000000003e-50

   1. Initial program 83.4%

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

      1. associate-+l- 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in b around inf 57.6%

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

      1. *-commutative 57.6%

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

   6. Simplified 57.6%

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

   if 4.00000000000000003e-50 < a < 1.08e74

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*r* 85.2%

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

      4. *-commutative 85.2%

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

      5. associate-+l- 85.2%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around inf 54.7%

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

   if 1.08e74 < a

   1. Initial program 83.9%

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

      1. associate-+l- 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 74.9%

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

      4. *-commutative 74.9%

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

      5. associate-+l- 74.9%

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

   3. Simplified 79.4%

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

      1. div-inv 79.4%

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

      2. associate-+l- 79.4%

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

      3. associate-*r* 84.0%

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

      4. associate-+l- 84.0%

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

      5. associate-*l* 84.0%

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

      6. associate-*r* 79.5%

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

   5. Applied egg-rr 79.5%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate-*l/ 63.4%

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

      2. *-commutative 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*l* 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{-263}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 12: 42.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.5 \cdot 10^{-263}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+74}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 2.5e-263)
   (* 9.0 (* (/ x c) (/ y z)))
   (if (<= a 7.2e-50)
     (/ b (* z c))
     (if (<= a 3e+74) (/ (* 9.0 (* x y)) (* z c)) (* t (* -4.0 (/ a c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 2.5e-263) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 7.2e-50) {
		tmp = b / (z * c);
	} else if (a <= 3e+74) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 2.5d-263) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (a <= 7.2d-50) then
        tmp = b / (z * c)
    else if (a <= 3d+74) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 2.5e-263) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 7.2e-50) {
		tmp = b / (z * c);
	} else if (a <= 3e+74) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 2.5e-263:
		tmp = 9.0 * ((x / c) * (y / z))
	elif a <= 7.2e-50:
		tmp = b / (z * c)
	elif a <= 3e+74:
		tmp = (9.0 * (x * y)) / (z * c)
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 2.5e-263)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (a <= 7.2e-50)
		tmp = Float64(b / Float64(z * c));
	elseif (a <= 3e+74)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 2.5e-263)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (a <= 7.2e-50)
		tmp = b / (z * c);
	elseif (a <= 3e+74)
		tmp = (9.0 * (x * y)) / (z * c);
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 2.5e-263], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-50], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+74], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 2.50000000000000003e-263

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-+l- 81.9%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in x around inf 42.4%

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

      1. frac-times 42.4%

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

   6. Applied egg-rr 42.4%

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

   if 2.50000000000000003e-263 < a < 7.19999999999999958e-50

   1. Initial program 83.4%

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

      1. associate-+l- 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in b around inf 57.6%

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

      1. *-commutative 57.6%

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

   6. Simplified 57.6%

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

   if 7.19999999999999958e-50 < a < 3e74

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*r* 85.2%

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

      4. *-commutative 85.2%

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

      5. associate-+l- 85.2%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around inf 54.7%

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

      1. associate-*r/ 54.8%

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

      2. *-commutative 54.8%

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

   6. Simplified 54.8%

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

   if 3e74 < a

   1. Initial program 83.9%

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

      1. associate-+l- 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 74.9%

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

      4. *-commutative 74.9%

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

      5. associate-+l- 74.9%

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

   3. Simplified 79.4%

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

      1. div-inv 79.4%

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

      2. associate-+l- 79.4%

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

      3. associate-*r* 84.0%

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

      4. associate-+l- 84.0%

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

      5. associate-*l* 84.0%

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

      6. associate-*r* 79.5%

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

   5. Applied egg-rr 79.5%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate-*l/ 63.4%

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

      2. *-commutative 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*l* 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.5 \cdot 10^{-263}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+74}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 13: 47.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.1e+256)
   (/ b (* z c))
   (if (<= z -2.8e-37)
     (* (* a t) (/ -4.0 c))
     (if (<= z 3e+36) (* b (/ (/ 1.0 c) z)) (* t (* -4.0 (/ a c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -2.8e-37) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 3e+36) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.1d+256)) then
        tmp = b / (z * c)
    else if (z <= (-2.8d-37)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (z <= 3d+36) then
        tmp = b * ((1.0d0 / c) / z)
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -2.8e-37) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 3e+36) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.1e+256:
		tmp = b / (z * c)
	elif z <= -2.8e-37:
		tmp = (a * t) * (-4.0 / c)
	elif z <= 3e+36:
		tmp = b * ((1.0 / c) / z)
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.1e+256)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= -2.8e-37)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (z <= 3e+36)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.1e+256)
		tmp = b / (z * c);
	elseif (z <= -2.8e-37)
		tmp = (a * t) * (-4.0 / c);
	elseif (z <= 3e+36)
		tmp = b * ((1.0 / c) / z);
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.1e+256], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-37], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+36], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e256

