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

Percentage Accurate: 80.2% → 92.9%

Time: 13.8s

Alternatives: 19

Speedup: 0.8×

• 37.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+54} \lor \neg \left(z \leq 2.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c} + \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.6e+54) (not (<= z 2.7e+21)))
   (+ (/ (+ (/ b z) (* 9.0 (* y (/ x z)))) c) (* (* (/ a c) t) -4.0))
   (/ (fma x (* 9.0 y) (+ b (* t (* a (* z -4.0))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.6e+54) || !(z <= 2.7e+21)) {
		tmp = (((b / z) + (9.0 * (y * (x / z)))) / c) + (((a / c) * t) * -4.0);
	} else {
		tmp = fma(x, (9.0 * y), (b + (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.6e+54) || !(z <= 2.7e+21))
		tmp = Float64(Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(y * Float64(x / z)))) / c) + Float64(Float64(Float64(a / c) * t) * -4.0));
	else
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.6e+54], N[Not[LessEqual[z, 2.7e+21]], $MachinePrecision]], N[(N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] + N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000001e54 or 2.7e21 < z

   1. Initial program 53.4%

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

      1. associate-+l- 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*r* 55.9%

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

      4. *-commutative 55.9%

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

      5. associate-+l- 55.9%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in x around 0 80.2%

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

      1. cancel-sign-sub-inv 80.2%

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

      2. metadata-eval 80.2%

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

      3. +-commutative 80.2%

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

      4. fma-def 80.2%

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

      5. times-frac 80.1%

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

      6. associate-/r* 79.1%

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

      7. *-commutative 79.1%

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

      8. associate-/l* 86.3%

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

      9. associate-/r/ 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in c around 0 88.3%

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

      1. associate-*r/ 93.2%

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

   9. Simplified 93.2%

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

   if -3.6000000000000001e54 < z < 2.7e21

   1. Initial program 97.9%

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

      1. associate-+l- 97.9%

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

      2. associate-*l* 98.7%

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

      3. fma-neg 98.7%

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

      4. neg-sub0 98.7%

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

      5. associate-+l- 98.7%

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

      6. neg-sub0 98.7%

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

      7. +-commutative 98.7%

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

      8. distribute-rgt-neg-out 98.7%

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

      9. *-commutative 98.7%

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

      10. associate-*l* 97.9%

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

      11. distribute-rgt-neg-in 97.9%

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

      12. *-commutative 97.9%

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

      13. distribute-rgt-neg-in 97.9%

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

      14. distribute-rgt-neg-in 97.9%

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

      15. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+54} \lor \neg \left(z \leq 2.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c} + \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-199}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} + t_2}{c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{b}{z} + t_2}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* (/ x (/ z y)) (/ 9.0 c)) (* -4.0 (* a (/ t c)))))
        (t_2 (* -4.0 (* a t))))
   (if (<= z -6.5e-14)
     t_1
     (if (<= z -6.8e-158)
       (+ (* (* (/ a c) t) -4.0) (/ b (* z c)))
       (if (<= z -2.7e-199)
         (/ (+ (* 9.0 (/ (* y x) z)) t_2) c)
         (if (<= z 7e-43)
           (/ (+ b (* 9.0 (* y x))) (* z c))
           (if (<= z 2.8e+79) (/ (+ (/ b z) t_2) c) t_1)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x / (z / y)) * (9.0 / c)) + (-4.0 * (a * (t / c)));
	double t_2 = -4.0 * (a * t);
	double tmp;
	if (z <= -6.5e-14) {
		tmp = t_1;
	} else if (z <= -6.8e-158) {
		tmp = (((a / c) * t) * -4.0) + (b / (z * c));
	} else if (z <= -2.7e-199) {
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c;
	} else if (z <= 7e-43) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else if (z <= 2.8e+79) {
		tmp = ((b / z) + t_2) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x / (z / y)) * (9.0d0 / c)) + ((-4.0d0) * (a * (t / c)))
    t_2 = (-4.0d0) * (a * t)
    if (z <= (-6.5d-14)) then
        tmp = t_1
    else if (z <= (-6.8d-158)) then
        tmp = (((a / c) * t) * (-4.0d0)) + (b / (z * c))
    else if (z <= (-2.7d-199)) then
        tmp = ((9.0d0 * ((y * x) / z)) + t_2) / c
    else if (z <= 7d-43) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else if (z <= 2.8d+79) then
        tmp = ((b / z) + t_2) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x / (z / y)) * (9.0 / c)) + (-4.0 * (a * (t / c)));
	double t_2 = -4.0 * (a * t);
	double tmp;
	if (z <= -6.5e-14) {
		tmp = t_1;
	} else if (z <= -6.8e-158) {
		tmp = (((a / c) * t) * -4.0) + (b / (z * c));
	} else if (z <= -2.7e-199) {
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c;
	} else if (z <= 7e-43) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else if (z <= 2.8e+79) {
		tmp = ((b / z) + t_2) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((x / (z / y)) * (9.0 / c)) + (-4.0 * (a * (t / c)))
	t_2 = -4.0 * (a * t)
	tmp = 0
	if z <= -6.5e-14:
		tmp = t_1
	elif z <= -6.8e-158:
		tmp = (((a / c) * t) * -4.0) + (b / (z * c))
	elif z <= -2.7e-199:
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c
	elif z <= 7e-43:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	elif z <= 2.8e+79:
		tmp = ((b / z) + t_2) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x / Float64(z / y)) * Float64(9.0 / c)) + Float64(-4.0 * Float64(a * Float64(t / c))))
	t_2 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -6.5e-14)
		tmp = t_1;
	elseif (z <= -6.8e-158)
		tmp = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + Float64(b / Float64(z * c)));
	elseif (z <= -2.7e-199)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / z)) + t_2) / c);
	elseif (z <= 7e-43)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	elseif (z <= 2.8e+79)
		tmp = Float64(Float64(Float64(b / z) + t_2) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x / (z / y)) * (9.0 / c)) + (-4.0 * (a * (t / c)));
	t_2 = -4.0 * (a * t);
	tmp = 0.0;
	if (z <= -6.5e-14)
		tmp = t_1;
	elseif (z <= -6.8e-158)
		tmp = (((a / c) * t) * -4.0) + (b / (z * c));
	elseif (z <= -2.7e-199)
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c;
	elseif (z <= 7e-43)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	elseif (z <= 2.8e+79)
		tmp = ((b / z) + t_2) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e-14], t$95$1, If[LessEqual[z, -6.8e-158], N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-199], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 7e-43], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+79], N[(N[(N[(b / z), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5000000000000001e-14 or 2.8000000000000001e79 < z

   1. Initial program 55.3%

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

      1. associate-+l- 55.3%

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

      2. *-commutative 55.3%

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

      3. associate-*r* 57.9%

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

      4. *-commutative 57.9%

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

      5. associate-+l- 57.9%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in x around 0 81.1%

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

      1. cancel-sign-sub-inv 81.1%

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

      2. metadata-eval 81.1%

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

      3. +-commutative 81.1%

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

      4. fma-def 81.1%

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

      5. times-frac 80.2%

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

      6. associate-/r* 79.3%

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

      7. *-commutative 79.3%

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

      8. associate-/l* 85.6%

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

      9. associate-/r/ 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in y around inf 77.9%

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

      1. associate-*r/ 78.0%

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

      2. *-commutative 78.0%

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

      3. *-commutative 78.0%

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

      4. times-frac 80.4%

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

      5. *-commutative 80.4%

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

      6. associate-/l* 85.3%

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

   9. Simplified 85.3%

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

   10. Taylor expanded in a around 0 84.4%

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

       1. associate-/l* 89.2%

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

       2. *-rgt-identity 89.2%

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

       3. associate-*r/ 89.2%

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

       4. associate-/r/ 89.1%

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

       5. associate-*l/ 89.2%

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

       6. *-lft-identity 89.2%

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

   12. Simplified 89.2%

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

   if -6.5000000000000001e-14 < z < -6.7999999999999999e-158

   1. Initial program 94.9%

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

      1. associate-+l- 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r* 95.0%

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

      4. *-commutative 95.0%

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

      5. associate-+l- 95.0%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 85.8%

