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

Percentage Accurate: 79.4% → 91.6%

Time: 19.6s

Alternatives: 19

Speedup: 0.8×

• 37.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.4% 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: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+265}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{9 \cdot x}{c} + \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{b}{z \cdot c}\right)\\ \end{array} \end{array} \]

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 (/ (+ (/ b z) (+ (* -4.0 (* a t)) (* 9.0 (/ (* y x) z)))) c)))
   (if (<= z -1.2e+29)
     t_1
     (if (<= z 5e-37)
       (/ (fma x (* 9.0 y) (+ b (* t (* a (* z -4.0))))) (* z c))
       (if (<= z 2.65e+265)
         t_1
         (+
          (* (/ y z) (/ (* 9.0 x) c))
          (fma -4.0 (* t (/ a 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 t_1 = ((b / z) + ((-4.0 * (a * t)) + (9.0 * ((y * x) / z)))) / c;
	double tmp;
	if (z <= -1.2e+29) {
		tmp = t_1;
	} else if (z <= 5e-37) {
		tmp = fma(x, (9.0 * y), (b + (t * (a * (z * -4.0))))) / (z * c);
	} else if (z <= 2.65e+265) {
		tmp = t_1;
	} else {
		tmp = ((y / z) * ((9.0 * x) / c)) + fma(-4.0, (t * (a / c)), (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)
	t_1 = Float64(Float64(Float64(b / z) + Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(y * x) / z)))) / c)
	tmp = 0.0
	if (z <= -1.2e+29)
		tmp = t_1;
	elseif (z <= 5e-37)
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	elseif (z <= 2.65e+265)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / z) * Float64(Float64(9.0 * x) / c)) + fma(-4.0, Float64(t * Float64(a / c)), Float64(b / 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_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] + N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.2e+29], t$95$1, If[LessEqual[z, 5e-37], 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], If[LessEqual[z, 2.65e+265], t$95$1, N[(N[(N[(y / z), $MachinePrecision] * N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e29 or 4.9999999999999997e-37 < z < 2.65000000000000017e265

   1. Initial program 67.6%

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

      1. associate-+l- 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r* 63.1%

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

      4. *-commutative 63.1%

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

      5. associate-+l- 63.1%

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

   3. Simplified 69.2%

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

      1. div-inv 69.0%

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

      2. associate-+l- 69.0%

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

      3. associate-*r* 67.4%

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

      4. associate-+l- 67.4%

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

      5. associate-*r* 69.0%

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

      6. associate-*l* 69.0%

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

      7. fma-neg 69.0%

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

   5. Applied egg-rr 69.0%

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

   6. Taylor expanded in x around 0 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-/l* 76.2%

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

      3. cancel-sign-sub-inv 76.2%

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

      4. metadata-eval 76.2%

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

      5. associate-/l* 77.1%

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

      6. +-commutative 77.1%

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

      7. associate-+r+ 77.1%

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

      8. +-commutative 77.1%

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

      9. fma-def 77.1%

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

      10. *-commutative 77.1%

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

      11. times-frac 81.6%

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

      12. +-commutative 81.6%

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

      13. associate-/l* 80.8%

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

      14. *-commutative 80.8%

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

   8. Simplified 87.8%

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

   9. Taylor expanded in c around 0 88.5%

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

   if -1.2e29 < z < 4.9999999999999997e-37

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. associate-*l* 97.2%

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

      3. fma-neg 98.0%

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

      4. neg-sub0 98.0%

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

      5. associate-+l- 98.0%

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

      6. neg-sub0 98.0%

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

      7. +-commutative 98.0%

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

      8. distribute-rgt-neg-out 98.0%

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

      9. *-commutative 98.0%

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

      10. associate-*l* 97.2%

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

      11. distribute-rgt-neg-in 97.2%

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

      12. *-commutative 97.2%

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

      13. distribute-rgt-neg-in 97.2%

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

      14. distribute-rgt-neg-in 97.2%

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

      15. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

   if 2.65000000000000017e265 < z

   1. Initial program 23.2%

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

      1. associate-+l- 23.2%

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

      2. *-commutative 23.2%

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

      3. associate-*r* 23.5%

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

      4. *-commutative 23.5%

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

      5. associate-+l- 23.5%

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

   3. Simplified 23.5%

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

      1. div-inv 23.5%

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

      2. associate-+l- 23.5%

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

      3. associate-*r* 23.2%

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

      4. associate-+l- 23.2%

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

      5. associate-*r* 23.5%

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

      6. associate-*l* 23.5%

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

      7. fma-neg 23.5%

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

   5. Applied egg-rr 23.5%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. associate--l+ 51.4%

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

      2. associate-/l* 71.4%

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

      3. cancel-sign-sub-inv 71.4%

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

      4. metadata-eval 71.4%

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

      5. associate-/l* 51.4%

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

      6. +-commutative 51.4%

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

      7. associate-+r+ 51.4%

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

      8. +-commutative 51.4%

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

      9. associate-*r/ 51.4%

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

      10. *-commutative 51.4%

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

      11. associate-*r* 51.4%

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

      12. *-commutative 51.4%

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

      13. times-frac 79.5%

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

      14. *-commutative 79.5%

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

      15. +-commutative 79.5%

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

   8. Simplified 94.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+265}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{9 \cdot x}{c} + \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{b}{z \cdot c}\right)\\ \end{array} \]

Alternative 2: 94.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+29} \lor \neg \left(z \leq 1.4 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{1}{z}, \mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, -4 \cdot \left(a \cdot t\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -2.55e+29) (not (<= z 1.4e-37)))
   (/ (fma b (/ 1.0 z) (fma 9.0 (/ y (/ z x)) (* -4.0 (* a t)))) c)
   (/ (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 <= -2.55e+29) || !(z <= 1.4e-37)) {
		tmp = fma(b, (1.0 / z), fma(9.0, (y / (z / x)), (-4.0 * (a * t)))) / c;
	} 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 <= -2.55e+29) || !(z <= 1.4e-37))
		tmp = Float64(fma(b, Float64(1.0 / z), fma(9.0, Float64(y / Float64(z / x)), Float64(-4.0 * Float64(a * t)))) / c);
	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, -2.55e+29], N[Not[LessEqual[z, 1.4e-37]], $MachinePrecision]], N[(N[(b * N[(1.0 / z), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $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 < -2.55e29 or 1.4000000000000001e-37 < z

   1. Initial program 63.2%

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

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 64.7%

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

      1. div-inv 64.4%

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

      2. associate-+l- 64.4%

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

      3. associate-*r* 63.0%

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

      4. associate-+l- 63.0%

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

      5. associate-*r* 64.4%

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

      6. associate-*l* 64.4%

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

      7. fma-neg 64.4%

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

   5. Applied egg-rr 64.4%

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

   6. Taylor expanded in x around 0 74.5%

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

      1. associate--l+ 74.5%

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

      2. associate-/l* 75.7%

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

      3. cancel-sign-sub-inv 75.7%

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

      4. metadata-eval 75.7%

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

      5. associate-/l* 74.5%

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

      6. +-commutative 74.5%

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

      7. associate-+r+ 74.5%

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

      8. +-commutative 74.5%

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

      9. fma-def 74.5%

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

      10. *-commutative 74.5%

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

      11. times-frac 81.4%

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

      12. +-commutative 81.4%

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

      13. associate-/l* 82.7%

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

      14. *-commutative 82.7%

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

   8. Simplified 88.5%

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

   9. Taylor expanded in c around 0 84.8%

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

       1. div-inv 84.8%

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

       2. fma-def 84.8%

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

       3. fma-def 84.8%

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

       4. associate-/l* 88.9%

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

   11. Applied egg-rr 88.9%

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

   if -2.55e29 < z < 1.4000000000000001e-37

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. associate-*l* 97.2%

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

      3. fma-neg 98.0%

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

      4. neg-sub0 98.0%

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

      5. associate-+l- 98.0%

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

      6. neg-sub0 98.0%

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

      7. +-commutative 98.0%

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

      8. distribute-rgt-neg-out 98.0%

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

      9. *-commutative 98.0%

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

      10. associate-*l* 97.2%

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

      11. distribute-rgt-neg-in 97.2%

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

      12. *-commutative 97.2%

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

      13. distribute-rgt-neg-in 97.2%

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

      14. distribute-rgt-neg-in 97.2%

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

      15. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+29} \lor \neg \left(z \leq 1.4 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{1}{z}, \mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, -4 \cdot \left(a \cdot t\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+28} \lor \neg \left(z \leq 5 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -2.8e+28) (not (<= z 5e-38)))
   (/ (+ (/ b z) (+ (* -4.0 (* a t)) (* 9.0 (/ (* y x) z)))) c)
   (/ (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 <= -2.8e+28) || !(z <= 5e-38)) {
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * ((y * x) / z)))) / c;
	} 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 <= -2.8e+28) || !(z <= 5e-38))
		tmp = Float64(Float64(Float64(b / z) + Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(y * x) / z)))) / c);
	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, -2.8e+28], N[Not[LessEqual[z, 5e-38]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $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 < -2.8000000000000001e28 or 5.00000000000000033e-38 < z

