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

Percentage Accurate: 80.0% → 89.4%

Time: 39.1s

Alternatives: 22

Speedup: 0.8×

• 38.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% 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: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y} - \frac{x}{z} \cdot -9\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.8e+55)
   (*
    y
    (- (/ (fma -4.0 (* a (/ t c)) (/ b (* z c))) y) (* (/ x z) (/ -9.0 c))))
   (if (<= z 2.6e+27)
     (/ (+ b (fma x (* y 9.0) (* t (* a (* z -4.0))))) (* z c))
     (/ (* y (- (/ (- (/ b z) (* 4.0 (* a t))) y) (* (/ x z) -9.0))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.8e+55) {
		tmp = y * ((fma(-4.0, (a * (t / c)), (b / (z * c))) / y) - ((x / z) * (-9.0 / c)));
	} else if (z <= 2.6e+27) {
		tmp = (b + fma(x, (y * 9.0), (t * (a * (z * -4.0))))) / (z * c);
	} else {
		tmp = (y * ((((b / z) - (4.0 * (a * t))) / y) - ((x / z) * -9.0))) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.8e+55)
		tmp = Float64(y * Float64(Float64(fma(-4.0, Float64(a * Float64(t / c)), Float64(b / Float64(z * c))) / y) - Float64(Float64(x / z) * Float64(-9.0 / c))));
	elseif (z <= 2.6e+27)
		tmp = Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(y * Float64(Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / y) - Float64(Float64(x / z) * -9.0))) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.8e+55], N[(y * N[(N[(N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(-9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+27], N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999994e55

   1. Initial program 68.0%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in y around -inf 80.6%

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

   7. Simplified 80.6%

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

   if -1.79999999999999994e55 < z < 2.60000000000000009e27

   1. Initial program 96.0%

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

   3. Simplified 96.9%

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

   if 2.60000000000000009e27 < z

   1. Initial program 58.4%

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

      1. associate-+l- 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*r* 54.6%

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

      4. *-commutative 54.6%

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

      5. associate-+l- 54.6%

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

      6. associate-*l* 54.6%

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

      7. associate-*l* 63.8%

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

      8. *-commutative 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in y around -inf 75.0%

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

   6. Taylor expanded in c around 0 86.8%

      \[\leadsto -1 \cdot \color{blue}{\frac{y \cdot \left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y}\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y} - \frac{x}{z} \cdot -9\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+54} \lor \neg \left(z \leq 4 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y} - \frac{x}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -6.5e+54) (not (<= z 4e+27)))
   (/ (* y (- (/ (- (/ b z) (* 4.0 (* a t))) y) (* (/ x z) -9.0))) c)
   (/ (+ b (fma x (* y 9.0) (* t (* a (* z -4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6.5e+54) || !(z <= 4e+27)) {
		tmp = (y * ((((b / z) - (4.0 * (a * t))) / y) - ((x / z) * -9.0))) / c;
	} else {
		tmp = (b + fma(x, (y * 9.0), (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6.5e+54) || !(z <= 4e+27))
		tmp = Float64(Float64(y * Float64(Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / y) - Float64(Float64(x / z) * -9.0))) / c);
	else
		tmp = Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -6.5e+54], N[Not[LessEqual[z, 4e+27]], $MachinePrecision]], N[(N[(y * N[(N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + 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 < -6.5e54 or 4.0000000000000001e27 < z

   1. Initial program 62.5%

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

      1. associate-+l- 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 60.4%

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

      4. *-commutative 60.4%

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

      5. associate-+l- 60.4%

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

      6. associate-*l* 60.4%

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

      7. associate-*l* 67.7%

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

      8. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in y around -inf 77.3%

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

   6. Taylor expanded in c around 0 86.2%

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

   if -6.5e54 < z < 4.0000000000000001e27

   1. Initial program 96.0%

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

   3. Simplified 96.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+54} \lor \neg \left(z \leq 4 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y} - \frac{x}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+91}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -5e-189)
     t_1
     (if (<= t_1 4e+91)
       (/ (+ (+ (* 9.0 (/ (* x y) c)) (/ b c)) (* -4.0 (/ (* a (* z t)) c))) z)
       (if (<= t_1 INFINITY)
         (/ (- b (- (* (* a t) (* z 4.0)) (* x (* y 9.0)))) (* z c))
         (* a (* t (/ -4.0 c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -5e-189) {
		tmp = t_1;
	} else if (t_1 <= 4e+91) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (z * t)) / c))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = a * (t * (-4.0 / c));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -5e-189) {
		tmp = t_1;
	} else if (t_1 <= 4e+91) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (z * t)) / c))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = a * (t * (-4.0 / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -5e-189:
		tmp = t_1
	elif t_1 <= 4e+91:
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (z * t)) / c))) / z
	elif t_1 <= math.inf:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c)
	else:
		tmp = a * (t * (-4.0 / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-189)
		tmp = t_1;
	elseif (t_1 <= 4e+91)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) + Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(y * 9.0)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e-189)
		tmp = t_1;
	elseif (t_1 <= 4e+91)
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (z * t)) / c))) / z;
	elseif (t_1 <= Inf)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	else
		tmp = a * (t * (-4.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-189], t$95$1, If[LessEqual[t$95$1, 4e+91], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999997e-189

   1. Initial program 93.6%

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

   if -4.9999999999999997e-189 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 4.00000000000000032e91

   1. Initial program 75.9%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in z around 0 99.0%

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

   if 4.00000000000000032e91 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.2%