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

      1. cancel-sign-sub-inv 85.8%

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

      2. metadata-eval 85.8%

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

      3. +-commutative 85.8%

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

      4. fma-def 85.8%

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

      5. times-frac 81.3%

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

      6. associate-/r* 81.1%

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

      7. *-commutative 81.1%

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

      8. associate-/l* 85.6%

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

      9. associate-/r/ 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in z around 0 94.9%

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

      1. associate-*l/ 94.9%

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

      2. *-commutative 94.9%

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

   9. Simplified 94.9%

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

   10. Taylor expanded in b around inf 90.6%

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

   if -6.7999999999999999e-158 < z < -2.69999999999999989e-199

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 79.8%

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

      1. cancel-sign-sub-inv 79.8%

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

      2. metadata-eval 79.8%

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

      3. +-commutative 79.8%

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

      4. fma-def 79.8%

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

      5. times-frac 80.0%

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

      6. associate-/r* 80.0%

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

      7. *-commutative 80.0%

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

      8. associate-/l* 80.0%

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

      9. associate-/r/ 80.0%

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

   6. Simplified 80.0%

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

   7. Taylor expanded in y around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

      4. times-frac 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-/l* 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in c around 0 100.0%

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

   if -2.69999999999999989e-199 < z < 6.99999999999999994e-43

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. associate-*l* 99.0%

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

      3. fma-neg 99.0%

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

      4. neg-sub0 99.0%

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

      5. associate-+l- 99.0%

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

      6. neg-sub0 99.0%

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

      7. +-commutative 99.0%

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

      8. distribute-rgt-neg-out 99.0%

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

      9. *-commutative 99.0%

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

      10. associate-*l* 97.9%

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

      11. distribute-rgt-neg-in 97.9%

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

      12. *-commutative 97.9%

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

      13. distribute-rgt-neg-in 97.9%

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

      14. distribute-rgt-neg-in 97.9%

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

      15. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around 0 89.7%

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

   if 6.99999999999999994e-43 < z < 2.8000000000000001e79

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. *-commutative 87.6%

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

      3. associate-*r* 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 x around 0 87.2%

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

      1. cancel-sign-sub-inv 87.2%

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

      2. metadata-eval 87.2%

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

      3. +-commutative 87.2%

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

      4. fma-def 87.2%

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

      5. times-frac 91.2%

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

      6. associate-/r* 91.2%

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

      7. *-commutative 91.2%

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

      8. associate-/l* 86.7%

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

      9. associate-/r/ 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in z around 0 91.3%

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

      1. associate-*l/ 95.3%

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

      2. *-commutative 95.3%

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

   9. Simplified 95.3%

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

   10. Taylor expanded in b around inf 94.2%

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

   11. Taylor expanded in c around 0 90.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-199}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 3: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ t_3 := \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-158}:\\ \;\;\;\;t_3 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-199}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} + t_2}{c}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{b}{z} + t_2}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1 + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ x (/ z y)) (/ 9.0 c)))
        (t_2 (* -4.0 (* a t)))
        (t_3 (* (* (/ a c) t) -4.0)))
   (if (<= z -5.5e-14)
     (+ t_3 t_1)
     (if (<= z -8.2e-158)
       (+ t_3 (/ b (* z c)))
       (if (<= z -2.7e-199)
         (/ (+ (* 9.0 (/ (* y x) z)) t_2) c)
         (if (<= z 7.5e-43)
           (/ (+ b (* 9.0 (* y x))) (* z c))
           (if (<= z 3.8e+78)
             (/ (+ (/ b z) t_2) c)
             (+ t_1 (* -4.0 (* a (/ t c)))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / (z / y)) * (9.0 / c);
	double t_2 = -4.0 * (a * t);
	double t_3 = ((a / c) * t) * -4.0;
	double tmp;
	if (z <= -5.5e-14) {
		tmp = t_3 + t_1;
	} else if (z <= -8.2e-158) {
		tmp = t_3 + (b / (z * c));
	} else if (z <= -2.7e-199) {
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c;
	} else if (z <= 7.5e-43) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else if (z <= 3.8e+78) {
		tmp = ((b / z) + t_2) / c;
	} else {
		tmp = t_1 + (-4.0 * (a * (t / c)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / (z / y)) * (9.0d0 / c)
    t_2 = (-4.0d0) * (a * t)
    t_3 = ((a / c) * t) * (-4.0d0)
    if (z <= (-5.5d-14)) then
        tmp = t_3 + t_1
    else if (z <= (-8.2d-158)) then
        tmp = t_3 + (b / (z * c))
    else if (z <= (-2.7d-199)) then
        tmp = ((9.0d0 * ((y * x) / z)) + t_2) / c
    else if (z <= 7.5d-43) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else if (z <= 3.8d+78) then
        tmp = ((b / z) + t_2) / c
    else
        tmp = t_1 + ((-4.0d0) * (a * (t / c)))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / (z / y)) * (9.0 / c);
	double t_2 = -4.0 * (a * t);
	double t_3 = ((a / c) * t) * -4.0;
	double tmp;
	if (z <= -5.5e-14) {
		tmp = t_3 + t_1;
	} else if (z <= -8.2e-158) {
		tmp = t_3 + (b / (z * c));
	} else if (z <= -2.7e-199) {
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c;
	} else if (z <= 7.5e-43) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else if (z <= 3.8e+78) {
		tmp = ((b / z) + t_2) / c;
	} else {
		tmp = t_1 + (-4.0 * (a * (t / c)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / (z / y)) * (9.0 / c)
	t_2 = -4.0 * (a * t)
	t_3 = ((a / c) * t) * -4.0
	tmp = 0
	if z <= -5.5e-14:
		tmp = t_3 + t_1
	elif z <= -8.2e-158:
		tmp = t_3 + (b / (z * c))
	elif z <= -2.7e-199:
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c
	elif z <= 7.5e-43:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	elif z <= 3.8e+78:
		tmp = ((b / z) + t_2) / c
	else:
		tmp = t_1 + (-4.0 * (a * (t / c)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / Float64(z / y)) * Float64(9.0 / c))
	t_2 = Float64(-4.0 * Float64(a * t))
	t_3 = Float64(Float64(Float64(a / c) * t) * -4.0)
	tmp = 0.0
	if (z <= -5.5e-14)
		tmp = Float64(t_3 + t_1);
	elseif (z <= -8.2e-158)
		tmp = Float64(t_3 + Float64(b / Float64(z * c)));
	elseif (z <= -2.7e-199)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / z)) + t_2) / c);
	elseif (z <= 7.5e-43)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	elseif (z <= 3.8e+78)
		tmp = Float64(Float64(Float64(b / z) + t_2) / c);
	else
		tmp = Float64(t_1 + Float64(-4.0 * Float64(a * Float64(t / c))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / (z / y)) * (9.0 / c);
	t_2 = -4.0 * (a * t);
	t_3 = ((a / c) * t) * -4.0;
	tmp = 0.0;
	if (z <= -5.5e-14)
		tmp = t_3 + t_1;
	elseif (z <= -8.2e-158)
		tmp = t_3 + (b / (z * c));
	elseif (z <= -2.7e-199)
		tmp = ((9.0 * ((y * x) / z)) + t_2) / c;
	elseif (z <= 7.5e-43)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	elseif (z <= 3.8e+78)
		tmp = ((b / z) + t_2) / c;
	else
		tmp = t_1 + (-4.0 * (a * (t / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -5.5e-14], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[z, -8.2e-158], N[(t$95$3 + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-199], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 7.5e-43], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+78], N[(N[(N[(b / z), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.49999999999999991e-14

   1. Initial program 61.9%

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

      1. associate-+l- 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 63.5%

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

      4. *-commutative 63.5%

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

      5. associate-+l- 63.5%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around 0 83.1%

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

      1. cancel-sign-sub-inv 83.1%

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

      2. metadata-eval 83.1%

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

      3. +-commutative 83.1%

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

      4. fma-def 83.1%

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

      5. times-frac 83.0%

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

      6. associate-/r* 83.0%

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

      7. *-commutative 83.0%

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

      8. associate-/l* 91.9%

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

      9. associate-/r/ 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in y around inf 77.5%