   1. Initial program 63.2%

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

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 64.7%

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

      1. div-inv 64.4%

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

      2. associate-+l- 64.4%

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

      3. associate-*r* 63.0%

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

      4. associate-+l- 63.0%

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

      5. associate-*r* 64.4%

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

      6. associate-*l* 64.4%

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

      7. fma-neg 64.4%

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

   5. Applied egg-rr 64.4%

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

   6. Taylor expanded in x around 0 74.5%

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

      1. associate--l+ 74.5%

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

      2. associate-/l* 75.7%

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

      3. cancel-sign-sub-inv 75.7%

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

      4. metadata-eval 75.7%

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

      5. associate-/l* 74.5%

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

      6. +-commutative 74.5%

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

      7. associate-+r+ 74.5%

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

      8. +-commutative 74.5%

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

      9. fma-def 74.5%

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

      10. *-commutative 74.5%

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

      11. times-frac 81.4%

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

      12. +-commutative 81.4%

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

      13. associate-/l* 82.7%

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

      14. *-commutative 82.7%

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

   8. Simplified 88.5%

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

   9. Taylor expanded in c around 0 84.8%

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

   if -2.8000000000000001e28 < z < 5.00000000000000033e-38

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. associate-*l* 97.2%

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

      3. fma-neg 98.0%

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

      4. neg-sub0 98.0%

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

      5. associate-+l- 98.0%

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

      6. neg-sub0 98.0%

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

      7. +-commutative 98.0%

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

      8. distribute-rgt-neg-out 98.0%

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

      9. *-commutative 98.0%

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

      10. associate-*l* 97.2%

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

      11. distribute-rgt-neg-in 97.2%

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

      12. *-commutative 97.2%

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

      13. distribute-rgt-neg-in 97.2%

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

      14. distribute-rgt-neg-in 97.2%

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

      15. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+28} \lor \neg \left(z \leq 5 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ t_2 := \frac{b + \left(t_1 - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{b + \left(t_1 - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

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 (* y (* 9.0 x)))
        (t_2 (/ (+ b (- t_1 (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_2 -2e-94)
     t_2
     (if (<= t_2 0.0)
       (/ (/ (+ b (* 9.0 (* y x))) z) c)
       (if (<= t_2 INFINITY)
         (/ (+ b (- t_1 (* (* z 4.0) (* a t)))) (* z c))
         (* -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 = y * (9.0 * x);
	double t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_2 <= -2e-94) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((b + (9.0 * (y * x))) / z) / c;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

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 = y * (9.0 * x);
	double t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_2 <= -2e-94) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((b + (9.0 * (y * x))) / z) / c;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = -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 = y * (9.0 * x)
	t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_2 <= -2e-94:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((b + (9.0 * (y * x))) / z) / c
	elif t_2 <= math.inf:
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c)
	else:
		tmp = -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(y * Float64(9.0 * x))
	t_2 = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -2e-94)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c);
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(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 = y * (9.0 * x);
	t_2 = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_2 <= -2e-94)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((b + (9.0 * (y * x))) / z) / c;
	elseif (t_2 <= Inf)
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	else
		tmp = -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[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(t$95$1 - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-94], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(b + N[(t$95$1 - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.9999999999999999e-94

   1. Initial program 91.5%

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

   if -1.9999999999999999e-94 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 54.0%

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

      1. associate-+l- 54.0%

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

      2. *-commutative 54.0%

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

      3. associate-*r* 50.4%

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

      4. *-commutative 50.4%

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

      5. associate-+l- 50.4%

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

   3. Simplified 54.0%

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

      1. div-inv 54.0%

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

      2. associate-+l- 54.0%

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

      3. associate-*r* 54.0%

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

      4. associate-+l- 54.0%

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

      5. associate-*r* 54.0%

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

      6. associate-*l* 54.0%

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

      7. fma-neg 54.0%

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

   5. Applied egg-rr 54.0%

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

   6. Taylor expanded in x around 0 66.2%

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

      1. associate--l+ 66.2%

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

      2. associate-/l* 54.2%

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

      3. cancel-sign-sub-inv 54.2%

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

      4. metadata-eval 54.2%

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

      5. associate-/l* 66.2%

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

      6. +-commutative 66.2%

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

      7. associate-+r+ 66.2%

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

      8. +-commutative 66.2%

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

      9. fma-def 66.2%

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

      10. *-commutative 66.2%

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

      11. times-frac 78.4%

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

      12. +-commutative 78.4%

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

      13. associate-/l* 66.4%

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

      14. *-commutative 66.4%

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

   8. Simplified 96.6%

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

   9. Taylor expanded in c around 0 99.6%

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

   10. Taylor expanded in z around 0 83.7%

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

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

   1. Initial program 91.2%

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

      1. associate-+l- 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*r* 88.7%

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

      4. *-commutative 88.7%

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

      5. associate-+l- 88.7%

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

   3. Simplified 93.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 0.4%

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

      4. *-commutative 0.4%

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

      5. associate-+l- 0.4%

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

   3. Simplified 0.4%

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

      1. div-inv 0.4%

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

      2. associate-+l- 0.4%

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

      3. associate-*r* 0.0%

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

      4. associate-+l- 0.0%

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

      5. associate-*r* 0.4%

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

      6. associate-*l* 0.4%

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

      7. fma-neg 4.8%

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

   5. Applied egg-rr 4.8%

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

   6. Taylor expanded in x around 0 37.1%

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

      1. associate--l+ 37.1%

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

      2. associate-/l* 61.0%

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

      3. cancel-sign-sub-inv 61.0%

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

      4. metadata-eval 61.0%

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

      5. associate-/l* 37.1%

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

      6. +-commutative 37.1%

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

      7. associate-+r+ 37.1%

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

      8. +-commutative 37.1%

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

      9. fma-def 37.1%

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

      10. *-commutative 37.1%

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

      11. times-frac 58.5%

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

      12. +-commutative 58.5%

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

      13. associate-/l* 82.5%

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

      14. *-commutative 82.5%

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

   8. Simplified 91.7%

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

   9. Taylor expanded in z around inf 42.2%

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

       1. *-commutative 42.2%

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

       2. associate-/l* 71.3%

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

       3. associate-/r/ 66.1%

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

   11. Simplified 66.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -2 \cdot 10^{-94}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 5: 80.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+248} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -6.8e+248) (not (<= t 7.2e-22)))
   (* -4.0 (* a (/ t c)))
   (/ (+ b (- (* y (* 9.0 x)) (* (* z 4.0) (* a t)))) (* 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 ((t <= -6.8e+248) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (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 ((t <= (-6.8d+248)) .or. (.not. (t <= 7.2d-22))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = (b + ((y * (9.0d0 * x)) - ((z * 4.0d0) * (a * t)))) / (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 ((t <= -6.8e+248) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (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 (t <= -6.8e+248) or not (t <= 7.2e-22):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (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 ((t <= -6.8e+248) || !(t <= 7.2e-22))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / 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 ((t <= -6.8e+248) || ~((t <= 7.2e-22)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = (b + ((y * (9.0 * x)) - ((z * 4.0) * (a * t)))) / (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[t, -6.8e+248], N[Not[LessEqual[t, 7.2e-22]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if t < -6.7999999999999999e248 or 7.1999999999999996e-22 < t

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-*r* 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-+l- 67.1%

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

   3. Simplified 67.1%

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

      1. div-inv 66.8%

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

      2. associate-+l- 66.8%

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

      3. associate-*r* 64.4%

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

      4. associate-+l- 64.4%

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

      5. associate-*r* 66.8%

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

      6. associate-*l* 66.8%

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

      7. fma-neg 68.0%

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

   5. Applied egg-rr 68.0%

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

   6. Taylor expanded in x around 0 71.0%

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

      1. associate--l+ 71.0%

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

      2. associate-/l* 83.8%

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

      3. cancel-sign-sub-inv 83.8%

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

      4. metadata-eval 83.8%

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

      5. associate-/l* 71.0%

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

      6. +-commutative 71.0%

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

      7. associate-+r+ 71.0%

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

      8. +-commutative 71.0%

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

      9. fma-def 71.0%

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

      10. *-commutative 71.0%

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

      11. times-frac 71.0%

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

      12. +-commutative 71.0%

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

      13. associate-/l* 83.8%

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

      14. *-commutative 83.8%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in z around inf 50.7%