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

      1. associate-+l- 90.2%

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

      2. *-commutative 90.2%

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

      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%

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

      6. associate-*l* 88.7%

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

      7. associate-*l* 90.6%

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

      8. *-commutative 90.6%

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

   3. Simplified 90.6%

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

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

   1. Initial program 0.0%

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

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

      6. associate-*l* 0.4%

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

      7. associate-*l* 0.4%

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

      8. *-commutative 0.4%

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

   3. Simplified 0.4%

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

   5. Taylor expanded in b around 0 0.0%

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

   6. Taylor expanded in x around 0 17.1%

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

      1. *-un-lft-identity 17.1%

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

      2. associate-*r* 17.1%

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

      3. times-frac 35.3%

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

      4. *-commutative 35.3%

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

   8. Applied egg-rr 35.3%

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

      1. *-lft-identity 35.3%

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

      2. times-frac 17.1%

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

      3. associate-*l* 17.1%

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

      4. times-frac 24.5%

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

      5. *-commutative 24.5%

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

      6. associate-/l* 35.2%

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

      7. associate-*l* 35.3%

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

      8. *-commutative 35.3%

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

      9. associate-/l* 78.1%

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

      10. *-inverses 78.1%

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

   10. Simplified 78.1%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot 1\right) \cdot \frac{-4}{c}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-189}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 4 \cdot 10^{+91}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+25} \lor \neg \left(z \leq 10^{+27}\right):\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y} - \frac{x}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -7e+25) (not (<= z 1e+27)))
   (/ (* y (- (/ (- (/ b z) (* 4.0 (* a t))) y) (* (/ x z) -9.0))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7e+25) || !(z <= 1e+27)) {
		tmp = (y * ((((b / z) - (4.0 * (a * t))) / y) - ((x / z) * -9.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-7d+25)) .or. (.not. (z <= 1d+27))) then
        tmp = (y * ((((b / z) - (4.0d0 * (a * t))) / y) - ((x / z) * (-9.0d0)))) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7e+25) || !(z <= 1e+27)) {
		tmp = (y * ((((b / z) - (4.0 * (a * t))) / y) - ((x / z) * -9.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7e+25) or not (z <= 1e+27):
		tmp = (y * ((((b / z) - (4.0 * (a * t))) / y) - ((x / z) * -9.0))) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7e+25) || !(z <= 1e+27))
		tmp = Float64(Float64(y * Float64(Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / y) - Float64(Float64(x / z) * -9.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -7e+25) || ~((z <= 1e+27)))
		tmp = (y * ((((b / z) - (4.0 * (a * t))) / y) - ((x / z) * -9.0))) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -7e+25], N[Not[LessEqual[z, 1e+27]], $MachinePrecision]], N[(N[(y * N[(N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999999e25 or 1e27 < z

   1. Initial program 63.7%

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

      1. associate-+l- 63.7%

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

      2. *-commutative 63.7%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

      5. associate-+l- 61.8%

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

      6. associate-*l* 61.8%

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

      7. associate-*l* 68.6%

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

      8. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in y around -inf 77.7%

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

   6. Taylor expanded in c around 0 87.1%

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

   if -6.99999999999999999e25 < z < 1e27

   1. Initial program 96.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+25} \lor \neg \left(z \leq 10^{+27}\right):\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{y} - \frac{x}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+143} \lor \neg \left(z \leq 2.26 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9.6e+143) (not (<= z 2.26e+52)))
   (/ (- (/ b z) (* 4.0 (* a t))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.6e+143) || !(z <= 2.26e+52)) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-9.6d+143)) .or. (.not. (z <= 2.26d+52))) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.6e+143) || !(z <= 2.26e+52)) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -9.6e+143) or not (z <= 2.26e+52):
		tmp = ((b / z) - (4.0 * (a * t))) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9.6e+143) || !(z <= 2.26e+52))
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -9.6e+143) || ~((z <= 2.26e+52)))
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9.6e+143], N[Not[LessEqual[z, 2.26e+52]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.59999999999999919e143 or 2.25999999999999993e52 < z

   1. Initial program 55.8%

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

      1. associate-+l- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*r* 54.4%

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

      4. *-commutative 54.4%

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

      5. associate-+l- 54.4%

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

      6. associate-*l* 54.4%

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

      7. associate-*l* 62.5%

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

      8. *-commutative 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in y around -inf 76.2%

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

   6. Taylor expanded in c around 0 86.2%

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

   7. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. cancel-sign-sub-inv 82.6%

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

      3. metadata-eval 82.6%

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

      4. distribute-neg-in 82.6%

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

      5. distribute-neg-frac2 82.6%

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

      6. distribute-lft-neg-in 82.6%

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

      7. metadata-eval 82.6%

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

   9. Simplified 82.6%

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

   if -9.59999999999999919e143 < z < 2.25999999999999993e52

   1. Initial program 94.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+143} \lor \neg \left(z \leq 2.26 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 1.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot \left(z \cdot \frac{t}{c}\right)\right) + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.7e+28)
   (/ (- b (- (* (* a t) (* z 4.0)) (* x (* y 9.0)))) (* z c))
   (/ (+ (* a (* -4.0 (* z (/ t c)))) (+ (* 9.0 (/ (* x y) c)) (/ b c))) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.7e+28) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = ((a * (-4.0 * (z * (t / c)))) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 1.7d+28) then
        tmp = (b - (((a * t) * (z * 4.0d0)) - (x * (y * 9.0d0)))) / (z * c)
    else
        tmp = ((a * ((-4.0d0) * (z * (t / c)))) + ((9.0d0 * ((x * y) / c)) + (b / c))) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.7e+28) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = ((a * (-4.0 * (z * (t / c)))) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 1.7e+28:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c)
	else:
		tmp = ((a * (-4.0 * (z * (t / c)))) + ((9.0 * ((x * y) / c)) + (b / c))) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.7e+28)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(y * 9.0)))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * Float64(z * Float64(t / c)))) + Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c))) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 1.7e+28)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	else
		tmp = ((a * (-4.0 * (z * (t / c)))) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.7e+28], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(-4.0 * N[(z * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.7e28