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

      1. associate-*r/ 77.5%

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

      2. *-commutative 77.5%

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

      3. *-commutative 77.5%

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

      4. times-frac 77.6%

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

      5. *-commutative 77.6%

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

      6. associate-/l* 82.1%

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

   9. Simplified 82.1%

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

   if -5.49999999999999991e-14 < z < -8.20000000000000008e-158

   1. Initial program 94.9%

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

      1. associate-+l- 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r* 95.0%

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

      4. *-commutative 95.0%

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

      5. associate-+l- 95.0%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 85.8%

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

      1. cancel-sign-sub-inv 85.8%

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

      2. metadata-eval 85.8%

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

      3. +-commutative 85.8%

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

      4. fma-def 85.8%

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

      5. times-frac 81.3%

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

      6. associate-/r* 81.1%

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

      7. *-commutative 81.1%

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

      8. associate-/l* 85.6%

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

      9. associate-/r/ 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in z around 0 94.9%

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

      1. associate-*l/ 94.9%

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

      2. *-commutative 94.9%

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

   9. Simplified 94.9%

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

   10. Taylor expanded in b around inf 90.6%

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

   if -8.20000000000000008e-158 < z < -2.69999999999999989e-199

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 79.8%

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

      1. cancel-sign-sub-inv 79.8%

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

      2. metadata-eval 79.8%

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

      3. +-commutative 79.8%

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

      4. fma-def 79.8%

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

      5. times-frac 80.0%

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

      6. associate-/r* 80.0%

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

      7. *-commutative 80.0%

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

      8. associate-/l* 80.0%

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

      9. associate-/r/ 80.0%

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

   6. Simplified 80.0%

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

   7. Taylor expanded in y around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

      4. times-frac 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-/l* 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in c around 0 100.0%

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

   if -2.69999999999999989e-199 < z < 7.50000000000000068e-43

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. associate-*l* 99.0%

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

      3. fma-neg 99.0%

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

      4. neg-sub0 99.0%

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

      5. associate-+l- 99.0%

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

      6. neg-sub0 99.0%

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

      7. +-commutative 99.0%

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

      8. distribute-rgt-neg-out 99.0%

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

      9. *-commutative 99.0%

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

      10. associate-*l* 97.9%

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

      11. distribute-rgt-neg-in 97.9%

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

      12. *-commutative 97.9%

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

      13. distribute-rgt-neg-in 97.9%

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

      14. distribute-rgt-neg-in 97.9%

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

      15. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around 0 89.7%

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

   if 7.50000000000000068e-43 < z < 3.7999999999999999e78

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. *-commutative 87.6%

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

      3. associate-*r* 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 x around 0 87.2%

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

      1. cancel-sign-sub-inv 87.2%

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

      2. metadata-eval 87.2%

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

      3. +-commutative 87.2%

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

      4. fma-def 87.2%

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

      5. times-frac 91.2%

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

      6. associate-/r* 91.2%

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

      7. *-commutative 91.2%

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

      8. associate-/l* 86.7%

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

      9. associate-/r/ 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in z around 0 91.3%

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

      1. associate-*l/ 95.3%

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

      2. *-commutative 95.3%

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

   9. Simplified 95.3%

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

   10. Taylor expanded in b around inf 94.2%

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

   11. Taylor expanded in c around 0 90.1%

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

   if 3.7999999999999999e78 < z

   1. Initial program 47.4%

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

      1. associate-+l- 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-*r* 51.1%

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

      4. *-commutative 51.1%

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

      5. associate-+l- 51.1%

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

   3. Simplified 54.9%

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

   4. Taylor expanded in x around 0 78.7%

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

      1. cancel-sign-sub-inv 78.7%

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

      2. metadata-eval 78.7%

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

      3. +-commutative 78.7%

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

      4. fma-def 78.7%

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

      5. times-frac 76.9%

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

      6. associate-/r* 74.8%

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

      7. *-commutative 74.8%

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

      8. associate-/l* 78.0%

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

      9. associate-/r/ 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in y around inf 78.4%

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

      1. associate-*r/ 78.5%

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

      2. *-commutative 78.5%

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

      3. *-commutative 78.5%

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

      4. times-frac 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-/l* 89.1%

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

   9. Simplified 89.1%

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

   10. Taylor expanded in a around 0 85.7%

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

       1. associate-/l* 85.4%

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

       2. *-rgt-identity 85.4%

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

       3. associate-*r/ 85.5%

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

       4. associate-/r/ 85.5%

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

       5. associate-*l/ 85.6%

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

       6. *-lft-identity 85.6%

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

   12. Simplified 85.6%

       \[\leadsto \frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]
3. Recombined 6 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-199}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 4: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+59} \lor \neg \left(c \leq 10^{+32}\right):\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -3.2e+59) (not (<= c 1e+32)))
   (+ (* (* (/ a c) t) -4.0) (/ (+ (/ b c) (* 9.0 (* x (/ y c)))) z))
   (/ (+ (/ b z) (+ (* 9.0 (/ (* y x) z)) (* -4.0 (* a t)))) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -3.2e+59) || !(c <= 1e+32)) {
		tmp = (((a / c) * t) * -4.0) + (((b / c) + (9.0 * (x * (y / c)))) / z);
	} else {
		tmp = ((b / z) + ((9.0 * ((y * x) / z)) + (-4.0 * (a * t)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 ((c <= (-3.2d+59)) .or. (.not. (c <= 1d+32))) then
        tmp = (((a / c) * t) * (-4.0d0)) + (((b / c) + (9.0d0 * (x * (y / c)))) / z)
    else
        tmp = ((b / z) + ((9.0d0 * ((y * x) / z)) + ((-4.0d0) * (a * t)))) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -3.2e+59) || !(c <= 1e+32)) {
		tmp = (((a / c) * t) * -4.0) + (((b / c) + (9.0 * (x * (y / c)))) / z);
	} else {
		tmp = ((b / z) + ((9.0 * ((y * x) / z)) + (-4.0 * (a * t)))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -3.2e+59) or not (c <= 1e+32):
		tmp = (((a / c) * t) * -4.0) + (((b / c) + (9.0 * (x * (y / c)))) / z)
	else:
		tmp = ((b / z) + ((9.0 * ((y * x) / z)) + (-4.0 * (a * t)))) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -3.2e+59) || !(c <= 1e+32))
		tmp = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + Float64(Float64(Float64(b / c) + Float64(9.0 * Float64(x * Float64(y / c)))) / z));
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(Float64(9.0 * Float64(Float64(y * x) / z)) + Float64(-4.0 * Float64(a * t)))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((c <= -3.2e+59) || ~((c <= 1e+32)))
		tmp = (((a / c) * t) * -4.0) + (((b / c) + (9.0 * (x * (y / c)))) / z);
	else
		tmp = ((b / z) + ((9.0 * ((y * x) / z)) + (-4.0 * (a * t)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -3.2e+59], N[Not[LessEqual[c, 1e+32]], $MachinePrecision]], N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.19999999999999982e59 or 1.00000000000000005e32 < c

   1. Initial program 65.5%

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

      1. associate-+l- 65.5%

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

      2. *-commutative 65.5%

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

      3. associate-*r* 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-+l- 66.4%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in x around 0 77.5%

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

      1. cancel-sign-sub-inv 77.5%

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

      2. metadata-eval 77.5%

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

      3. +-commutative 77.5%

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

      4. fma-def 77.5%

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

      5. times-frac 79.0%

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

      6. associate-/r* 81.5%

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

      7. *-commutative 81.5%

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

      8. associate-/l* 93.5%

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

      9. associate-/r/ 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in z around 0 92.0%

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

      1. associate-*l/ 94.6%

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

      2. *-commutative 94.6%

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

   9. Simplified 94.6%

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

   if -3.19999999999999982e59 < c < 1.00000000000000005e32

   1. Initial program 87.1%

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

      1. associate-+l- 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*r* 87.8%

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

      4. *-commutative 87.8%

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

      5. associate-+l- 87.8%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 85.7%

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

      1. cancel-sign-sub-inv 85.7%

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

      2. metadata-eval 85.7%

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

      3. +-commutative 85.7%

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

      4. fma-def 85.7%

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

      5. times-frac 81.2%

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

      6. associate-/r* 79.5%

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

      7. *-commutative 79.5%

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

      8. associate-/l* 78.1%

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

      9. associate-/r/ 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in z around 0 83.1%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   9. Simplified 82.4%

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

   10. Taylor expanded in c around 0 97.8%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+59} \lor \neg \left(c \leq 10^{+32}\right):\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)\right)}{c}\\ \end{array} \]