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -1.1e256 < z < -2.8000000000000001e-37

   1. Initial program 65.7%

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

      1. associate-+l- 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-+l- 70.6%

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

   3. Simplified 70.7%

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

      1. associate-/r* 78.8%

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

      2. div-inv 78.8%

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

      3. associate-+l- 78.8%

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

      4. associate-*r* 72.2%

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

      5. associate-+l- 72.2%

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

      6. associate-*l* 72.2%

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

      7. associate-*r* 78.8%

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

   5. Applied egg-rr 78.8%

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

   6. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r/ 61.0%

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

      3. associate-*l/ 61.0%

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

      4. *-commutative 61.0%

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

      5. *-commutative 61.0%

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

   8. Simplified 61.0%

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

   if -2.8000000000000001e-37 < z < 3e36

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*r* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-+l- 96.2%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in b around inf 53.9%

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

      1. *-commutative 53.9%

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

   6. Simplified 53.9%

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

      1. div-inv 54.6%

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

      2. associate-/r* 54.5%

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

   8. Applied egg-rr 54.5%

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

   9. Taylor expanded in z around 0 54.6%

      \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 54.6%

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

   11. Simplified 54.6%

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

   if 3e36 < z

   1. Initial program 61.0%

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

      1. associate-+l- 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-*r* 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-+l- 63.0%

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

   3. Simplified 72.6%

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

      1. div-inv 72.5%

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

      2. associate-+l- 72.5%

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

      3. associate-*r* 60.9%

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

      4. associate-+l- 60.9%

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

      5. associate-*l* 61.0%

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

      6. associate-*r* 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in z around inf 56.6%

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

      1. associate-*l/ 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. associate-*l* 59.6%

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

   8. Simplified 59.6%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 14: 48.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-37}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.1e+256)
   (/ b (* z c))
   (if (<= z -4e-37)
     (* (/ (* a t) c) -4.0)
     (if (<= z 5.8e+36) (* b (/ (/ 1.0 c) z)) (* t (* -4.0 (/ a c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -4e-37) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= 5.8e+36) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.1d+256)) then
        tmp = b / (z * c)
    else if (z <= (-4d-37)) then
        tmp = ((a * t) / c) * (-4.0d0)
    else if (z <= 5.8d+36) then
        tmp = b * ((1.0d0 / c) / z)
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.1e+256) {
		tmp = b / (z * c);
	} else if (z <= -4e-37) {
		tmp = ((a * t) / c) * -4.0;
	} else if (z <= 5.8e+36) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.1e+256:
		tmp = b / (z * c)
	elif z <= -4e-37:
		tmp = ((a * t) / c) * -4.0
	elif z <= 5.8e+36:
		tmp = b * ((1.0 / c) / z)
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.1e+256)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= -4e-37)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	elseif (z <= 5.8e+36)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.1e+256)
		tmp = b / (z * c);
	elseif (z <= -4e-37)
		tmp = ((a * t) / c) * -4.0;
	elseif (z <= 5.8e+36)
		tmp = b * ((1.0 / c) / z);
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.1e+256], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-37], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 5.8e+36], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e256

   1. Initial program 50.9%

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

      1. associate-+l- 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -1.1e256 < z < -4.00000000000000027e-37

   1. Initial program 65.7%

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

      1. associate-+l- 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-+l- 70.6%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

   6. Simplified 61.0%

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

   if -4.00000000000000027e-37 < z < 5.8e36

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*r* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-+l- 96.2%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in b around inf 53.9%

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

      1. *-commutative 53.9%

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

   6. Simplified 53.9%

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

      1. div-inv 54.6%

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

      2. associate-/r* 54.5%

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

   8. Applied egg-rr 54.5%

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

   9. Taylor expanded in z around 0 54.6%

      \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 54.6%

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

   11. Simplified 54.6%

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

   if 5.8e36 < z

   1. Initial program 61.0%

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

      1. associate-+l- 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-*r* 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-+l- 63.0%

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

   3. Simplified 72.6%

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

      1. div-inv 72.5%

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

      2. associate-+l- 72.5%

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

      3. associate-*r* 60.9%

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

      4. associate-+l- 60.9%

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

      5. associate-*l* 61.0%

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

      6. associate-*r* 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in z around inf 56.6%