   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* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-+l- 86.0%

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

      6. associate-*l* 85.9%

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

      7. associate-*l* 86.9%

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

      8. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   if 1.7e28 < c

   1. Initial program 70.6%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. *-commutative 80.0%

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

   7. Applied egg-rr 80.0%

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

      1. associate-/l* 80.0%

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

      2. associate-*r/ 81.2%

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

      3. *-commutative 81.2%

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

      4. associate-*r* 81.2%

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

      5. associate-/l* 85.3%

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

   9. Simplified 85.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot \left(z \cdot \frac{t}{c}\right)\right) + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;b \leq -9500000000000:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - t\_1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - t\_1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 4.0 (* a t))))
   (if (<= b -9500000000000.0)
     (/ (/ (+ b (* y (* x 9.0))) c) z)
     (if (<= b 1.05e-85)
       (/ (- (* 9.0 (/ (* x y) z)) t_1) c)
       (/ (- (/ b z) t_1) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 4.0 * (a * t);
	double tmp;
	if (b <= -9500000000000.0) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else if (b <= 1.05e-85) {
		tmp = ((9.0 * ((x * y) / z)) - t_1) / c;
	} else {
		tmp = ((b / z) - t_1) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (a * t)
    if (b <= (-9500000000000.0d0)) then
        tmp = ((b + (y * (x * 9.0d0))) / c) / z
    else if (b <= 1.05d-85) then
        tmp = ((9.0d0 * ((x * y) / z)) - t_1) / c
    else
        tmp = ((b / z) - t_1) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 4.0 * (a * t);
	double tmp;
	if (b <= -9500000000000.0) {
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	} else if (b <= 1.05e-85) {
		tmp = ((9.0 * ((x * y) / z)) - t_1) / c;
	} else {
		tmp = ((b / z) - t_1) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 4.0 * (a * t)
	tmp = 0
	if b <= -9500000000000.0:
		tmp = ((b + (y * (x * 9.0))) / c) / z
	elif b <= 1.05e-85:
		tmp = ((9.0 * ((x * y) / z)) - t_1) / c
	else:
		tmp = ((b / z) - t_1) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(4.0 * Float64(a * t))
	tmp = 0.0
	if (b <= -9500000000000.0)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c) / z);
	elseif (b <= 1.05e-85)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - t_1) / c);
	else
		tmp = Float64(Float64(Float64(b / z) - t_1) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 4.0 * (a * t);
	tmp = 0.0;
	if (b <= -9500000000000.0)
		tmp = ((b + (y * (x * 9.0))) / c) / z;
	elseif (b <= 1.05e-85)
		tmp = ((9.0 * ((x * y) / z)) - t_1) / c;
	else
		tmp = ((b / z) - t_1) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9500000000000.0], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 1.05e-85], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5e12

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.5%

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

   6. Taylor expanded in a around 0 75.8%

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

   7. Taylor expanded in c around 0 84.7%

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

      1. associate-*r* 84.7%

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

   9. Simplified 84.7%

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

   if -9.5e12 < b < 1.05e-85

   1. Initial program 80.5%

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

      1. associate-+l- 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*r* 80.1%

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

      4. *-commutative 80.1%

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

      5. associate-+l- 80.1%

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

      6. associate-*l* 80.1%

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

      7. associate-*l* 81.1%

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

      8. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in z around inf 79.4%

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

   6. Taylor expanded in b around 0 85.9%

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

   if 1.05e-85 < b

   1. Initial program 84.2%

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

      1. associate-+l- 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-*r* 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-+l- 82.9%