Alternative 5: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+54} \lor \neg \left(z \leq 1.75 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c} + \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.3e+54) (not (<= z 1.75e+22)))
   (+ (/ (+ (/ b z) (* 9.0 (* y (/ x z)))) c) (* (* (/ a c) t) -4.0))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.3e+54) || !(z <= 1.75e+22)) {
		tmp = (((b / z) + (9.0 * (y * (x / z)))) / c) + (((a / c) * t) * -4.0);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.3d+54)) .or. (.not. (z <= 1.75d+22))) then
        tmp = (((b / z) + (9.0d0 * (y * (x / z)))) / c) + (((a / c) * t) * (-4.0d0))
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.3e+54) || !(z <= 1.75e+22)) {
		tmp = (((b / z) + (9.0 * (y * (x / z)))) / c) + (((a / c) * t) * -4.0);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.3e+54) or not (z <= 1.75e+22):
		tmp = (((b / z) + (9.0 * (y * (x / z)))) / c) + (((a / c) * t) * -4.0)
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.3e+54) || !(z <= 1.75e+22))
		tmp = Float64(Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(y * Float64(x / z)))) / c) + Float64(Float64(Float64(a / c) * t) * -4.0));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.3e+54) || ~((z <= 1.75e+22)))
		tmp = (((b / z) + (9.0 * (y * (x / z)))) / c) + (((a / c) * t) * -4.0);
	else
		tmp = (b + ((y * (9.0 * x)) - (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.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.3e+54], N[Not[LessEqual[z, 1.75e+22]], $MachinePrecision]], N[(N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] + N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e54 or 1.75e22 < z

   1. Initial program 53.4%

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

      1. associate-+l- 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*r* 55.9%

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

      4. *-commutative 55.9%

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

      5. associate-+l- 55.9%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in x around 0 80.2%

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

      1. cancel-sign-sub-inv 80.2%

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

      2. metadata-eval 80.2%

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

      3. +-commutative 80.2%

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

      4. fma-def 80.2%

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

      5. times-frac 80.1%

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

      6. associate-/r* 79.1%

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

      7. *-commutative 79.1%

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

      8. associate-/l* 86.3%

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

      9. associate-/r/ 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in c around 0 88.3%

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

      1. associate-*r/ 93.2%

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

   9. Simplified 93.2%

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

   if -3.3e54 < z < 1.75e22

   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 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+54} \lor \neg \left(z \leq 1.75 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c} + \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+59}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1 + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ x (/ z y)) (/ 9.0 c))))
   (if (<= z -6e+59)
     (+ (* (* (/ a c) t) -4.0) t_1)
     (if (<= z 1.4e+91)
       (/ (+ b (- (* y (* 9.0 x)) (* (* z 4.0) (* a t)))) (* z c))
       (+ t_1 (* -4.0 (* a (/ t c))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / (z / y)) * (9.0 / c);
	double tmp;
	if (z <= -6e+59) {
		tmp = (((a / c) * t) * -4.0) + t_1;
	} else if (z <= 1.4e+91) {
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = t_1 + (-4.0 * (a * (t / c)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (z / y)) * (9.0d0 / c)
    if (z <= (-6d+59)) then
        tmp = (((a / c) * t) * (-4.0d0)) + t_1
    else if (z <= 1.4d+91) then
        tmp = (b + ((y * (9.0d0 * x)) - ((z * 4.0d0) * (a * t)))) / (z * c)
    else
        tmp = t_1 + ((-4.0d0) * (a * (t / c)))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / (z / y)) * (9.0 / c);
	double tmp;
	if (z <= -6e+59) {
		tmp = (((a / c) * t) * -4.0) + t_1;
	} else if (z <= 1.4e+91) {
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = t_1 + (-4.0 * (a * (t / c)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / (z / y)) * (9.0 / c)
	tmp = 0
	if z <= -6e+59:
		tmp = (((a / c) * t) * -4.0) + t_1
	elif z <= 1.4e+91:
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (z * c)
	else:
		tmp = t_1 + (-4.0 * (a * (t / c)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / Float64(z / y)) * Float64(9.0 / c))
	tmp = 0.0
	if (z <= -6e+59)
		tmp = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + t_1);
	elseif (z <= 1.4e+91)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	else
		tmp = Float64(t_1 + Float64(-4.0 * Float64(a * Float64(t / c))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / (z / y)) * (9.0 / c);
	tmp = 0.0;
	if (z <= -6e+59)
		tmp = (((a / c) * t) * -4.0) + t_1;
	elseif (z <= 1.4e+91)
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (z * c);
	else
		tmp = t_1 + (-4.0 * (a * (t / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+59], N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 1.4e+91], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000001e59

   1. Initial program 53.2%

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

      1. associate-+l- 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-*r* 55.1%

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

      4. *-commutative 55.1%

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

      5. associate-+l- 55.1%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in x around 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. metadata-eval 79.3%

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

      3. +-commutative 79.3%

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

      4. fma-def 79.3%

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

      5. times-frac 81.0%

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

      6. associate-/r* 81.0%

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

      7. *-commutative 81.0%

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

      8. associate-/l* 92.0%

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

      9. associate-/r/ 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in y around inf 77.3%

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

      1. associate-*r/ 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. times-frac 77.4%

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

      5. *-commutative 77.4%

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

      6. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

   if -6.0000000000000001e59 < z < 1.3999999999999999e91

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*r* 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 93.7%

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

   if 1.3999999999999999e91 < z

   1. Initial program 45.3%

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

      1. associate-+l- 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*r* 49.2%

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

      4. *-commutative 49.2%

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

      5. associate-+l- 49.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. cancel-sign-sub-inv 77.9%

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

      2. metadata-eval 77.9%

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

      3. +-commutative 77.9%

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

      4. fma-def 77.9%

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

      5. times-frac 77.8%

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

      6. associate-/r* 75.7%

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

      7. *-commutative 75.7%

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

      8. associate-/l* 79.0%

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

      9. associate-/r/ 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in y around inf 77.6%

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

      1. associate-*r/ 77.6%

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

      2. *-commutative 77.6%

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

      3. *-commutative 77.6%

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

      4. times-frac 83.2%

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

      5. *-commutative 83.2%

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

      6. associate-/l* 88.7%

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

   9. Simplified 88.7%

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

   10. Taylor expanded in a around 0 85.1%

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

       1. associate-/l* 84.8%

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

       2. *-rgt-identity 84.8%

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

       3. associate-*r/ 84.9%

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

       4. associate-/r/ 84.9%

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

       5. associate-*l/ 85.0%

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

       6. *-lft-identity 85.0%

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

   12. Simplified 85.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+59}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 7: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+90}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1 + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ x (/ z y)) (/ 9.0 c))))
   (if (<= z -5e+55)
     (+ (* (* (/ a c) t) -4.0) t_1)
     (if (<= z 9e+90)
       (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))
       (+ t_1 (* -4.0 (* a (/ t c))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / (z / y)) * (9.0 / c);
	double tmp;
	if (z <= -5e+55) {
		tmp = (((a / c) * t) * -4.0) + t_1;
	} else if (z <= 9e+90) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1 + (-4.0 * (a * (t / c)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (z / y)) * (9.0d0 / c)
    if (z <= (-5d+55)) then
        tmp = (((a / c) * t) * (-4.0d0)) + t_1
    else if (z <= 9d+90) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = t_1 + ((-4.0d0) * (a * (t / c)))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / (z / y)) * (9.0 / c);
	double tmp;
	if (z <= -5e+55) {
		tmp = (((a / c) * t) * -4.0) + t_1;
	} else if (z <= 9e+90) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1 + (-4.0 * (a * (t / c)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / (z / y)) * (9.0 / c)
	tmp = 0
	if z <= -5e+55:
		tmp = (((a / c) * t) * -4.0) + t_1
	elif z <= 9e+90:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = t_1 + (-4.0 * (a * (t / c)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / Float64(z / y)) * Float64(9.0 / c))
	tmp = 0.0
	if (z <= -5e+55)
		tmp = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + t_1);
	elseif (z <= 9e+90)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(t_1 + Float64(-4.0 * Float64(a * Float64(t / c))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / (z / y)) * (9.0 / c);
	tmp = 0.0;
	if (z <= -5e+55)
		tmp = (((a / c) * t) * -4.0) + t_1;
	elseif (z <= 9e+90)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = t_1 + (-4.0 * (a * (t / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+55], N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 9e+90], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000046e55