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

       1. *-commutative 50.7%

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

       2. associate-/l* 62.1%

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

       3. associate-/r/ 64.8%

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

   11. Simplified 64.8%

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

   if -6.7999999999999999e248 < t < 7.1999999999999996e-22

   1. Initial program 84.9%

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

      1. associate-+l- 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

   3. Simplified 83.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+248} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 6: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+59} \lor \neg \left(z \leq 1.4 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -3.2e+59) (not (<= z 1.4e-37)))
   (/ (+ (/ b z) (+ (* -4.0 (* a t)) (* 9.0 (/ (* y x) z)))) c)
   (/ (+ 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 <= -3.2e+59) || !(z <= 1.4e-37)) {
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * ((y * x) / z)))) / c;
	} 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 <= (-3.2d+59)) .or. (.not. (z <= 1.4d-37))) then
        tmp = ((b / z) + (((-4.0d0) * (a * t)) + (9.0d0 * ((y * x) / z)))) / c
    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 <= -3.2e+59) || !(z <= 1.4e-37)) {
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * ((y * x) / z)))) / c;
	} 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 <= -3.2e+59) or not (z <= 1.4e-37):
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * ((y * x) / z)))) / c
	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 <= -3.2e+59) || !(z <= 1.4e-37))
		tmp = Float64(Float64(Float64(b / z) + Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(y * x) / z)))) / c);
	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 <= -3.2e+59) || ~((z <= 1.4e-37)))
		tmp = ((b / z) + ((-4.0 * (a * t)) + (9.0 * ((y * x) / z)))) / c;
	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, -3.2e+59], N[Not[LessEqual[z, 1.4e-37]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $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 < -3.19999999999999982e59 or 1.4000000000000001e-37 < z

   1. Initial program 62.4%

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

      1. associate-+l- 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 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 64.0%

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

      1. div-inv 63.7%

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

      2. associate-+l- 63.7%

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

      3. associate-*r* 62.2%

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

      4. associate-+l- 62.2%

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

      5. associate-*r* 63.7%

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

      6. associate-*l* 63.7%

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

      7. fma-neg 63.7%

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

   5. Applied egg-rr 63.7%

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

   6. Taylor expanded in x around 0 74.4%

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

      1. associate--l+ 74.4%

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

      2. associate-/l* 75.0%

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

      3. cancel-sign-sub-inv 75.0%

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

      4. metadata-eval 75.0%

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

      5. associate-/l* 74.4%

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

      6. +-commutative 74.4%

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

      7. associate-+r+ 74.4%

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

      8. +-commutative 74.4%

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

      9. fma-def 74.4%

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

      10. *-commutative 74.4%

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

      11. times-frac 81.0%

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

      12. +-commutative 81.0%

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

      13. associate-/l* 81.6%

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

      14. *-commutative 81.6%

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

   8. Simplified 88.5%

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

   9. Taylor expanded in c around 0 85.3%

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

   if -3.19999999999999982e59 < z < 1.4000000000000001e-37

   1. Initial program 95.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+59} \lor \neg \left(z \leq 1.4 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* a (/ t c)))) (t_2 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= t -7.5e+131)
     t_1
     (if (<= t -2.3e+103)
       (/ b (* z c))
       (if (<= t -3e+96)
         t_1
         (if (<= t -2.3e+44)
           t_2
           (if (<= t -5.2e-301)
             (/ (/ b z) c)
             (if (<= t 9.8e-86) t_2 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 = -4.0 * (a * (t / c));
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if (t <= -3e+96) {
		tmp = t_1;
	} else if (t <= -2.3e+44) {
		tmp = t_2;
	} else if (t <= -5.2e-301) {
		tmp = (b / z) / c;
	} else if (t <= 9.8e-86) {
		tmp = t_2;
	} 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 = (-4.0d0) * (a * (t / c))
    t_2 = 9.0d0 * ((y / c) * (x / z))
    if (t <= (-7.5d+131)) then
        tmp = t_1
    else if (t <= (-2.3d+103)) then
        tmp = b / (z * c)
    else if (t <= (-3d+96)) then
        tmp = t_1
    else if (t <= (-2.3d+44)) then
        tmp = t_2
    else if (t <= (-5.2d-301)) then
        tmp = (b / z) / c
    else if (t <= 9.8d-86) then
        tmp = t_2
    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 = -4.0 * (a * (t / c));
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if (t <= -3e+96) {
		tmp = t_1;
	} else if (t <= -2.3e+44) {
		tmp = t_2;
	} else if (t <= -5.2e-301) {
		tmp = (b / z) / c;
	} else if (t <= 9.8e-86) {
		tmp = t_2;
	} 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 = -4.0 * (a * (t / c))
	t_2 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if t <= -7.5e+131:
		tmp = t_1
	elif t <= -2.3e+103:
		tmp = b / (z * c)
	elif t <= -3e+96:
		tmp = t_1
	elif t <= -2.3e+44:
		tmp = t_2
	elif t <= -5.2e-301:
		tmp = (b / z) / c
	elif t <= 9.8e-86:
		tmp = t_2
	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(-4.0 * Float64(a * Float64(t / c)))
	t_2 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= -3e+96)
		tmp = t_1;
	elseif (t <= -2.3e+44)
		tmp = t_2;
	elseif (t <= -5.2e-301)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= 9.8e-86)
		tmp = t_2;
	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 = -4.0 * (a * (t / c));
	t_2 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = b / (z * c);
	elseif (t <= -3e+96)
		tmp = t_1;
	elseif (t <= -2.3e+44)
		tmp = t_2;
	elseif (t <= -5.2e-301)
		tmp = (b / z) / c;
	elseif (t <= 9.8e-86)
		tmp = t_2;
	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[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+131], t$95$1, If[LessEqual[t, -2.3e+103], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e+96], t$95$1, If[LessEqual[t, -2.3e+44], t$95$2, If[LessEqual[t, -5.2e-301], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 9.8e-86], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999995e131 or -2.30000000000000008e103 < t < -3e96 or 9.79999999999999944e-86 < t

   1. Initial program 71.3%

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

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 73.2%

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

      4. *-commutative 73.2%

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

      5. associate-+l- 73.2%

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

   3. Simplified 73.2%

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

      1. div-inv 72.9%

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

      2. associate-+l- 72.9%

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

      3. associate-*r* 71.1%

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

      4. associate-+l- 71.1%

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

      5. associate-*r* 72.9%

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

      6. associate-*l* 72.9%

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

      7. fma-neg 73.8%

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

   5. Applied egg-rr 73.8%

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

   6. Taylor expanded in x around 0 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 80.9%

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

      3. cancel-sign-sub-inv 80.9%

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

      4. metadata-eval 80.9%

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

      5. associate-/l* 72.3%

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

      6. +-commutative 72.3%

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

      7. associate-+r+ 72.3%

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

      8. +-commutative 72.3%

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

      9. fma-def 72.3%

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

      10. *-commutative 72.3%

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

      11. times-frac 74.2%

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

      12. +-commutative 74.2%

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

      13. associate-/l* 82.6%

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

      14. *-commutative 82.6%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in z around inf 44.3%

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

       1. *-commutative 44.3%

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

       2. associate-/l* 52.6%

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

       3. associate-/r/ 57.2%

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

   11. Simplified 57.2%

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

   if -7.4999999999999995e131 < t < -2.30000000000000008e103

   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 b around inf 58.3%

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

      1. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -3e96 < t < -2.30000000000000004e44 or -5.1999999999999996e-301 < t < 9.79999999999999944e-86