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

      6. associate-*l* 82.8%

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

      7. associate-*l* 82.9%

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

      8. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in y around -inf 61.2%

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

   6. Taylor expanded in c around 0 80.6%

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

   7. Taylor expanded in y around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. cancel-sign-sub-inv 73.3%

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

      3. metadata-eval 73.3%

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

      4. distribute-neg-in 73.3%

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

      5. distribute-neg-frac2 73.3%

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

      6. distribute-lft-neg-in 73.3%

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

      7. metadata-eval 73.3%

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

   9. Simplified 73.3%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{b}{-z} + 4 \cdot \left(a \cdot t\right)}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9500000000000:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-299}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-25}:\\ \;\;\;\;9 \cdot \frac{\frac{x}{z} \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* -4.0 t) c))))
   (if (<= a -3.2e-23)
     t_1
     (if (<= a -1.65e-299)
       (/ b (* z c))
       (if (<= a 1.46e-25) (* 9.0 (/ (* (/ x z) y) c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (a <= -3.2e-23) {
		tmp = t_1;
	} else if (a <= -1.65e-299) {
		tmp = b / (z * c);
	} else if (a <= 1.46e-25) {
		tmp = 9.0 * (((x / z) * y) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((-4.0d0) * t) / c)
    if (a <= (-3.2d-23)) then
        tmp = t_1
    else if (a <= (-1.65d-299)) then
        tmp = b / (z * c)
    else if (a <= 1.46d-25) then
        tmp = 9.0d0 * (((x / z) * y) / c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (a <= -3.2e-23) {
		tmp = t_1;
	} else if (a <= -1.65e-299) {
		tmp = b / (z * c);
	} else if (a <= 1.46e-25) {
		tmp = 9.0 * (((x / z) * y) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((-4.0 * t) / c)
	tmp = 0
	if a <= -3.2e-23:
		tmp = t_1
	elif a <= -1.65e-299:
		tmp = b / (z * c)
	elif a <= 1.46e-25:
		tmp = 9.0 * (((x / z) * y) / c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(-4.0 * t) / c))
	tmp = 0.0
	if (a <= -3.2e-23)
		tmp = t_1;
	elseif (a <= -1.65e-299)
		tmp = Float64(b / Float64(z * c));
	elseif (a <= 1.46e-25)
		tmp = Float64(9.0 * Float64(Float64(Float64(x / z) * y) / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((-4.0 * t) / c);
	tmp = 0.0;
	if (a <= -3.2e-23)
		tmp = t_1;
	elseif (a <= -1.65e-299)
		tmp = b / (z * c);
	elseif (a <= 1.46e-25)
		tmp = 9.0 * (((x / z) * y) / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e-23], t$95$1, If[LessEqual[a, -1.65e-299], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.46e-25], N[(9.0 * N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.19999999999999976e-23 or 1.46e-25 < a

   1. Initial program 83.4%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in t around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-/l* 54.7%

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

      3. associate-*r* 54.7%

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

      4. *-commutative 54.7%

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

      5. *-commutative 54.7%

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

      6. associate-*l/ 54.7%

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

   7. Simplified 54.7%

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

   if -3.19999999999999976e-23 < a < -1.6500000000000001e-299

   1. Initial program 82.4%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 50.6%

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

      1. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   if -1.6500000000000001e-299 < a < 1.46e-25

   1. Initial program 85.5%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around inf 47.2%

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

      1. *-commutative 47.2%

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

      2. *-commutative 47.2%

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

      3. *-commutative 47.2%

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

      4. times-frac 43.8%

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

   7. Simplified 43.8%

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

      1. associate-*l/ 41.0%

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

   9. Applied egg-rr 41.0%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-299}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-25}:\\ \;\;\;\;9 \cdot \frac{\frac{x}{z} \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+118}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* -4.0 t) c))))
   (if (<= a -2.5e-20)
     t_1
     (if (<= a -4.5e-291)
       (/ b (* z c))
       (if (<= a 3.9e+118) (* 9.0 (* (/ x z) (/ y c))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (a <= -2.5e-20) {
		tmp = t_1;
	} else if (a <= -4.5e-291) {
		tmp = b / (z * c);
	} else if (a <= 3.9e+118) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((-4.0d0) * t) / c)
    if (a <= (-2.5d-20)) then
        tmp = t_1
    else if (a <= (-4.5d-291)) then
        tmp = b / (z * c)
    else if (a <= 3.9d+118) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (a <= -2.5e-20) {
		tmp = t_1;
	} else if (a <= -4.5e-291) {
		tmp = b / (z * c);
	} else if (a <= 3.9e+118) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((-4.0 * t) / c)
	tmp = 0
	if a <= -2.5e-20:
		tmp = t_1
	elif a <= -4.5e-291:
		tmp = b / (z * c)
	elif a <= 3.9e+118:
		tmp = 9.0 * ((x / z) * (y / c))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(-4.0 * t) / c))
	tmp = 0.0
	if (a <= -2.5e-20)
		tmp = t_1;
	elseif (a <= -4.5e-291)
		tmp = Float64(b / Float64(z * c));
	elseif (a <= 3.9e+118)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((-4.0 * t) / c);
	tmp = 0.0;
	if (a <= -2.5e-20)
		tmp = t_1;
	elseif (a <= -4.5e-291)
		tmp = b / (z * c);
	elseif (a <= 3.9e+118)
		tmp = 9.0 * ((x / z) * (y / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-20], t$95$1, If[LessEqual[a, -4.5e-291], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+118], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4999999999999999e-20 or 3.9e118 < a

   1. Initial program 84.7%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in t around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 57.3%

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

      3. associate-*r* 57.3%

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

      4. *-commutative 57.3%

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

      5. *-commutative 57.3%

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

      6. associate-*l/ 57.3%

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

   7. Simplified 57.3%

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

   if -2.4999999999999999e-20 < a < -4.49999999999999974e-291

   1. Initial program 82.4%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 50.6%

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

      1. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   if -4.49999999999999974e-291 < a < 3.9e118

   1. Initial program 83.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around inf 42.5%

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

      1. *-commutative 42.5%

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

      2. *-commutative 42.5%

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

      3. *-commutative 42.5%

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

      4. times-frac 41.6%

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

   7. Simplified 41.6%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+118}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.05 \cdot 10^{+131}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z 2.05e+131)
   (/ (- b (- (* (* a t) (* z 4.0)) (* x (* y 9.0)))) (* z c))
   (/ (- (/ b z) (* 4.0 (* a t))) c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 2.05e+131) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= 2.05d+131) then
        tmp = (b - (((a * t) * (z * 4.0d0)) - (x * (y * 9.0d0)))) / (z * c)
    else
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 2.05e+131) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= 2.05e+131:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c)
	else:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= 2.05e+131)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(y * 9.0)))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= 2.05e+131)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (y * 9.0)))) / (z * c);
	else
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 2.05e+131], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.05000000000000004e131