   1. Initial program 53.2%

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

      1. associate-+l- 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-*r* 55.1%

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

      4. *-commutative 55.1%

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

      5. associate-+l- 55.1%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in x around 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. metadata-eval 79.3%

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

      3. +-commutative 79.3%

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

      4. fma-def 79.3%

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

      5. times-frac 81.0%

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

      6. associate-/r* 81.0%

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

      7. *-commutative 81.0%

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

      8. associate-/l* 92.0%

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

      9. associate-/r/ 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in y around inf 77.3%

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

      1. associate-*r/ 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. times-frac 77.4%

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

      5. *-commutative 77.4%

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

      6. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

   if -5.00000000000000046e55 < z < 9e90

   1. Initial program 96.9%

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

   if 9e90 < z

   1. Initial program 45.3%

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

      1. associate-+l- 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*r* 49.2%

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

      4. *-commutative 49.2%

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

      5. associate-+l- 49.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. cancel-sign-sub-inv 77.9%

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

      2. metadata-eval 77.9%

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

      3. +-commutative 77.9%

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

      4. fma-def 77.9%

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

      5. times-frac 77.8%

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

      6. associate-/r* 75.7%

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

      7. *-commutative 75.7%

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

      8. associate-/l* 79.0%

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

      9. associate-/r/ 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in y around inf 77.6%

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

      1. associate-*r/ 77.6%

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

      2. *-commutative 77.6%

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

      3. *-commutative 77.6%

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

      4. times-frac 83.2%

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

      5. *-commutative 83.2%

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

      6. associate-/l* 88.7%

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

   9. Simplified 88.7%

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

   10. Taylor expanded in a around 0 85.1%

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

       1. associate-/l* 84.8%

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

       2. *-rgt-identity 84.8%

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

       3. associate-*r/ 84.9%

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

       4. associate-/r/ 84.9%

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

       5. associate-*l/ 85.0%

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

       6. *-lft-identity 85.0%

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

   12. Simplified 85.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+90}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} \cdot \frac{9}{c} + -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 8: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+60}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.1e+60)
   (+ (* (* (/ a c) t) -4.0) (* (/ x (/ z y)) (/ 9.0 c)))
   (if (<= z 2.4e-18)
     (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))
     (/ (+ (/ b z) (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z))))) c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.1e+60) {
		tmp = (((a / c) * t) * -4.0) + ((x / (z / y)) * (9.0 / c));
	} else if (z <= 2.4e-18) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z))))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 <= (-4.1d+60)) then
        tmp = (((a / c) * t) * (-4.0d0)) + ((x / (z / y)) * (9.0d0 / c))
    else if (z <= 2.4d-18) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = ((b / z) + (((-4.0d0) * (a * t)) + (9.0d0 * (x * (y / z))))) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.1e+60) {
		tmp = (((a / c) * t) * -4.0) + ((x / (z / y)) * (9.0 / c));
	} else if (z <= 2.4e-18) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z))))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -4.1e+60:
		tmp = (((a / c) * t) * -4.0) + ((x / (z / y)) * (9.0 / c))
	elif z <= 2.4e-18:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z))))) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4.1e+60)
		tmp = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + Float64(Float64(x / Float64(z / y)) * Float64(9.0 / c)));
	elseif (z <= 2.4e-18)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z))))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -4.1e+60)
		tmp = (((a / c) * t) * -4.0) + ((x / (z / y)) * (9.0 / c));
	elseif (z <= 2.4e-18)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z))))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -4.1e+60], N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-18], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e60

   1. Initial program 53.2%

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

      1. associate-+l- 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-*r* 55.1%

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

      4. *-commutative 55.1%

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

      5. associate-+l- 55.1%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in x around 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. metadata-eval 79.3%

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

      3. +-commutative 79.3%

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

      4. fma-def 79.3%

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

      5. times-frac 81.0%

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

      6. associate-/r* 81.0%

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

      7. *-commutative 81.0%

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

      8. associate-/l* 92.0%

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

      9. associate-/r/ 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in y around inf 77.3%

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

      1. associate-*r/ 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. times-frac 77.4%

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

      5. *-commutative 77.4%

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

      6. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

   if -4.1e60 < z < 2.39999999999999994e-18

   1. Initial program 98.6%

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

   if 2.39999999999999994e-18 < z

   1. Initial program 56.7%

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

      1. associate-+l- 56.7%

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

      2. *-commutative 56.7%

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

      3. associate-*r* 59.5%

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

      4. *-commutative 59.5%

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

      5. associate-+l- 59.5%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in x around 0 81.4%

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

      1. cancel-sign-sub-inv 81.4%

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

      2. metadata-eval 81.4%

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

      3. +-commutative 81.4%

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

      4. fma-def 81.4%

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

      5. times-frac 81.3%

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

      6. associate-/r* 79.8%

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

      7. *-commutative 79.8%

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

      8. associate-/l* 80.7%

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

      9. associate-/r/ 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in z around 0 79.5%

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

      1. associate-*l/ 82.2%

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

      2. *-commutative 82.2%

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

   9. Simplified 82.2%

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

   10. Taylor expanded in c around 0 89.3%

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

       1. div-inv 89.3%

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

       2. *-commutative 89.3%

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

   12. Applied egg-rr 89.3%

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

       1. associate-*l* 93.3%

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

       2. associate-*r/ 93.3%

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

       3. *-rgt-identity 93.3%

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

   14. Simplified 93.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+60}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{x}{\frac{z}{y}} \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)}{c}\\ \end{array} \]

Alternative 9: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-164}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* (* (/ a c) t) -4.0) (/ b (* z c)))))
   (if (<= t -1.05e+96)
     t_1
     (if (<= t -1.6e-68)
       (/ (+ (* 9.0 (/ (* y x) z)) (* -4.0 (* a t))) c)
       (if (<= t 2e-164) (/ (+ b (* 9.0 (* y x))) (* z c)) t_1)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((a / c) * t) * -4.0) + (b / (z * c));
	double tmp;
	if (t <= -1.05e+96) {
		tmp = t_1;
	} else if (t <= -1.6e-68) {
		tmp = ((9.0 * ((y * x) / z)) + (-4.0 * (a * t))) / c;
	} else if (t <= 2e-164) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 = (((a / c) * t) * (-4.0d0)) + (b / (z * c))
    if (t <= (-1.05d+96)) then
        tmp = t_1
    else if (t <= (-1.6d-68)) then
        tmp = ((9.0d0 * ((y * x) / z)) + ((-4.0d0) * (a * t))) / c
    else if (t <= 2d-164) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((a / c) * t) * -4.0) + (b / (z * c));
	double tmp;
	if (t <= -1.05e+96) {
		tmp = t_1;
	} else if (t <= -1.6e-68) {
		tmp = ((9.0 * ((y * x) / z)) + (-4.0 * (a * t))) / c;
	} else if (t <= 2e-164) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (((a / c) * t) * -4.0) + (b / (z * c))
	tmp = 0
	if t <= -1.05e+96:
		tmp = t_1
	elif t <= -1.6e-68:
		tmp = ((9.0 * ((y * x) / z)) + (-4.0 * (a * t))) / c
	elif t <= 2e-164:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + Float64(b / Float64(z * c)))
	tmp = 0.0
	if (t <= -1.05e+96)
		tmp = t_1;
	elseif (t <= -1.6e-68)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / z)) + Float64(-4.0 * Float64(a * t))) / c);
	elseif (t <= 2e-164)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((a / c) * t) * -4.0) + (b / (z * c));
	tmp = 0.0;
	if (t <= -1.05e+96)
		tmp = t_1;
	elseif (t <= -1.6e-68)
		tmp = ((9.0 * ((y * x) / z)) + (-4.0 * (a * t))) / c;
	elseif (t <= 2e-164)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+96], t$95$1, If[LessEqual[t, -1.6e-68], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 2e-164], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0500000000000001e96 or 1.99999999999999992e-164 < t

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 76.8%

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

      4. *-commutative 76.8%

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

      5. associate-+l- 76.8%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in x around 0 76.7%