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around inf 42.8%

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

      1. times-frac 48.1%

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

   6. Simplified 48.1%

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

   if -2.30000000000000004e44 < t < -5.1999999999999996e-301

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-+l- 74.8%

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

   3. Simplified 78.3%

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

      1. div-inv 78.2%

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

      2. associate-+l- 78.2%

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

      3. associate-*r* 79.3%

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

      4. associate-+l- 79.3%

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

      5. associate-*r* 78.2%

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

      6. associate-*l* 78.2%

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

      7. fma-neg 78.2%

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

   5. Applied egg-rr 78.2%

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

   6. Taylor expanded in b around inf 45.6%

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

      1. associate-/l/ 45.6%

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

   8. Simplified 45.6%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+96}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-86}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 8: 49.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{9 \cdot x}{c}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-85}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* a (/ t c)))))
   (if (<= t -8.5e+138)
     t_1
     (if (<= t -1e+46)
       (* (/ x (/ c y)) (/ 9.0 z))
       (if (<= t -4.1e-224)
         (/ (/ b z) c)
         (if (<= t -4e-257)
           (* (/ y z) (/ (* 9.0 x) c))
           (if (<= t -4.1e-300)
             (/ b (* z c))
             (if (<= t 1.18e-85) (* 9.0 (* (/ y c) (/ x z))) 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -8.5e+138) {
		tmp = t_1;
	} else if (t <= -1e+46) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -4.1e-224) {
		tmp = (b / z) / c;
	} else if (t <= -4e-257) {
		tmp = (y / z) * ((9.0 * x) / c);
	} else if (t <= -4.1e-300) {
		tmp = b / (z * c);
	} else if (t <= 1.18e-85) {
		tmp = 9.0 * ((y / c) * (x / z));
	} 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 = (-4.0d0) * (a * (t / c))
    if (t <= (-8.5d+138)) then
        tmp = t_1
    else if (t <= (-1d+46)) then
        tmp = (x / (c / y)) * (9.0d0 / z)
    else if (t <= (-4.1d-224)) then
        tmp = (b / z) / c
    else if (t <= (-4d-257)) then
        tmp = (y / z) * ((9.0d0 * x) / c)
    else if (t <= (-4.1d-300)) then
        tmp = b / (z * c)
    else if (t <= 1.18d-85) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -8.5e+138) {
		tmp = t_1;
	} else if (t <= -1e+46) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -4.1e-224) {
		tmp = (b / z) / c;
	} else if (t <= -4e-257) {
		tmp = (y / z) * ((9.0 * x) / c);
	} else if (t <= -4.1e-300) {
		tmp = b / (z * c);
	} else if (t <= 1.18e-85) {
		tmp = 9.0 * ((y / c) * (x / z));
	} 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 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -8.5e+138:
		tmp = t_1
	elif t <= -1e+46:
		tmp = (x / (c / y)) * (9.0 / z)
	elif t <= -4.1e-224:
		tmp = (b / z) / c
	elif t <= -4e-257:
		tmp = (y / z) * ((9.0 * x) / c)
	elif t <= -4.1e-300:
		tmp = b / (z * c)
	elif t <= 1.18e-85:
		tmp = 9.0 * ((y / c) * (x / z))
	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(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -8.5e+138)
		tmp = t_1;
	elseif (t <= -1e+46)
		tmp = Float64(Float64(x / Float64(c / y)) * Float64(9.0 / z));
	elseif (t <= -4.1e-224)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= -4e-257)
		tmp = Float64(Float64(y / z) * Float64(Float64(9.0 * x) / c));
	elseif (t <= -4.1e-300)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 1.18e-85)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	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 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -8.5e+138)
		tmp = t_1;
	elseif (t <= -1e+46)
		tmp = (x / (c / y)) * (9.0 / z);
	elseif (t <= -4.1e-224)
		tmp = (b / z) / c;
	elseif (t <= -4e-257)
		tmp = (y / z) * ((9.0 * x) / c);
	elseif (t <= -4.1e-300)
		tmp = b / (z * c);
	elseif (t <= 1.18e-85)
		tmp = 9.0 * ((y / c) * (x / z));
	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[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+138], t$95$1, If[LessEqual[t, -1e+46], N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-224], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -4e-257], N[(N[(y / z), $MachinePrecision] * N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-300], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e-85], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -8.5000000000000006e138 or 1.18e-85 < t

   1. Initial program 70.3%

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

      1. associate-+l- 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r* 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 72.2%

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

      1. div-inv 71.9%

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

      2. associate-+l- 71.9%

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

      3. associate-*r* 70.1%

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

      4. associate-+l- 70.1%

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

      5. associate-*r* 71.9%

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

      6. associate-*l* 71.9%

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

      7. fma-neg 72.9%

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

   5. Applied egg-rr 72.9%

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

   6. Taylor expanded in x around 0 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-/l* 80.2%

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

      3. cancel-sign-sub-inv 80.2%

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

      4. metadata-eval 80.2%

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

      5. associate-/l* 71.3%

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

      6. +-commutative 71.3%

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

      7. associate-+r+ 71.3%

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

      8. +-commutative 71.3%

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

      9. fma-def 71.4%

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

      10. *-commutative 71.4%

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

      11. times-frac 74.1%

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

      12. +-commutative 74.1%

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

      13. associate-/l* 82.9%

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

      14. *-commutative 82.9%

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

   8. Simplified 86.3%

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

   9. Taylor expanded in z around inf 45.9%

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

       1. *-commutative 45.9%

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

       2. associate-/l* 54.5%

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

       3. associate-/r/ 59.3%

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

   11. Simplified 59.3%

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

   if -8.5000000000000006e138 < t < -9.9999999999999999e45

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 83.6%

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

      1. div-inv 83.5%

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

      2. associate-+l- 83.5%

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

      3. associate-*r* 91.5%

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

      4. associate-+l- 91.5%

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

      5. associate-*r* 83.5%

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

      6. associate-*l* 83.6%

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

      7. fma-neg 83.6%

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

   5. Applied egg-rr 83.6%

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

   6. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. times-frac 43.0%

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

      4. associate-/l* 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in y around 0 43.0%

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

       1. *-commutative 43.0%

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

       2. associate-/l* 43.1%

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

   11. Simplified 43.1%

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

   if -9.9999999999999999e45 < t < -4.09999999999999986e-224

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

   3. Simplified 75.3%

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

      1. div-inv 75.3%

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

      2. associate-+l- 75.3%

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

      3. associate-*r* 76.7%

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

      4. associate-+l- 76.7%

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

      5. associate-*r* 75.3%

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

      6. associate-*l* 75.3%

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

      7. fma-neg 75.3%

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

   5. Applied egg-rr 75.3%

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

   6. Taylor expanded in b around inf 42.5%

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

      1. associate-/l/ 45.4%

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

   8. Simplified 45.4%

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

   if -4.09999999999999986e-224 < t < -3.9999999999999999e-257

   1. Initial program 86.0%

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

      1. associate-+l- 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

   3. Simplified 86.0%

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

      1. div-inv 85.6%

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

      2. associate-+l- 85.6%

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

      3. associate-*r* 85.6%

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

      4. associate-+l- 85.6%

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

      5. associate-*r* 85.6%

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

      6. associate-*l* 85.4%

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

      7. fma-neg 85.4%

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

   5. Applied egg-rr 85.4%

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

   6. Taylor expanded in x around inf 72.3%

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

      1. associate-*r/ 72.1%

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

      2. *-commutative 72.1%

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

      3. associate-*r* 72.3%

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

      4. *-commutative 72.3%

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

      5. times-frac 43.5%

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

      6. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   if -3.9999999999999999e-257 < t < -4.1000000000000001e-300

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*r* 73.5%

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

      4. *-commutative 73.5%

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

      5. associate-+l- 73.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in b around inf 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

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

   if -4.1000000000000001e-300 < t < 1.18e-85

   1. Initial program 89.2%

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

      1. associate-+l- 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-+l- 78.6%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 43.5%

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

      1. times-frac 50.2%

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

   6. Simplified 50.2%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{9 \cdot x}{c}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-85}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 9: 49.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{y \cdot \frac{9}{z}}{\frac{c}{x}}\\ t_2 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ (* y (/ 9.0 z)) (/ c x))) (t_2 (* -4.0 (* a (/ t c)))))
   (if (<= t -9e+138)
     t_2
     (if (<= t -2.6e+47)
       (* (/ x (/ c y)) (/ 9.0 z))
       (if (<= t -5.5e-227)
         (/ (/ b z) c)
         (if (<= t -1.3e-255)
           t_1
           (if (<= t -3.35e-301)
             (/ b (* z c))
             (if (<= t 1.55e-25) t_1 t_2))))))))