   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* 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-+l- 88.1%

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

      6. associate-*l* 88.1%

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

      7. associate-*l* 87.3%

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

      8. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   if 2.05000000000000004e131 < z

   1. Initial program 49.9%

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

      1. associate-+l- 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*r* 46.6%

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

      4. *-commutative 46.6%

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

      5. associate-+l- 46.6%

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

      6. associate-*l* 46.6%

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

      7. associate-*l* 53.0%

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

      8. *-commutative 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in y around -inf 75.2%

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

   6. Taylor expanded in c around 0 89.5%

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

   7. Taylor expanded in y around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. cancel-sign-sub-inv 93.4%

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

      3. metadata-eval 93.4%

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

      4. distribute-neg-in 93.4%

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

      5. distribute-neg-frac2 93.4%

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

      6. distribute-lft-neg-in 93.4%

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

      7. metadata-eval 93.4%

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

   9. Simplified 93.4%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{b}{-z} + 4 \cdot \left(a \cdot t\right)}}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.05 \cdot 10^{+131}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;y \leq 14600:\\ \;\;\;\;\frac{b + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.15e+56)
   (* 9.0 (* y (/ (/ x c) z)))
   (if (<= y 14600.0)
     (/ (+ b (* a (* t (* z -4.0)))) (* z c))
     (/ (+ b (* y (* x 9.0))) (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.15e+56) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (y <= 14600.0) {
		tmp = (b + (a * (t * (z * -4.0)))) / (z * c);
	} else {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-1.15d+56)) then
        tmp = 9.0d0 * (y * ((x / c) / z))
    else if (y <= 14600.0d0) then
        tmp = (b + (a * (t * (z * (-4.0d0))))) / (z * c)
    else
        tmp = (b + (y * (x * 9.0d0))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.15e+56) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (y <= 14600.0) {
		tmp = (b + (a * (t * (z * -4.0)))) / (z * c);
	} else {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.15e+56:
		tmp = 9.0 * (y * ((x / c) / z))
	elif y <= 14600.0:
		tmp = (b + (a * (t * (z * -4.0)))) / (z * c)
	else:
		tmp = (b + (y * (x * 9.0))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.15e+56)
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / c) / z)));
	elseif (y <= 14600.0)
		tmp = Float64(Float64(b + Float64(a * Float64(t * Float64(z * -4.0)))) / Float64(z * c));
	else
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -1.15e+56)
		tmp = 9.0 * (y * ((x / c) / z));
	elseif (y <= 14600.0)
		tmp = (b + (a * (t * (z * -4.0)))) / (z * c);
	else
		tmp = (b + (y * (x * 9.0))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.15e+56], N[(9.0 * N[(y * N[(N[(x / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 14600.0], N[(N[(b + N[(a * N[(t * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000007e56

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-+l- 84.8%

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

      6. associate-*l* 84.8%

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

      7. associate-*l* 86.6%

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

      8. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around inf 81.6%

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

   6. Taylor expanded in x around inf 66.9%

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

      1. *-rgt-identity 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-*r/ 66.8%

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

      4. *-commutative 66.8%

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

      5. *-commutative 66.8%

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

      6. associate-*r* 66.9%

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

      7. *-commutative 66.9%

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

      8. *-commutative 66.9%

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

      9. associate-*r/ 66.9%

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

      10. *-rgt-identity 66.9%

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

      11. *-commutative 66.9%

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

      12. associate-/r* 70.4%

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

   8. Simplified 70.4%

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

   if -1.15000000000000007e56 < y < 14600

   1. Initial program 84.6%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-*r* 72.7%

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

      3. associate-*l* 72.7%

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

   7. Simplified 72.7%

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

   if 14600 < y

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-*r* 79.4%

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

      4. *-commutative 79.4%

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

      5. associate-+l- 79.4%

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

      6. associate-*l* 79.3%

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

      7. associate-*l* 77.9%

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

      8. *-commutative 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in z around inf 72.2%

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

   6. Taylor expanded in z around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-*r* 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;y \leq 14600:\\ \;\;\;\;\frac{b + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+21} \lor \neg \left(z \leq 2.65 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.1e+21) (not (<= z 2.65e-99)))
   (/ (- (/ b z) (* 4.0 (* a t))) c)
   (/ (+ b (* y (* x 9.0))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.1e+21) || !(z <= 2.65e-99)) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.1d+21)) .or. (.not. (z <= 2.65d-99))) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + (y * (x * 9.0d0))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.1e+21) || !(z <= 2.65e-99)) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.1e+21) or not (z <= 2.65e-99):
		tmp = ((b / z) - (4.0 * (a * t))) / c
	else:
		tmp = (b + (y * (x * 9.0))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.1e+21) || !(z <= 2.65e-99))
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.1e+21) || ~((z <= 2.65e-99)))
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	else
		tmp = (b + (y * (x * 9.0))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.1e+21], N[Not[LessEqual[z, 2.65e-99]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e21 or 2.6500000000000002e-99 < z