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

      1. cancel-sign-sub-inv 76.7%

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

      2. metadata-eval 76.7%

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

      3. +-commutative 76.7%

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

      4. fma-def 76.7%

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

      5. times-frac 77.3%

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

      6. associate-/r* 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-/l* 84.7%

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

      9. associate-/r/ 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in z around 0 86.9%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   9. Simplified 88.1%

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

   10. Taylor expanded in b around inf 74.1%

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

   if -1.0500000000000001e96 < t < -1.5999999999999999e-68

   1. Initial program 67.5%

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

      1. associate-+l- 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 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 70.6%

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

   4. Taylor expanded in x around 0 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. +-commutative 83.6%

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

      4. fma-def 83.6%

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

      5. times-frac 83.3%

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

      6. associate-/r* 86.4%

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

      7. *-commutative 86.4%

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

      8. associate-/l* 86.4%

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

      9. associate-/r/ 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in y around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. *-commutative 64.7%

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

      3. *-commutative 64.7%

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

      4. times-frac 64.8%

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

      5. *-commutative 64.8%

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

      6. associate-/l* 61.5%

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

   9. Simplified 61.5%

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

   10. Taylor expanded in c around 0 71.0%

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

   if -1.5999999999999999e-68 < t < 1.99999999999999992e-164

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. associate-*l* 91.5%

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

      3. fma-neg 91.5%

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

      4. neg-sub0 91.5%

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

      5. associate-+l- 91.5%

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

      6. neg-sub0 91.5%

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

      7. +-commutative 91.5%

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

      8. distribute-rgt-neg-out 91.5%

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

      9. *-commutative 91.5%

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

      10. associate-*l* 85.1%

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

      11. distribute-rgt-neg-in 85.1%

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

      12. *-commutative 85.1%

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

      13. distribute-rgt-neg-in 85.1%

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

      14. distribute-rgt-neg-in 85.1%

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

      15. metadata-eval 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around 0 82.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-164}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \end{array} \]

Alternative 10: 68.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.9e+39)
   (* (* (/ a c) t) -4.0)
   (if (<= z 3.3e+15)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (* -4.0 (/ a (/ c t))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.9e+39) {
		tmp = ((a / c) * t) * -4.0;
	} else if (z <= 3.3e+15) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.9d+39)) then
        tmp = ((a / c) * t) * (-4.0d0)
    else if (z <= 3.3d+15) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.9e+39) {
		tmp = ((a / c) * t) * -4.0;
	} else if (z <= 3.3e+15) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.9e+39:
		tmp = ((a / c) * t) * -4.0
	elif z <= 3.3e+15:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.9e+39)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (z <= 3.3e+15)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.9e+39)
		tmp = ((a / c) * t) * -4.0;
	elseif (z <= 3.3e+15)
		tmp = (b + (9.0 * (y * x))) / (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.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.9e+39], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 3.3e+15], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9000000000000001e39

   1. Initial program 56.5%

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

      1. associate-+l- 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-*r* 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 63.4%

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

   4. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 72.1%

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

      3. associate-/r/ 62.2%

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

   6. Simplified 62.2%

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

   if -3.9000000000000001e39 < z < 3.3e15

   1. Initial program 97.9%

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

      1. associate-+l- 97.9%

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

      2. associate-*l* 98.6%

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

      3. fma-neg 98.6%

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

      4. neg-sub0 98.6%

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

      5. associate-+l- 98.6%

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

      6. neg-sub0 98.6%

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

      7. +-commutative 98.6%

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

      8. distribute-rgt-neg-out 98.6%

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

      9. *-commutative 98.6%

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

      10. associate-*l* 97.9%

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

      11. distribute-rgt-neg-in 97.9%

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

      12. *-commutative 97.9%

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

      13. distribute-rgt-neg-in 97.9%

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

      14. distribute-rgt-neg-in 97.9%

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

      15. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around 0 83.9%

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

   if 3.3e15 < z

   1. Initial program 55.5%

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

      1. associate-+l- 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 58.4%

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

      4. *-commutative 58.4%

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

      5. associate-+l- 58.4%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. associate-/l* 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 11: 73.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;z \leq 10^{-44}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.8e+39)
   (* (* (/ a c) t) -4.0)
   (if (<= z 1e-44)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (/ (+ (/ b z) (* -4.0 (* a t))) c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.8e+39) {
		tmp = ((a / c) * t) * -4.0;
	} else if (z <= 1e-44) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 <= (-4.8d+39)) then
        tmp = ((a / c) * t) * (-4.0d0)
    else if (z <= 1d-44) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.8e+39) {
		tmp = ((a / c) * t) * -4.0;
	} else if (z <= 1e-44) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -4.8e+39:
		tmp = ((a / c) * t) * -4.0
	elif z <= 1e-44:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4.8e+39)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (z <= 1e-44)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -4.8e+39)
		tmp = ((a / c) * t) * -4.0;
	elseif (z <= 1e-44)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -4.8e+39], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 1e-44], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000002e39

   1. Initial program 56.5%

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

      1. associate-+l- 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-*r* 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 63.4%

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

   4. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 72.1%

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

      3. associate-/r/ 62.2%

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

   6. Simplified 62.2%

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

   if -4.8000000000000002e39 < z < 9.99999999999999953e-45

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. associate-*l* 99.3%

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

      3. fma-neg 99.3%

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

      4. neg-sub0 99.3%

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

      5. associate-+l- 99.3%

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

      6. neg-sub0 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-rgt-neg-out 99.3%

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

      9. *-commutative 99.3%

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

      10. associate-*l* 98.5%

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

      11. distribute-rgt-neg-in 98.5%

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

      12. *-commutative 98.5%

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

      13. distribute-rgt-neg-in 98.5%

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

      14. distribute-rgt-neg-in 98.5%

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

      15. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around 0 85.9%

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

   if 9.99999999999999953e-45 < z

   1. Initial program 59.6%

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

      1. associate-+l- 59.6%

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

      2. *-commutative 59.6%

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

      3. associate-*r* 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-+l- 62.1%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 81.3%

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

      1. cancel-sign-sub-inv 81.3%

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

      2. metadata-eval 81.3%

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

      3. +-commutative 81.3%

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

      4. fma-def 81.3%

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

      5. times-frac 81.2%

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

      6. associate-/r* 79.8%

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

      7. *-commutative 79.8%

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

      8. associate-/l* 80.6%

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

      9. associate-/r/ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in z around 0 79.5%

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

      1. associate-*l/ 82.1%

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

      2. *-commutative 82.1%

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

   9. Simplified 82.1%

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

   10. Taylor expanded in b around inf 76.8%

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

   11. Taylor expanded in c around 0 78.2%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;z \leq 10^{-44}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 12: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.7e+39)
   (+ (* (* (/ a c) t) -4.0) (/ b (* z c)))
   (if (<= z 7.8e-44)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (/ (+ (/ b z) (* -4.0 (* a t))) c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.7e+39) {
		tmp = (((a / c) * t) * -4.0) + (b / (z * c));
	} else if (z <= 7.8e-44) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.7d+39)) then
        tmp = (((a / c) * t) * (-4.0d0)) + (b / (z * c))
    else if (z <= 7.8d-44) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.7e+39) {
		tmp = (((a / c) * t) * -4.0) + (b / (z * c));
	} else if (z <= 7.8e-44) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.7e+39:
		tmp = (((a / c) * t) * -4.0) + (b / (z * c))
	elif z <= 7.8e-44:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.7e+39)
		tmp = Float64(Float64(Float64(Float64(a / c) * t) * -4.0) + Float64(b / Float64(z * c)));
	elseif (z <= 7.8e-44)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.7e+39)
		tmp = (((a / c) * t) * -4.0) + (b / (z * c));
	elseif (z <= 7.8e-44)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.7e+39], N[(N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-44], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000012e39

   1. Initial program 56.5%

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

      1. associate-+l- 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-*r* 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 63.4%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. cancel-sign-sub-inv 80.8%

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

      2. metadata-eval 80.8%

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

      3. +-commutative 80.8%

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

      4. fma-def 80.8%

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

      5. times-frac 82.4%

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

      6. associate-/r* 82.3%

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

      7. *-commutative 82.3%

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

      8. associate-/l* 92.5%

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

      9. associate-/r/ 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in z around 0 80.8%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   9. Simplified 82.4%