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 = (y * (9.0 / z)) / (c / x);
	double t_2 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -9e+138) {
		tmp = t_2;
	} else if (t <= -2.6e+47) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -5.5e-227) {
		tmp = (b / z) / c;
	} else if (t <= -1.3e-255) {
		tmp = t_1;
	} else if (t <= -3.35e-301) {
		tmp = b / (z * c);
	} else if (t <= 1.55e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (y * (9.0d0 / z)) / (c / x)
    t_2 = (-4.0d0) * (a * (t / c))
    if (t <= (-9d+138)) then
        tmp = t_2
    else if (t <= (-2.6d+47)) then
        tmp = (x / (c / y)) * (9.0d0 / z)
    else if (t <= (-5.5d-227)) then
        tmp = (b / z) / c
    else if (t <= (-1.3d-255)) then
        tmp = t_1
    else if (t <= (-3.35d-301)) then
        tmp = b / (z * c)
    else if (t <= 1.55d-25) then
        tmp = t_1
    else
        tmp = t_2
    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 = (y * (9.0 / z)) / (c / x);
	double t_2 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -9e+138) {
		tmp = t_2;
	} else if (t <= -2.6e+47) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -5.5e-227) {
		tmp = (b / z) / c;
	} else if (t <= -1.3e-255) {
		tmp = t_1;
	} else if (t <= -3.35e-301) {
		tmp = b / (z * c);
	} else if (t <= 1.55e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (y * (9.0 / z)) / (c / x)
	t_2 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -9e+138:
		tmp = t_2
	elif t <= -2.6e+47:
		tmp = (x / (c / y)) * (9.0 / z)
	elif t <= -5.5e-227:
		tmp = (b / z) / c
	elif t <= -1.3e-255:
		tmp = t_1
	elif t <= -3.35e-301:
		tmp = b / (z * c)
	elif t <= 1.55e-25:
		tmp = t_1
	else:
		tmp = t_2
	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(y * Float64(9.0 / z)) / Float64(c / x))
	t_2 = Float64(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -9e+138)
		tmp = t_2;
	elseif (t <= -2.6e+47)
		tmp = Float64(Float64(x / Float64(c / y)) * Float64(9.0 / z));
	elseif (t <= -5.5e-227)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= -1.3e-255)
		tmp = t_1;
	elseif (t <= -3.35e-301)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 1.55e-25)
		tmp = t_1;
	else
		tmp = t_2;
	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 = (y * (9.0 / z)) / (c / x);
	t_2 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -9e+138)
		tmp = t_2;
	elseif (t <= -2.6e+47)
		tmp = (x / (c / y)) * (9.0 / z);
	elseif (t <= -5.5e-227)
		tmp = (b / z) / c;
	elseif (t <= -1.3e-255)
		tmp = t_1;
	elseif (t <= -3.35e-301)
		tmp = b / (z * c);
	elseif (t <= 1.55e-25)
		tmp = t_1;
	else
		tmp = t_2;
	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[(y * N[(9.0 / z), $MachinePrecision]), $MachinePrecision] / N[(c / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+138], t$95$2, If[LessEqual[t, -2.6e+47], N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-227], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -1.3e-255], t$95$1, If[LessEqual[t, -3.35e-301], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-25], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.99999999999999963e138 or 1.54999999999999997e-25 < t

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 71.4%

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

      1. div-inv 71.1%

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

      2. associate-+l- 71.1%

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

      3. associate-*r* 69.0%

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

      4. associate-+l- 69.0%

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

      5. associate-*r* 71.1%

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

      6. associate-*l* 71.1%

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

      7. fma-neg 72.2%

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

   5. Applied egg-rr 72.2%

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

   6. Taylor expanded in x around 0 71.5%

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

      1. associate--l+ 71.5%

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

      2. associate-/l* 81.6%

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

      3. cancel-sign-sub-inv 81.6%

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

      4. metadata-eval 81.6%

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

      5. associate-/l* 71.5%

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

      6. +-commutative 71.5%

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

      7. associate-+r+ 71.5%

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

      8. +-commutative 71.5%

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

      9. fma-def 71.5%

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

      10. *-commutative 71.5%

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

      11. times-frac 72.6%

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

      12. +-commutative 72.6%

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

      13. associate-/l* 82.6%

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

      14. *-commutative 82.6%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in z around inf 49.8%

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

       1. *-commutative 49.8%

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

       2. associate-/l* 59.7%

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

       3. associate-/r/ 65.1%

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

   11. Simplified 65.1%

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

   if -8.99999999999999963e138 < t < -2.60000000000000003e47

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 83.6%

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

      1. div-inv 83.5%

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

      2. associate-+l- 83.5%

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

      3. associate-*r* 91.5%

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

      4. associate-+l- 91.5%

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

      5. associate-*r* 83.5%

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

      6. associate-*l* 83.6%

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

      7. fma-neg 83.6%

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

   5. Applied egg-rr 83.6%

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

   6. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. times-frac 43.0%

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

      4. associate-/l* 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in y around 0 43.0%

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

       1. *-commutative 43.0%

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

       2. associate-/l* 43.1%

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

   11. Simplified 43.1%

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

   if -2.60000000000000003e47 < t < -5.5e-227

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

   3. Simplified 75.3%

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

      1. div-inv 75.3%

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

      2. associate-+l- 75.3%

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

      3. associate-*r* 76.7%

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

      4. associate-+l- 76.7%

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

      5. associate-*r* 75.3%

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

      6. associate-*l* 75.3%

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

      7. fma-neg 75.3%

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

   5. Applied egg-rr 75.3%

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

   6. Taylor expanded in b around inf 42.5%

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

      1. associate-/l/ 45.4%

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

   8. Simplified 45.4%

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

   if -5.5e-227 < t < -1.3000000000000001e-255 or -3.35000000000000011e-301 < t < 1.54999999999999997e-25

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-+l- 79.1%

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

   3. Simplified 86.6%

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

      1. div-inv 86.4%

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

      2. associate-+l- 86.4%

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

      3. associate-*r* 86.5%

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

      4. associate-+l- 86.5%

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

      5. associate-*r* 86.4%

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

      6. associate-*l* 86.5%

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

      7. fma-neg 86.5%

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

   5. Applied egg-rr 86.5%

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

   6. Taylor expanded in x around inf 44.4%

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

      1. associate-*r/ 44.4%

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

      2. *-commutative 44.4%

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

      3. times-frac 47.6%

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

      4. associate-/l* 47.6%

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

   8. Simplified 47.6%

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

      1. associate-*l/ 48.7%

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

   10. Applied egg-rr 48.7%

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

   if -1.3000000000000001e-255 < t < -3.35000000000000011e-301

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*r* 73.5%

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

      4. *-commutative 73.5%

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

      5. associate-+l- 73.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in b around inf 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+138}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-255}:\\ \;\;\;\;\frac{y \cdot \frac{9}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;\frac{y \cdot \frac{9}{z}}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 10: 49.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+47}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-86}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* a (/ t c)))))
   (if (<= t -2.1e+139)
     t_1
     (if (<= t -1.75e+47)
       (* 9.0 (/ (* y x) (* z c)))
       (if (<= t -2.8e-301)
         (/ (/ b z) c)
         (if (<= t 3.5e-86) (* 9.0 (* (/ y c) (/ x z))) 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -2.1e+139) {
		tmp = t_1;
	} else if (t <= -1.75e+47) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= -2.8e-301) {
		tmp = (b / z) / c;
	} else if (t <= 3.5e-86) {
		tmp = 9.0 * ((y / c) * (x / z));
	} 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 = (-4.0d0) * (a * (t / c))
    if (t <= (-2.1d+139)) then
        tmp = t_1
    else if (t <= (-1.75d+47)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (t <= (-2.8d-301)) then
        tmp = (b / z) / c
    else if (t <= 3.5d-86) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -2.1e+139) {
		tmp = t_1;
	} else if (t <= -1.75e+47) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= -2.8e-301) {
		tmp = (b / z) / c;
	} else if (t <= 3.5e-86) {
		tmp = 9.0 * ((y / c) * (x / z));
	} 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 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -2.1e+139:
		tmp = t_1
	elif t <= -1.75e+47:
		tmp = 9.0 * ((y * x) / (z * c))
	elif t <= -2.8e-301:
		tmp = (b / z) / c
	elif t <= 3.5e-86:
		tmp = 9.0 * ((y / c) * (x / z))
	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(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -2.1e+139)
		tmp = t_1;
	elseif (t <= -1.75e+47)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (t <= -2.8e-301)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= 3.5e-86)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	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 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -2.1e+139)
		tmp = t_1;
	elseif (t <= -1.75e+47)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (t <= -2.8e-301)
		tmp = (b / z) / c;
	elseif (t <= 3.5e-86)
		tmp = 9.0 * ((y / c) * (x / z));
	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[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+139], t$95$1, If[LessEqual[t, -1.75e+47], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-301], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 3.5e-86], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0999999999999999e139 or 3.50000000000000021e-86 < t