   1. Initial program 71.0%

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

      1. associate-+l- 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-*r* 69.4%

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

      4. *-commutative 69.4%

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

      5. associate-+l- 69.4%

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

      6. associate-*l* 69.4%

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

      7. associate-*l* 74.8%

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

      8. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in y around -inf 72.1%

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

   6. Taylor expanded in c around 0 87.4%

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

   7. Taylor expanded in y around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. cancel-sign-sub-inv 77.5%

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

      3. metadata-eval 77.5%

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

      4. distribute-neg-in 77.5%

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

      5. distribute-neg-frac2 77.5%

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

      6. distribute-lft-neg-in 77.5%

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

      7. metadata-eval 77.5%

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

   9. Simplified 77.5%

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

   if -3.1e21 < z < 2.6500000000000002e-99

   1. Initial program 95.8%

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

      1. associate-+l- 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-*r* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-+l- 96.2%

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

      6. associate-*l* 96.2%

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

      7. associate-*l* 91.1%

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

      8. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 86.7%

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

   6. Taylor expanded in z around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*r* 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*r* 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+21} \lor \neg \left(z \leq 2.65 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right) - t\_1}{c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - t\_1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 4.0 (* a t))))
   (if (<= z -5.6e+19)
     (/ (- (* 9.0 (* x (/ y z))) t_1) c)
     (if (<= z 2.5e-99)
       (/ (+ b (* y (* x 9.0))) (* z c))
       (/ (- (/ b z) t_1) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 4.0 * (a * t);
	double tmp;
	if (z <= -5.6e+19) {
		tmp = ((9.0 * (x * (y / z))) - t_1) / c;
	} else if (z <= 2.5e-99) {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	} else {
		tmp = ((b / z) - t_1) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (a * t)
    if (z <= (-5.6d+19)) then
        tmp = ((9.0d0 * (x * (y / z))) - t_1) / c
    else if (z <= 2.5d-99) then
        tmp = (b + (y * (x * 9.0d0))) / (z * c)
    else
        tmp = ((b / z) - t_1) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 4.0 * (a * t);
	double tmp;
	if (z <= -5.6e+19) {
		tmp = ((9.0 * (x * (y / z))) - t_1) / c;
	} else if (z <= 2.5e-99) {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	} else {
		tmp = ((b / z) - t_1) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 4.0 * (a * t)
	tmp = 0
	if z <= -5.6e+19:
		tmp = ((9.0 * (x * (y / z))) - t_1) / c
	elif z <= 2.5e-99:
		tmp = (b + (y * (x * 9.0))) / (z * c)
	else:
		tmp = ((b / z) - t_1) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -5.6e+19)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * Float64(y / z))) - t_1) / c);
	elseif (z <= 2.5e-99)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) - t_1) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 4.0 * (a * t);
	tmp = 0.0;
	if (z <= -5.6e+19)
		tmp = ((9.0 * (x * (y / z))) - t_1) / c;
	elseif (z <= 2.5e-99)
		tmp = (b + (y * (x * 9.0))) / (z * c);
	else
		tmp = ((b / z) - t_1) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+19], N[(N[(N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.5e-99], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6e19

   1. Initial program 71.2%

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

      1. associate-+l- 71.2%

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

      2. *-commutative 71.2%

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

      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%

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

      6. associate-*l* 71.4%

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

      7. associate-*l* 75.3%

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

      8. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in z around inf 73.3%

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

   6. Taylor expanded in b around 0 69.9%

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

      1. associate-/l* 76.0%

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

   8. Applied egg-rr 76.0%

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

   if -5.6e19 < z < 2.49999999999999985e-99

   1. Initial program 95.8%

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

      1. associate-+l- 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-*r* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-+l- 96.2%

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

      6. associate-*l* 96.2%

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

      7. associate-*l* 91.1%

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

      8. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 86.7%

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

   6. Taylor expanded in z around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*r* 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*r* 82.2%

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

   8. Simplified 82.2%

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

   if 2.49999999999999985e-99 < z

   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* 68.2%

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

      4. *-commutative 68.2%

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

      5. associate-+l- 68.2%

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

      6. associate-*l* 68.1%

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

      7. associate-*l* 74.5%

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

      8. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around -inf 66.1%

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

   6. Taylor expanded in c around 0 87.1%

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

   7. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. cancel-sign-sub-inv 82.3%

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

      3. metadata-eval 82.3%

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

      4. distribute-neg-in 82.3%

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

      5. distribute-neg-frac2 82.3%

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

      6. distribute-lft-neg-in 82.3%

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

      7. metadata-eval 82.3%

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

   9. Simplified 82.3%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{b}{-z} + 4 \cdot \left(a \cdot t\right)}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 17.5:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.5e+157)
   (* a (/ (* -4.0 t) c))
   (if (<= z 17.5)
     (/ (+ b (* y (* x 9.0))) (* z c))
     (* -4.0 (* (* a t) (/ 1.0 c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.5e+157) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 17.5) {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) * (1.0 / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.5d+157)) then
        tmp = a * (((-4.0d0) * t) / c)
    else if (z <= 17.5d0) then
        tmp = (b + (y * (x * 9.0d0))) / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) * (1.0d0 / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.5e+157) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 17.5) {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) * (1.0 / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.5e+157:
		tmp = a * ((-4.0 * t) / c)
	elif z <= 17.5:
		tmp = (b + (y * (x * 9.0))) / (z * c)
	else:
		tmp = -4.0 * ((a * t) * (1.0 / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.5e+157)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	elseif (z <= 17.5)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) * Float64(1.0 / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.5e+157)
		tmp = a * ((-4.0 * t) / c);
	elseif (z <= 17.5)
		tmp = (b + (y * (x * 9.0))) / (z * c);
	else
		tmp = -4.0 * ((a * t) * (1.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.5e+157], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 17.5], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000002e157