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

   10. Taylor expanded in b around inf 67.6%

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

   if -3.70000000000000012e39 < z < 7.8000000000000004e-44

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. associate-*l* 99.3%

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

      3. fma-neg 99.3%

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

      4. neg-sub0 99.3%

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

      5. associate-+l- 99.3%

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

      6. neg-sub0 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-rgt-neg-out 99.3%

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

      9. *-commutative 99.3%

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

      10. associate-*l* 98.5%

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

      11. distribute-rgt-neg-in 98.5%

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

      12. *-commutative 98.5%

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

      13. distribute-rgt-neg-in 98.5%

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

      14. distribute-rgt-neg-in 98.5%

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

      15. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around 0 85.9%

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

   if 7.8000000000000004e-44 < z

   1. Initial program 59.6%

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

      1. associate-+l- 59.6%

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

      2. *-commutative 59.6%

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

      3. associate-*r* 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-+l- 62.1%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 81.3%

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

      1. cancel-sign-sub-inv 81.3%

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

      2. metadata-eval 81.3%

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

      3. +-commutative 81.3%

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

      4. fma-def 81.3%

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

      5. times-frac 81.2%

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

      6. associate-/r* 79.8%

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

      7. *-commutative 79.8%

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

      8. associate-/l* 80.6%

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

      9. associate-/r/ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in z around 0 79.5%

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

      1. associate-*l/ 82.1%

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

      2. *-commutative 82.1%

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

   9. Simplified 82.1%

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

   10. Taylor expanded in b around inf 76.8%

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

   11. Taylor expanded in c around 0 78.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 13: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{if}\;t \leq -1750000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-210}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-138}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ a c) t) -4.0)))
   (if (<= t -1750000000.0)
     t_1
     (if (<= t -1.45e-210)
       (* 9.0 (* x (/ y (* z c))))
       (if (<= t 4.6e-138) (/ b (* z c)) t_1)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a / c) * t) * -4.0;
	double tmp;
	if (t <= -1750000000.0) {
		tmp = t_1;
	} else if (t <= -1.45e-210) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t <= 4.6e-138) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 = ((a / c) * t) * (-4.0d0)
    if (t <= (-1750000000.0d0)) then
        tmp = t_1
    else if (t <= (-1.45d-210)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (t <= 4.6d-138) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a / c) * t) * -4.0;
	double tmp;
	if (t <= -1750000000.0) {
		tmp = t_1;
	} else if (t <= -1.45e-210) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t <= 4.6e-138) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((a / c) * t) * -4.0
	tmp = 0
	if t <= -1750000000.0:
		tmp = t_1
	elif t <= -1.45e-210:
		tmp = 9.0 * (x * (y / (z * c)))
	elif t <= 4.6e-138:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a / c) * t) * -4.0)
	tmp = 0.0
	if (t <= -1750000000.0)
		tmp = t_1;
	elseif (t <= -1.45e-210)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t <= 4.6e-138)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((a / c) * t) * -4.0;
	tmp = 0.0;
	if (t <= -1750000000.0)
		tmp = t_1;
	elseif (t <= -1.45e-210)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (t <= 4.6e-138)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[t, -1750000000.0], t$95$1, If[LessEqual[t, -1.45e-210], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-138], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e9 or 4.5999999999999998e-138 < t

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-/l* 60.2%

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

      3. associate-/r/ 58.0%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   6. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot -4} \]

   if -1.75e9 < t < -1.45000000000000003e-210

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 46.9%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. expm1-log1p-u 22.4%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 22.5%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. associate-/l* 24.6%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{c \cdot z}{x}}}\right)} - 1\right) \]

   6. Applied egg-rr 24.6%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{c \cdot z}{x}}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 24.5%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{c \cdot z}{x}}\right)\right)} \]

      2. expm1-log1p 46.8%

         \[\leadsto 9 \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{x}}} \]

      3. associate-/r/ 41.9%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c \cdot z} \cdot x\right)} \]

      4. *-commutative 41.9%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   8. Simplified 41.9%

      \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   if -1.45000000000000003e-210 < t < 4.5999999999999998e-138

   1. Initial program 95.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 95.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. associate-*l* 95.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}{z \cdot c} \]

      3. fma-neg 95.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)}}{z \cdot c} \]

      4. neg-sub0 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      5. associate-+l- 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      6. neg-sub0 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right)}{z \cdot c} \]

      7. +-commutative 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{b + \left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}\right)}{z \cdot c} \]

      8. distribute-rgt-neg-out 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot \left(-a\right)}\right)}{z \cdot c} \]

      9. *-commutative 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(t \cdot \left(z \cdot 4\right)\right)} \cdot \left(-a\right)\right)}{z \cdot c} \]

      10. associate-*l* 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{t \cdot \left(\left(z \cdot 4\right) \cdot \left(-a\right)\right)}\right)}{z \cdot c} \]

      11. distribute-rgt-neg-in 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(-\left(z \cdot 4\right) \cdot a\right)}\right)}{z \cdot c} \]

      12. *-commutative 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(-\color{blue}{a \cdot \left(z \cdot 4\right)}\right)\right)}{z \cdot c} \]

      13. distribute-rgt-neg-in 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(a \cdot \left(-z \cdot 4\right)\right)}\right)}{z \cdot c} \]

      14. distribute-rgt-neg-in 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \color{blue}{\left(z \cdot \left(-4\right)\right)}\right)\right)}{z \cdot c} \]

      15. metadata-eval 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot \color{blue}{-4}\right)\right)\right)}{z \cdot c} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 59.2%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1750000000:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-210}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-138}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \]

Alternative 14: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{if}\;t \leq -440000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-210}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ a c) t) -4.0)))
   (if (<= t -440000000.0)
     t_1
     (if (<= t -7e-210)
       (* 9.0 (/ (* y x) (* z c)))
       (if (<= t 1.9e-138) (/ b (* z c)) t_1)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a / c) * t) * -4.0;
	double tmp;
	if (t <= -440000000.0) {
		tmp = t_1;
	} else if (t <= -7e-210) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= 1.9e-138) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 = ((a / c) * t) * (-4.0d0)
    if (t <= (-440000000.0d0)) then
        tmp = t_1
    else if (t <= (-7d-210)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (t <= 1.9d-138) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a / c) * t) * -4.0;
	double tmp;
	if (t <= -440000000.0) {
		tmp = t_1;
	} else if (t <= -7e-210) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= 1.9e-138) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((a / c) * t) * -4.0
	tmp = 0
	if t <= -440000000.0:
		tmp = t_1
	elif t <= -7e-210:
		tmp = 9.0 * ((y * x) / (z * c))
	elif t <= 1.9e-138:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a / c) * t) * -4.0)
	tmp = 0.0
	if (t <= -440000000.0)
		tmp = t_1;
	elseif (t <= -7e-210)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (t <= 1.9e-138)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((a / c) * t) * -4.0;
	tmp = 0.0;
	if (t <= -440000000.0)
		tmp = t_1;
	elseif (t <= -7e-210)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (t <= 1.9e-138)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[t, -440000000.0], t$95$1, If[LessEqual[t, -7e-210], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-138], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e8 or 1.9000000000000001e-138 < t

   1. Initial program 73.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 60.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

      3. associate-/r/ 58.0%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   6. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot -4} \]

   if -4.4e8 < t < -7.00000000000000031e-210

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 46.9%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   if -7.00000000000000031e-210 < t < 1.9000000000000001e-138

   1. Initial program 95.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 95.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. associate-*l* 95.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}{z \cdot c} \]

      3. fma-neg 95.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)}}{z \cdot c} \]

      4. neg-sub0 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      5. associate-+l- 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      6. neg-sub0 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right)}{z \cdot c} \]

      7. +-commutative 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{b + \left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}\right)}{z \cdot c} \]

      8. distribute-rgt-neg-out 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot \left(-a\right)}\right)}{z \cdot c} \]

      9. *-commutative 95.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(t \cdot \left(z \cdot 4\right)\right)} \cdot \left(-a\right)\right)}{z \cdot c} \]

      10. associate-*l* 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{t \cdot \left(\left(z \cdot 4\right) \cdot \left(-a\right)\right)}\right)}{z \cdot c} \]