   1. Initial program 70.6%

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

      1. associate-+l- 70.6%

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

      2. *-commutative 70.6%

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

      3. associate-*r* 72.4%

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

      4. *-commutative 72.4%

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

      5. associate-+l- 72.4%

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

   3. Simplified 72.4%

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

      1. div-inv 72.2%

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

      2. associate-+l- 72.2%

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

      3. associate-*r* 70.3%

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

      4. associate-+l- 70.3%

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

      5. associate-*r* 72.2%

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

      6. associate-*l* 72.2%

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

      7. fma-neg 73.1%

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

   5. Applied egg-rr 73.1%

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

   6. Taylor expanded in x around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-/l* 80.4%

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

      3. cancel-sign-sub-inv 80.4%

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

      4. metadata-eval 80.4%

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

      5. associate-/l* 71.6%

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

      6. +-commutative 71.6%

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

      7. associate-+r+ 71.6%

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

      8. +-commutative 71.6%

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

      9. fma-def 71.6%

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

      10. *-commutative 71.6%

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

      11. times-frac 74.3%

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

      12. +-commutative 74.3%

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

      13. associate-/l* 83.1%

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

      14. *-commutative 83.1%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in z around inf 45.5%

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

       1. *-commutative 45.5%

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

       2. associate-/l* 54.0%

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

       3. associate-/r/ 58.7%

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

   11. Simplified 58.7%

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

   if -2.0999999999999999e139 < t < -1.75000000000000008e47

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 43.1%

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

   if -1.75000000000000008e47 < t < -2.8000000000000001e-301

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-+l- 74.8%

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

   3. Simplified 78.3%

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

      1. div-inv 78.2%

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

      2. associate-+l- 78.2%

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

      3. associate-*r* 79.3%

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

      4. associate-+l- 79.3%

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

      5. associate-*r* 78.2%

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

      6. associate-*l* 78.2%

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

      7. fma-neg 78.2%

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

   5. Applied egg-rr 78.2%

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

   6. Taylor expanded in b around inf 45.6%

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

      1. associate-/l/ 45.6%

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

   8. Simplified 45.6%

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

   if -2.8000000000000001e-301 < t < 3.50000000000000021e-86

   1. Initial program 89.0%

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

      1. associate-+l- 89.0%

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

      2. *-commutative 89.0%

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

      3. associate-*r* 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-+l- 78.1%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around inf 42.3%

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

      1. times-frac 49.2%

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

   6. Simplified 49.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+47}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-86}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 11: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-85}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* a (/ t c)))))
   (if (<= t -2.1e+139)
     t_1
     (if (<= t -1.8e+45)
       (* (/ x (/ c y)) (/ 9.0 z))
       (if (<= t -5.9e-300)
         (/ (/ b z) c)
         (if (<= t 1.5e-85) (* 9.0 (* (/ y c) (/ x z))) 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -2.1e+139) {
		tmp = t_1;
	} else if (t <= -1.8e+45) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -5.9e-300) {
		tmp = (b / z) / c;
	} else if (t <= 1.5e-85) {
		tmp = 9.0 * ((y / c) * (x / z));
	} 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 = (-4.0d0) * (a * (t / c))
    if (t <= (-2.1d+139)) then
        tmp = t_1
    else if (t <= (-1.8d+45)) then
        tmp = (x / (c / y)) * (9.0d0 / z)
    else if (t <= (-5.9d-300)) then
        tmp = (b / z) / c
    else if (t <= 1.5d-85) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -2.1e+139) {
		tmp = t_1;
	} else if (t <= -1.8e+45) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -5.9e-300) {
		tmp = (b / z) / c;
	} else if (t <= 1.5e-85) {
		tmp = 9.0 * ((y / c) * (x / z));
	} 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 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -2.1e+139:
		tmp = t_1
	elif t <= -1.8e+45:
		tmp = (x / (c / y)) * (9.0 / z)
	elif t <= -5.9e-300:
		tmp = (b / z) / c
	elif t <= 1.5e-85:
		tmp = 9.0 * ((y / c) * (x / z))
	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(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -2.1e+139)
		tmp = t_1;
	elseif (t <= -1.8e+45)
		tmp = Float64(Float64(x / Float64(c / y)) * Float64(9.0 / z));
	elseif (t <= -5.9e-300)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= 1.5e-85)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	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 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -2.1e+139)
		tmp = t_1;
	elseif (t <= -1.8e+45)
		tmp = (x / (c / y)) * (9.0 / z);
	elseif (t <= -5.9e-300)
		tmp = (b / z) / c;
	elseif (t <= 1.5e-85)
		tmp = 9.0 * ((y / c) * (x / z));
	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[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+139], t$95$1, If[LessEqual[t, -1.8e+45], N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.9e-300], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 1.5e-85], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0999999999999999e139 or 1.50000000000000011e-85 < t

   1. Initial program 70.3%

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

      1. associate-+l- 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r* 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 72.2%

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

      1. div-inv 71.9%

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

      2. associate-+l- 71.9%

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

      3. associate-*r* 70.1%

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

      4. associate-+l- 70.1%

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

      5. associate-*r* 71.9%

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

      6. associate-*l* 71.9%

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

      7. fma-neg 72.9%

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

   5. Applied egg-rr 72.9%

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

   6. Taylor expanded in x around 0 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-/l* 80.2%

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

      3. cancel-sign-sub-inv 80.2%

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

      4. metadata-eval 80.2%

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

      5. associate-/l* 71.3%

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

      6. +-commutative 71.3%

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

      7. associate-+r+ 71.3%

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

      8. +-commutative 71.3%

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

      9. fma-def 71.4%

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

      10. *-commutative 71.4%

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

      11. times-frac 74.1%

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

      12. +-commutative 74.1%

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

      13. associate-/l* 82.9%

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

      14. *-commutative 82.9%

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

   8. Simplified 86.3%

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

   9. Taylor expanded in z around inf 45.9%

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

       1. *-commutative 45.9%

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

       2. associate-/l* 54.5%

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

       3. associate-/r/ 59.3%

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

   11. Simplified 59.3%

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

   if -2.0999999999999999e139 < t < -1.8e45

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 83.6%

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

      1. div-inv 83.5%

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

      2. associate-+l- 83.5%

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

      3. associate-*r* 91.5%

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

      4. associate-+l- 91.5%

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

      5. associate-*r* 83.5%

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

      6. associate-*l* 83.6%

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

      7. fma-neg 83.6%

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

   5. Applied egg-rr 83.6%

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

   6. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. times-frac 43.0%

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

      4. associate-/l* 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in y around 0 43.0%

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

       1. *-commutative 43.0%

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

       2. associate-/l* 43.1%

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

   11. Simplified 43.1%

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

   if -1.8e45 < t < -5.8999999999999998e-300

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-+l- 74.8%

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

   3. Simplified 78.3%

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

      1. div-inv 78.2%

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

      2. associate-+l- 78.2%

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

      3. associate-*r* 79.3%

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

      4. associate-+l- 79.3%

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

      5. associate-*r* 78.2%

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

      6. associate-*l* 78.2%

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

      7. fma-neg 78.2%

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

   5. Applied egg-rr 78.2%

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

   6. Taylor expanded in b around inf 45.6%

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

      1. associate-/l/ 45.6%

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

   8. Simplified 45.6%

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

   if -5.8999999999999998e-300 < t < 1.50000000000000011e-85

   1. Initial program 89.2%

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

      1. associate-+l- 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-+l- 78.6%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 43.5%

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

      1. times-frac 50.2%

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

   6. Simplified 50.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-85}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 12: 69.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

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
 (if (<= t -1.7e+139)
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* y x) z))) c)
   (if (<= t 2e-22) (/ (/ (+ b (* 9.0 (* y x))) z) c) (* -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 (t <= -1.7e+139) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((y * x) / z))) / c;
	} else if (t <= 2e-22) {
		tmp = ((b + (9.0 * (y * x))) / z) / c;
	} else {
		tmp = -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 (t <= (-1.7d+139)) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((y * x) / z))) / c
    else if (t <= 2d-22) then
        tmp = ((b + (9.0d0 * (y * x))) / z) / c
    else
        tmp = (-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 (t <= -1.7e+139) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((y * x) / z))) / c;
	} else if (t <= 2e-22) {
		tmp = ((b + (9.0 * (y * x))) / z) / c;
	} else {
		tmp = -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 t <= -1.7e+139:
		tmp = ((-4.0 * (a * t)) + (9.0 * ((y * x) / z))) / c
	elif t <= 2e-22:
		tmp = ((b + (9.0 * (y * x))) / z) / c
	else:
		tmp = -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 (t <= -1.7e+139)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	elseif (t <= 2e-22)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c);
	else
		tmp = 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)
	tmp = 0.0;
	if (t <= -1.7e+139)
		tmp = ((-4.0 * (a * t)) + (9.0 * ((y * x) / z))) / c;
	elseif (t <= 2e-22)
		tmp = ((b + (9.0 * (y * x))) / z) / c;
	else
		tmp = -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[t, -1.7e+139], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 2e-22], N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7000000000000001e139