   1. Initial program 57.8%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in t around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-/l* 63.4%

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

      3. associate-*r* 63.4%

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

      4. *-commutative 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-*l/ 63.4%

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

   7. Simplified 63.4%

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

   if -3.50000000000000002e157 < z < 17.5

   1. Initial program 94.0%

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

      1. associate-+l- 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-*r* 93.8%

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

      4. *-commutative 93.8%

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

      5. associate-+l- 93.8%

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

      6. associate-*l* 93.7%

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

      7. associate-*l* 90.5%

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

      8. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 87.1%

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

   6. Taylor expanded in z around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*r* 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-*r* 77.6%

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

   8. Simplified 77.6%

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

   if 17.5 < z

   1. Initial program 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in t around inf 65.0%

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

      1. div-inv 65.1%

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

   7. Applied egg-rr 65.1%

      \[\leadsto -4 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 17.5:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.15e+157)
   (* a (/ (* -4.0 t) c))
   (if (<= z 0.04)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -4.0 (* (* a t) (/ 1.0 c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.15e+157) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 0.04) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) * (1.0 / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.15d+157)) then
        tmp = a * (((-4.0d0) * t) / c)
    else if (z <= 0.04d0) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) * (1.0d0 / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.15e+157) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 0.04) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) * (1.0 / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.15e+157:
		tmp = a * ((-4.0 * t) / c)
	elif z <= 0.04:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * ((a * t) * (1.0 / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.15e+157)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	elseif (z <= 0.04)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) * Float64(1.0 / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.15e+157)
		tmp = a * ((-4.0 * t) / c);
	elseif (z <= 0.04)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * ((a * t) * (1.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.15e+157], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.04], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000002e157

   1. Initial program 57.8%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in t around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-/l* 63.4%

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

      3. associate-*r* 63.4%

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

      4. *-commutative 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-*l/ 63.4%

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

   7. Simplified 63.4%

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

   if -1.15000000000000002e157 < z < 0.0400000000000000008

   1. Initial program 94.0%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

   7. Simplified 77.5%

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

   if 0.0400000000000000008 < z

   1. Initial program 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in t around inf 65.0%

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

      1. div-inv 65.1%

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

   7. Applied egg-rr 65.1%

      \[\leadsto -4 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-76}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6.8e+20)
   (* a (/ (* -4.0 t) c))
   (if (<= z 3.5e-76)
     (* 9.0 (* x (/ y (* z c))))
     (* -4.0 (* (* a t) (/ 1.0 c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.8e+20) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 3.5e-76) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = -4.0 * ((a * t) * (1.0 / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-6.8d+20)) then
        tmp = a * (((-4.0d0) * t) / c)
    else if (z <= 3.5d-76) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else
        tmp = (-4.0d0) * ((a * t) * (1.0d0 / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.8e+20) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 3.5e-76) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = -4.0 * ((a * t) * (1.0 / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -6.8e+20:
		tmp = a * ((-4.0 * t) / c)
	elif z <= 3.5e-76:
		tmp = 9.0 * (x * (y / (z * c)))
	else:
		tmp = -4.0 * ((a * t) * (1.0 / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.8e+20)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	elseif (z <= 3.5e-76)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) * Float64(1.0 / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -6.8e+20)
		tmp = a * ((-4.0 * t) / c);
	elseif (z <= 3.5e-76)
		tmp = 9.0 * (x * (y / (z * c)));
	else
		tmp = -4.0 * ((a * t) * (1.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6.8e+20], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-76], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e20

   1. Initial program 71.2%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. associate-/l* 54.0%

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

      3. associate-*r* 54.0%

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

      4. *-commutative 54.0%

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

      5. *-commutative 54.0%

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

      6. associate-*l/ 54.0%

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

   7. Simplified 54.0%

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

   if -6.8e20 < z < 3.49999999999999997e-76

   1. Initial program 96.0%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 54.7%

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

      1. associate-/l* 57.5%

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

      2. *-commutative 57.5%

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

   7. Simplified 57.5%

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

   if 3.49999999999999997e-76 < z

   1. Initial program 68.3%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. div-inv 61.7%

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

   7. Applied egg-rr 61.7%

      \[\leadsto -4 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-76}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-33} \lor \neg \left(a \leq 3 \cdot 10^{-78}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -5.4e-33) (not (<= a 3e-78)))
   (* a (/ (* -4.0 t) c))
   (/ (/ b c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -5.4e-33) || !(a <= 3e-78)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-5.4d-33)) .or. (.not. (a <= 3d-78))) then
        tmp = a * (((-4.0d0) * t) / c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -5.4e-33) || !(a <= 3e-78)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -5.4e-33) or not (a <= 3e-78):
		tmp = a * ((-4.0 * t) / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -5.4e-33) || !(a <= 3e-78))
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -5.4e-33) || ~((a <= 3e-78)))
		tmp = a * ((-4.0 * t) / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -5.4e-33], N[Not[LessEqual[a, 3e-78]], $MachinePrecision]], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4000000000000002e-33 or 2.99999999999999988e-78 < a