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

      1. associate-*l/ 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. associate-*l* 59.6%

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

   8. Simplified 59.6%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+256}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-37}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 15: 50.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-39} \lor \neg \left(z \leq 3.6 \cdot 10^{+36}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -6.5e-39) (not (<= z 3.6e+36)))
   (* t (* -4.0 (/ a c)))
   (* b (/ (/ 1.0 c) z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6.5e-39) || !(z <= 3.6e+36)) {
		tmp = t * (-4.0 * (a / c));
	} else {
		tmp = b * ((1.0 / c) / z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-6.5d-39)) .or. (.not. (z <= 3.6d+36))) then
        tmp = t * ((-4.0d0) * (a / c))
    else
        tmp = b * ((1.0d0 / c) / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6.5e-39) || !(z <= 3.6e+36)) {
		tmp = t * (-4.0 * (a / c));
	} else {
		tmp = b * ((1.0 / c) / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -6.5e-39) or not (z <= 3.6e+36):
		tmp = t * (-4.0 * (a / c))
	else:
		tmp = b * ((1.0 / c) / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6.5e-39) || !(z <= 3.6e+36))
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	else
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -6.5e-39) || ~((z <= 3.6e+36)))
		tmp = t * (-4.0 * (a / c));
	else
		tmp = b * ((1.0 / c) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -6.5e-39], N[Not[LessEqual[z, 3.6e+36]], $MachinePrecision]], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000027e-39 or 3.5999999999999997e36 < z

   1. Initial program 62.3%

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

      1. associate-+l- 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-+l- 66.3%

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

   3. Simplified 71.2%

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

      1. div-inv 71.1%

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

      2. associate-+l- 71.1%

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

      3. associate-*r* 62.3%

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

      4. associate-+l- 62.3%

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

      5. associate-*l* 62.3%

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

      6. associate-*r* 71.1%

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

   5. Applied egg-rr 71.1%

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

   6. Taylor expanded in z around inf 55.9%

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

      1. associate-*l/ 55.5%

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

      2. *-commutative 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-*l* 55.5%

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

   8. Simplified 55.5%

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

   if -6.50000000000000027e-39 < z < 3.5999999999999997e36

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*r* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-+l- 96.2%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in b around inf 53.9%

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

      1. *-commutative 53.9%

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

   6. Simplified 53.9%

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

      1. div-inv 54.6%

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

      2. associate-/r* 54.5%

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

   8. Applied egg-rr 54.5%

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

   9. Taylor expanded in z around 0 54.6%

      \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 54.6%

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

   11. Simplified 54.6%

       \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-39} \lor \neg \left(z \leq 3.6 \cdot 10^{+36}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \end{array} \]

Alternative 16: 35.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ b \cdot \frac{\frac{1}{c}}{z} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (* b (/ (/ 1.0 c) z)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * ((1.0 / c) / z);
}

Fortran

NOTE: x and y 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 * ((1.0d0 / c) / z)
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * ((1.0 / c) / z);
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	return b * ((1.0 / c) / z)

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	return Float64(b * Float64(Float64(1.0 / c) / z))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b * ((1.0 / c) / z);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.9%

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

   1. associate-+l- 80.9%

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

   2. *-commutative 80.9%

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

   3. associate-*r* 82.1%

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

   4. *-commutative 82.1%

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

   5. associate-+l- 82.1%

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

3. Simplified 84.0%

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

4. Taylor expanded in b around inf 38.6%

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

   1. *-commutative 38.6%

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

6. Simplified 38.6%

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

   1. div-inv 39.0%

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

   2. associate-/r* 38.9%

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

8. Applied egg-rr 38.9%

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

9. Taylor expanded in z around 0 39.0%

   \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]
10. Step-by-step derivation

    1. associate-/r* 39.0%

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

11. Simplified 39.0%

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

12. Final simplification 39.0%

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

Alternative 17: 35.7% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x and y 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);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x and y 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;
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] = sort([x, y])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x and y 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 80.9%

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

   1. associate-+l- 80.9%

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

   2. *-commutative 80.9%

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

   3. associate-*r* 82.1%

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

   4. *-commutative 82.1%

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

   5. associate-+l- 82.1%

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

3. Simplified 84.0%

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

4. Taylor expanded in b around inf 38.6%

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

   1. *-commutative 38.6%

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

6. Simplified 38.6%

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

7. Final simplification 38.6%

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

Developer target: 80.2% accurate, 0.2× 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 2023287 
(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)))