   1. Initial program 83.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 87.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 87.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 83.2%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 83.2%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 87.4%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 87.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 87.4%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 87.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 87.4%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 87.4%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 79.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 79.0%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 79.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 87.4%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 87.4%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 87.4%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 87.4%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 87.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 91.7%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 91.7%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 83.2%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 83.2%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in c around 0 91.6%

      \[\leadsto \color{blue}{\frac{\frac{b}{z} + \left(9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)\right)}{c}} \]

   10. Taylor expanded in b around 0 88.0%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

   if -1.7000000000000001e139 < t < 2.0000000000000001e-22

   1. Initial program 83.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 82.0%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 82.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 83.7%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 83.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 82.0%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 82.0%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 82.0%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 82.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 79.5%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 79.5%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 76.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 76.6%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 76.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 79.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 79.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 79.5%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 79.5%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 79.5%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 85.9%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 83.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 83.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in c around 0 87.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{z} + \left(9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)\right)}{c}} \]

   10. Taylor expanded in z around 0 69.0%

       \[\leadsto \frac{\color{blue}{\frac{9 \cdot \left(y \cdot x\right) + b}{z}}}{c} \]

   if 2.0000000000000001e-22 < t

   1. Initial program 64.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 64.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 64.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 65.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 65.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 65.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 64.0%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 64.0%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 65.4%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 65.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 66.8%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 66.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 65.9%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 65.9%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 82.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 82.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 82.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 65.9%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 65.9%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 65.9%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 65.9%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 65.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 65.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 65.9%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 65.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 82.4%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 82.4%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 44.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 44.9%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 61.0%

          \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

       3. associate-/r/ 62.9%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{t}{c} \cdot a\right)} \]

   11. Simplified 62.9%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{t}{c} \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 13: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+37} \lor \neg \left(t \leq 7.8 \cdot 10^{-85}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* a (/ t c)))))
   (if (<= t -7.5e+131)
     t_1
     (if (<= t -2.3e+103)
       (/ b (* z c))
       (if (or (<= t -2.6e+37) (not (<= t 7.8e-85))) t_1 (/ (/ 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 t_1 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if ((t <= -2.6e+37) || !(t <= 7.8e-85)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * (t / c))
    if (t <= (-7.5d+131)) then
        tmp = t_1
    else if (t <= (-2.3d+103)) then
        tmp = b / (z * c)
    else if ((t <= (-2.6d+37)) .or. (.not. (t <= 7.8d-85))) then
        tmp = t_1
    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 t_1 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if ((t <= -2.6e+37) || !(t <= 7.8e-85)) {
		tmp = t_1;
	} 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):
	t_1 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -7.5e+131:
		tmp = t_1
	elif t <= -2.3e+103:
		tmp = b / (z * c)
	elif (t <= -2.6e+37) or not (t <= 7.8e-85):
		tmp = t_1
	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)
	t_1 = Float64(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = Float64(b / Float64(z * c));
	elseif ((t <= -2.6e+37) || !(t <= 7.8e-85))
		tmp = t_1;
	else
		tmp = Float64(Float64(b / 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)
	t_1 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = b / (z * c);
	elseif ((t <= -2.6e+37) || ~((t <= 7.8e-85)))
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+131], t$95$1, If[LessEqual[t, -2.3e+103], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.6e+37], N[Not[LessEqual[t, 7.8e-85]], $MachinePrecision]], t$95$1, N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999995e131 or -2.30000000000000008e103 < t < -2.5999999999999999e37 or 7.79999999999999977e-85 < t

   1. Initial program 72.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 72.2%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 72.2%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 72.2%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 72.2%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 72.2%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 72.2%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 73.0%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 73.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 72.6%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 72.6%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 72.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 72.6%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 72.6%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 72.6%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 72.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 74.1%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 74.1%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 83.1%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 83.1%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 44.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 44.8%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 53.0%

          \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

       3. associate-/r/ 57.6%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{t}{c} \cdot a\right)} \]

   11. Simplified 57.6%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{t}{c} \cdot a\right)} \]

   if -7.4999999999999995e131 < t < -2.30000000000000008e103

   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 b around inf 58.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -2.5999999999999999e37 < t < 7.79999999999999977e-85

   1. Initial program 83.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 82.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 82.7%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 83.4%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 83.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 82.7%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 82.7%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 82.7%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 82.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in b around inf 46.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 45.3%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+37} \lor \neg \left(t \leq 7.8 \cdot 10^{-85}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 14: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* a (/ t c)))))
   (if (<= t -7.5e+131)
     t_1
     (if (<= t -2.3e+103)
       (/ b (* z c))
       (if (<= t -3.1e+38)
         (* -4.0 (/ a (/ c t)))
         (if (<= t 1.2e-84) (/ (/ 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if (t <= -3.1e+38) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 1.2e-84) {
		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 = (-4.0d0) * (a * (t / c))
    if (t <= (-7.5d+131)) then
        tmp = t_1
    else if (t <= (-2.3d+103)) then
        tmp = b / (z * c)
    else if (t <= (-3.1d+38)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 1.2d-84) 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if (t <= -3.1e+38) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 1.2e-84) {
		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 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -7.5e+131:
		tmp = t_1
	elif t <= -2.3e+103:
		tmp = b / (z * c)
	elif t <= -3.1e+38:
		tmp = -4.0 * (a / (c / t))
	elif t <= 1.2e-84:
		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(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= -3.1e+38)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 1.2e-84)
		tmp = Float64(Float64(b / 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 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = b / (z * c);
	elseif (t <= -3.1e+38)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 1.2e-84)
		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[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+131], t$95$1, If[LessEqual[t, -2.3e+103], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e+38], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-84], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999995e131 or 1.20000000000000009e-84 < t

   1. Initial program 70.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 72.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 72.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 70.6%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 70.6%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 72.4%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 72.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 73.4%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 73.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 71.9%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 71.9%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 80.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 80.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 80.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 71.9%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 71.9%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 71.9%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 71.9%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 71.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 71.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 73.7%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 82.3%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 82.3%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 45.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 45.1%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 53.6%

          \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

       3. associate-/r/ 58.2%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{t}{c} \cdot a\right)} \]

   11. Simplified 58.2%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{t}{c} \cdot a\right)} \]

   if -7.4999999999999995e131 < t < -2.30000000000000008e103

   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 b around inf 58.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -2.30000000000000008e103 < t < -3.10000000000000018e38

   1. Initial program 82.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 71.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 71.1%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 82.4%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 82.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 71.1%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 71.1%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 71.1%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 71.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 77.0%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 88.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 88.0%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 88.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 77.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 77.0%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 77.0%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 77.0%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 77.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 77.0%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 87.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 87.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 43.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. associate-/l* 53.9%

          \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   11. Simplified 53.9%

       \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if -3.10000000000000018e38 < t < 1.20000000000000009e-84

   1. Initial program 83.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 82.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 82.7%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 83.4%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 83.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 82.7%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 82.7%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 82.7%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 82.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in b around inf 46.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 45.3%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 15: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+37}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* a (/ t c)))))
   (if (<= t -7.5e+131)
     t_1
     (if (<= t -2.3e+103)
       (/ b (* z c))
       (if (<= t -2.9e+37)
         (* -4.0 (/ a (/ c t)))
         (if (<= t 3.6e-84) (* (/ b z) (/ 1.0 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if (t <= -2.9e+37) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.6e-84) {
		tmp = (b / z) * (1.0 / 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 = (-4.0d0) * (a * (t / c))
    if (t <= (-7.5d+131)) then
        tmp = t_1
    else if (t <= (-2.3d+103)) then
        tmp = b / (z * c)
    else if (t <= (-2.9d+37)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 3.6d-84) then
        tmp = (b / z) * (1.0d0 / 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 = -4.0 * (a * (t / c));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -2.3e+103) {
		tmp = b / (z * c);
	} else if (t <= -2.9e+37) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.6e-84) {
		tmp = (b / z) * (1.0 / 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 = -4.0 * (a * (t / c))
	tmp = 0
	if t <= -7.5e+131:
		tmp = t_1
	elif t <= -2.3e+103:
		tmp = b / (z * c)
	elif t <= -2.9e+37:
		tmp = -4.0 * (a / (c / t))
	elif t <= 3.6e-84:
		tmp = (b / z) * (1.0 / 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(-4.0 * Float64(a * Float64(t / c)))
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= -2.9e+37)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 3.6e-84)
		tmp = Float64(Float64(b / z) * Float64(1.0 / 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 = -4.0 * (a * (t / c));
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -2.3e+103)
		tmp = b / (z * c);
	elseif (t <= -2.9e+37)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 3.6e-84)
		tmp = (b / z) * (1.0 / 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[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+131], t$95$1, If[LessEqual[t, -2.3e+103], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e+37], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-84], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999995e131 or 3.60000000000000003e-84 < t