      11. distribute-rgt-neg-in 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(-\left(z \cdot 4\right) \cdot a\right)}\right)}{z \cdot c} \]

      12. *-commutative 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(-\color{blue}{a \cdot \left(z \cdot 4\right)}\right)\right)}{z \cdot c} \]

      13. distribute-rgt-neg-in 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(a \cdot \left(-z \cdot 4\right)\right)}\right)}{z \cdot c} \]

      14. distribute-rgt-neg-in 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \color{blue}{\left(z \cdot \left(-4\right)\right)}\right)\right)}{z \cdot c} \]

      15. metadata-eval 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot \color{blue}{-4}\right)\right)\right)}{z \cdot c} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 59.2%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -440000000:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-210}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \]

Alternative 15: 50.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-17} \lor \neg \left(z \leq 8 \cdot 10^{-36}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.5e-17) (not (<= z 8e-36)))
   (* -4.0 (/ (* a t) c))
   (/ b (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.5e-17) || !(z <= 8e-36)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 <= (-1.5d-17)) .or. (.not. (z <= 8d-36))) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.5e-17) || !(z <= 8e-36)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.5e-17) or not (z <= 8e-36):
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.5e-17) || !(z <= 8e-36))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.5e-17) || ~((z <= 8e-36)))
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.5e-17], N[Not[LessEqual[z, 8e-36]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000003e-17 or 7.9999999999999995e-36 < z

   1. Initial program 60.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 62.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 59.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -1.50000000000000003e-17 < z < 7.9999999999999995e-36

   1. Initial program 98.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 98.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. associate-*l* 99.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}{z \cdot c} \]

      3. fma-neg 99.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)}}{z \cdot c} \]

      4. neg-sub0 99.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      5. associate-+l- 99.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      6. neg-sub0 99.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right)}{z \cdot c} \]

      7. +-commutative 99.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{b + \left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}\right)}{z \cdot c} \]

      8. distribute-rgt-neg-out 99.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot \left(-a\right)}\right)}{z \cdot c} \]

      9. *-commutative 99.3%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(t \cdot \left(z \cdot 4\right)\right)} \cdot \left(-a\right)\right)}{z \cdot c} \]

      10. associate-*l* 98.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{t \cdot \left(\left(z \cdot 4\right) \cdot \left(-a\right)\right)}\right)}{z \cdot c} \]

      11. distribute-rgt-neg-in 98.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(-\left(z \cdot 4\right) \cdot a\right)}\right)}{z \cdot c} \]

      12. *-commutative 98.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(-\color{blue}{a \cdot \left(z \cdot 4\right)}\right)\right)}{z \cdot c} \]

      13. distribute-rgt-neg-in 98.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(a \cdot \left(-z \cdot 4\right)\right)}\right)}{z \cdot c} \]

      14. distribute-rgt-neg-in 98.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \color{blue}{\left(z \cdot \left(-4\right)\right)}\right)\right)}{z \cdot c} \]

      15. metadata-eval 98.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot \color{blue}{-4}\right)\right)\right)}{z \cdot c} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 52.7%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-17} \lor \neg \left(z \leq 8 \cdot 10^{-36}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 16: 50.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1800000000 \lor \neg \left(t \leq 1.14 \cdot 10^{-138}\right):\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1800000000.0) (not (<= t 1.14e-138)))
   (* (* (/ a c) t) -4.0)
   (/ (/ b c) z)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1800000000.0) || !(t <= 1.14e-138)) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1800000000.0d0)) .or. (.not. (t <= 1.14d-138))) then
        tmp = ((a / c) * t) * (-4.0d0)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1800000000.0) || !(t <= 1.14e-138)) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1800000000.0) or not (t <= 1.14e-138):
		tmp = ((a / c) * t) * -4.0
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1800000000.0) || !(t <= 1.14e-138))
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1800000000.0) || ~((t <= 1.14e-138)))
		tmp = ((a / c) * t) * -4.0;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1800000000.0], N[Not[LessEqual[t, 1.14e-138]], $MachinePrecision]], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e9 or 1.1399999999999999e-138 < t

   1. Initial program 73.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 60.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

      3. associate-/r/ 58.0%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   6. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot -4} \]

   if -1.8e9 < t < 1.1399999999999999e-138

   1. Initial program 86.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 86.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 86.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 45.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 46.9%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 46.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1800000000 \lor \neg \left(t \leq 1.14 \cdot 10^{-138}\right):\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 17: 50.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -440000000 \lor \neg \left(t \leq 9.2 \cdot 10^{-141}\right):\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -440000000.0) (not (<= t 9.2e-141)))
   (* (* (/ a c) t) -4.0)
   (* (/ b c) (/ 1.0 z))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -440000000.0) || !(t <= 9.2e-141)) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = (b / c) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-440000000.0d0)) .or. (.not. (t <= 9.2d-141))) then
        tmp = ((a / c) * t) * (-4.0d0)
    else
        tmp = (b / c) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -440000000.0) || !(t <= 9.2e-141)) {
		tmp = ((a / c) * t) * -4.0;
	} else {
		tmp = (b / c) * (1.0 / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -440000000.0) or not (t <= 9.2e-141):
		tmp = ((a / c) * t) * -4.0
	else:
		tmp = (b / c) * (1.0 / z)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -440000000.0) || !(t <= 9.2e-141))
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	else
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -440000000.0) || ~((t <= 9.2e-141)))
		tmp = ((a / c) * t) * -4.0;
	else
		tmp = (b / c) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -440000000.0], N[Not[LessEqual[t, 9.2e-141]], $MachinePrecision]], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e8 or 9.1999999999999998e-141 < t

   1. Initial program 73.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 60.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

      3. associate-/r/ 58.0%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   6. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot -4} \]

   if -4.4e8 < t < 9.1999999999999998e-141

   1. Initial program 86.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 86.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 86.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 45.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 46.9%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 46.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   7. Step-by-step derivation

      1. div-inv 46.9%

         \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   8. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -440000000 \lor \neg \left(t \leq 9.2 \cdot 10^{-141}\right):\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 18: 35.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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);
assert(t < a);
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.
NOTE: t and a 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;
assert t < a;
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])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
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.
NOTE: t and a 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 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. associate-*l* 77.8%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}{z \cdot c} \]

   3. fma-neg 78.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)}}{z \cdot c} \]

   4. neg-sub0 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

   5. associate-+l- 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

   6. neg-sub0 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b\right)}{z \cdot c} \]

   7. +-commutative 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{b + \left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}\right)}{z \cdot c} \]

   8. distribute-rgt-neg-out 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot \left(-a\right)}\right)}{z \cdot c} \]

   9. *-commutative 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{\left(t \cdot \left(z \cdot 4\right)\right)} \cdot \left(-a\right)\right)}{z \cdot c} \]

   10. associate-*l* 78.9%

       \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \color{blue}{t \cdot \left(\left(z \cdot 4\right) \cdot \left(-a\right)\right)}\right)}{z \cdot c} \]

   11. distribute-rgt-neg-in 78.9%

       \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(-\left(z \cdot 4\right) \cdot a\right)}\right)}{z \cdot c} \]

   12. *-commutative 78.9%

       \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(-\color{blue}{a \cdot \left(z \cdot 4\right)}\right)\right)}{z \cdot c} \]

   13. distribute-rgt-neg-in 78.9%

       \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \color{blue}{\left(a \cdot \left(-z \cdot 4\right)\right)}\right)}{z \cdot c} \]

   14. distribute-rgt-neg-in 78.9%

       \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \color{blue}{\left(z \cdot \left(-4\right)\right)}\right)\right)}{z \cdot c} \]

   15. metadata-eval 78.9%

       \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot \color{blue}{-4}\right)\right)\right)}{z \cdot c} \]

3. Simplified 78.9%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}} \]

4. Taylor expanded in b around inf 33.2%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]

5. Final simplification 33.2%

   \[\leadsto \frac{b}{z \cdot c} \]

Alternative 19: 34.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{\frac{b}{c}}{z} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ (/ b c) z))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b / c) / z
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

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* 78.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 78.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 78.5%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 78.9%

   \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 33.2%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. associate-/r* 34.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

6. Simplified 34.5%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

7. Final simplification 34.5%

   \[\leadsto \frac{\frac{b}{c}}{z} \]

Developer target: 81.3% 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 2023268 
(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)))