   1. Initial program 70.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 72.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 72.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 70.6%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 70.6%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 72.4%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 72.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 73.4%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 73.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 71.9%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 71.9%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 80.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 80.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 80.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 71.9%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 71.9%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 71.9%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 71.9%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 71.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 71.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 73.7%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 82.3%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 82.3%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 45.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 45.1%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 53.6%

          \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

       3. associate-/r/ 58.2%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{t}{c} \cdot a\right)} \]

   11. Simplified 58.2%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{t}{c} \cdot a\right)} \]

   if -7.4999999999999995e131 < t < -2.30000000000000008e103

   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 b around inf 58.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -2.30000000000000008e103 < t < -2.89999999999999978e37

   1. Initial program 82.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 71.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 71.1%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 82.4%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 82.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 71.1%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 71.1%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 71.1%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 71.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 77.0%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 88.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 88.0%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 88.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 77.0%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 77.0%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 77.0%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 77.0%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 77.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 77.0%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 87.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 87.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 43.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. associate-/l* 53.9%

          \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   11. Simplified 53.9%

       \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if -2.89999999999999978e37 < t < 3.60000000000000003e-84

   1. Initial program 83.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 82.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 82.7%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 83.4%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 83.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 82.7%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 82.7%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 82.7%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 82.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in b around inf 46.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 45.3%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
   9. Step-by-step derivation

      1. div-inv 45.3%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   10. Applied egg-rr 45.3%

       \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+37}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 16: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+139} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 (<= t -1.1e+139) (not (<= t 7.2e-22)))
   (* -4.0 (* a (/ t c)))
   (/ (+ b (* 9.0 (* y x))) (* 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 ((t <= -1.1e+139) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (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 ((t <= (-1.1d+139)) .or. (.not. (t <= 7.2d-22))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = (b + (9.0d0 * (y * x))) / (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 ((t <= -1.1e+139) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (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 (t <= -1.1e+139) or not (t <= 7.2e-22):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = (b + (9.0 * (y * x))) / (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 ((t <= -1.1e+139) || !(t <= 7.2e-22))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / 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 ((t <= -1.1e+139) || ~((t <= 7.2e-22)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = (b + (9.0 * (y * x))) / (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[t, -1.1e+139], N[Not[LessEqual[t, 7.2e-22]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e139 or 7.1999999999999996e-22 < t

   1. Initial program 69.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 71.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 71.1%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 69.0%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 69.0%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 71.1%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 71.1%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 72.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 72.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 71.5%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 71.5%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 71.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 71.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 71.5%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 71.5%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 71.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 71.5%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 72.6%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 82.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 49.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 49.8%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 59.7%

          \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

       3. associate-/r/ 65.1%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{t}{c} \cdot a\right)} \]

   11. Simplified 65.1%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{t}{c} \cdot a\right)} \]

   if -1.1e139 < t < 7.1999999999999996e-22

   1. Initial program 83.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 67.9%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+139} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \]

Alternative 17: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+139} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \end{array} \]

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 (<= t -1.05e+139) (not (<= t 7.2e-22)))
   (* -4.0 (* a (/ t c)))
   (/ (/ (+ b (* 9.0 (* y x))) 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 ((t <= -1.05e+139) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = ((b + (9.0 * (y * x))) / 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 ((t <= (-1.05d+139)) .or. (.not. (t <= 7.2d-22))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = ((b + (9.0d0 * (y * x))) / 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 ((t <= -1.05e+139) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = ((b + (9.0 * (y * x))) / 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 (t <= -1.05e+139) or not (t <= 7.2e-22):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = ((b + (9.0 * (y * x))) / 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 ((t <= -1.05e+139) || !(t <= 7.2e-22))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / 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 ((t <= -1.05e+139) || ~((t <= 7.2e-22)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = ((b + (9.0 * (y * x))) / 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[t, -1.05e+139], N[Not[LessEqual[t, 7.2e-22]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e139 or 7.1999999999999996e-22 < t

   1. Initial program 69.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 71.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 71.1%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 69.0%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 69.0%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 71.1%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 71.1%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 72.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 72.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 71.5%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 71.5%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 81.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 71.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 71.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 71.5%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 71.5%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 71.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 71.5%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 72.6%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 82.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in z around inf 49.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 49.8%

          \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

       2. associate-/l* 59.7%

          \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

       3. associate-/r/ 65.1%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{t}{c} \cdot a\right)} \]

   11. Simplified 65.1%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{t}{c} \cdot a\right)} \]

   if -1.0499999999999999e139 < t < 7.1999999999999996e-22

   1. Initial program 83.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 82.0%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 82.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 83.7%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 83.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 82.0%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 82.0%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 82.0%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 82.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in x around 0 79.5%

      \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate--l+ 79.5%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-/l* 76.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

      3. cancel-sign-sub-inv 76.6%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a}{\frac{c}{t}}\right)} \]

      4. metadata-eval 76.6%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a}{\frac{c}{t}}\right) \]

      5. associate-/l* 79.5%

         \[\leadsto \frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \color{blue}{\frac{a \cdot t}{c}}\right) \]

      6. +-commutative 79.5%

         \[\leadsto \frac{b}{c \cdot z} + \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      7. associate-+r+ 79.5%

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) + 9 \cdot \frac{y \cdot x}{c \cdot z}} \]

      8. +-commutative 79.5%

         \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z} + \left(\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      9. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]

      10. *-commutative 79.5%

          \[\leadsto \mathsf{fma}\left(9, \frac{y \cdot x}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      11. times-frac 85.9%

          \[\leadsto \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot \frac{x}{c}}, \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right) \]

      12. +-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      13. associate-/l* 83.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z}\right) \]

      14. *-commutative 83.0%

          \[\leadsto \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{\color{blue}{z \cdot c}}\right) \]

   8. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \frac{\frac{b}{z}}{c}\right)\right)} \]

   9. Taylor expanded in c around 0 87.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{z} + \left(9 \cdot \frac{y \cdot x}{z} + -4 \cdot \left(a \cdot t\right)\right)}{c}} \]

   10. Taylor expanded in z around 0 69.0%

       \[\leadsto \frac{\color{blue}{\frac{9 \cdot \left(y \cdot x\right) + b}{z}}}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+139} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]

Alternative 18: 36.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1000000000000:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

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 1000000000000.0) (/ b (* z 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 <= 1000000000000.0) {
		tmp = b / (z * 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 <= 1000000000000.0d0) then
        tmp = b / (z * 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 <= 1000000000000.0) {
		tmp = b / (z * 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 <= 1000000000000.0:
		tmp = b / (z * 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 <= 1000000000000.0)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / 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 <= 1000000000000.0)
		tmp = b / (z * 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[LessEqual[z, 1000000000000.0], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1e12

   1. Initial program 86.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 86.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 86.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 40.4%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 1e12 < z

   1. Initial program 58.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 58.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 58.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 58.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 58.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 58.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. div-inv 58.3%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

      2. associate-+l- 58.3%

         \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)\right)} \cdot \frac{1}{z \cdot c} \]

      3. associate-*r* 58.1%

         \[\leadsto \left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)\right) \cdot \frac{1}{z \cdot c} \]

      4. associate-+l- 58.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\right)} \cdot \frac{1}{z \cdot c} \]

      5. associate-*r* 58.3%

         \[\leadsto \left(\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      6. associate-*l* 58.3%

         \[\leadsto \left(\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c} \]

      7. fma-neg 58.3%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)} + b\right) \cdot \frac{1}{z \cdot c} \]

   5. Applied egg-rr 58.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 9 \cdot y, -\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right) \cdot \frac{1}{z \cdot c}} \]

   6. Taylor expanded in b around inf 21.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 27.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   8. Simplified 27.7%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1000000000000:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 19: 35.3% 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 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 76.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 76.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 76.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 78.2%

   \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 35.0%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 35.0%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 35.0%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 35.0%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 80.3% 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 2023279 
(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)))