   1. Initial program 83.8%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in t around inf 50.3%

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

      1. *-commutative 50.3%

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

      2. associate-/l* 52.6%

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

      3. associate-*r* 52.6%

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

      4. *-commutative 52.6%

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

      5. *-commutative 52.6%

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

      6. associate-*l/ 52.6%

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

   7. Simplified 52.6%

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

   if -5.4000000000000002e-33 < a < 2.99999999999999988e-78

   1. Initial program 83.5%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in z around 0 85.8%

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

   6. Taylor expanded in a around 0 77.5%

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

   7. Taylor expanded in x around 0 48.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-33} \lor \neg \left(a \leq 3 \cdot 10^{-78}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -9000000000000:\\ \;\;\;\;\frac{\frac{1}{\frac{c}{b}}}{z}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -9000000000000.0)
   (/ (/ 1.0 (/ c b)) z)
   (if (<= b 2.6e+80) (* t (/ (* -4.0 a) c)) (/ 1.0 (/ (* z c) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -9000000000000.0) {
		tmp = (1.0 / (c / b)) / z;
	} else if (b <= 2.6e+80) {
		tmp = t * ((-4.0 * a) / c);
	} else {
		tmp = 1.0 / ((z * c) / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-9000000000000.0d0)) then
        tmp = (1.0d0 / (c / b)) / z
    else if (b <= 2.6d+80) then
        tmp = t * (((-4.0d0) * a) / c)
    else
        tmp = 1.0d0 / ((z * c) / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -9000000000000.0) {
		tmp = (1.0 / (c / b)) / z;
	} else if (b <= 2.6e+80) {
		tmp = t * ((-4.0 * a) / c);
	} else {
		tmp = 1.0 / ((z * c) / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -9000000000000.0:
		tmp = (1.0 / (c / b)) / z
	elif b <= 2.6e+80:
		tmp = t * ((-4.0 * a) / c)
	else:
		tmp = 1.0 / ((z * c) / b)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -9000000000000.0)
		tmp = Float64(Float64(1.0 / Float64(c / b)) / z);
	elseif (b <= 2.6e+80)
		tmp = Float64(t * Float64(Float64(-4.0 * a) / c));
	else
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -9000000000000.0)
		tmp = (1.0 / (c / b)) / z;
	elseif (b <= 2.6e+80)
		tmp = t * ((-4.0 * a) / c);
	else
		tmp = 1.0 / ((z * c) / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -9000000000000.0], N[(N[(1.0 / N[(c / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 2.6e+80], N[(t * N[(N[(-4.0 * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9e12

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.5%

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

   6. Taylor expanded in a around 0 75.8%

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

   7. Taylor expanded in x around 0 63.8%

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

      1. clear-num 63.8%

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

      2. inv-pow 63.8%

         \[\leadsto \frac{\color{blue}{{\left(\frac{c}{b}\right)}^{-1}}}{z} \]

   9. Applied egg-rr 63.8%

      \[\leadsto \frac{\color{blue}{{\left(\frac{c}{b}\right)}^{-1}}}{z} \]
   10. Step-by-step derivation

       1. unpow-1 63.8%

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

   11. Simplified 63.8%

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

   if -9e12 < b < 2.59999999999999982e80

   1. Initial program 81.2%

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

      1. associate-+l- 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*r* 81.5%

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

      4. *-commutative 81.5%

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

      5. associate-+l- 81.5%

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

      6. associate-*l* 81.5%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in b around 0 72.4%

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

   6. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. metadata-eval 49.4%

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

      3. distribute-lft-neg-in 49.4%

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

      4. associate-*r* 49.4%

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

      5. *-commutative 49.4%

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

      6. distribute-rgt-neg-in 49.4%

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

      7. distribute-lft-neg-in 49.4%

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

      8. metadata-eval 49.4%

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

      9. associate-*r/ 50.5%

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

      10. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   if 2.59999999999999982e80 < b

   1. Initial program 85.1%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   7. Simplified 57.1%

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

      1. *-commutative 57.1%

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

      2. clear-num 57.1%

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

      3. inv-pow 57.1%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

      4. *-commutative 57.1%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot c}}{b}\right)}^{-1} \]

   9. Applied egg-rr 57.1%

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

       1. unpow-1 57.1%

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

       2. associate-/l* 54.7%

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

   11. Simplified 54.7%

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

   12. Taylor expanded in z around 0 57.1%

       \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9000000000000:\\ \;\;\;\;\frac{\frac{1}{\frac{c}{b}}}{z}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6000000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -6000000000000.0)
   (/ (/ b c) z)
   (if (<= b 2.8e+80) (* t (/ (* -4.0 a) c)) (/ 1.0 (/ (* z c) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -6000000000000.0) {
		tmp = (b / c) / z;
	} else if (b <= 2.8e+80) {
		tmp = t * ((-4.0 * a) / c);
	} else {
		tmp = 1.0 / ((z * c) / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-6000000000000.0d0)) then
        tmp = (b / c) / z
    else if (b <= 2.8d+80) then
        tmp = t * (((-4.0d0) * a) / c)
    else
        tmp = 1.0d0 / ((z * c) / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -6000000000000.0) {
		tmp = (b / c) / z;
	} else if (b <= 2.8e+80) {
		tmp = t * ((-4.0 * a) / c);
	} else {
		tmp = 1.0 / ((z * c) / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -6000000000000.0:
		tmp = (b / c) / z
	elif b <= 2.8e+80:
		tmp = t * ((-4.0 * a) / c)
	else:
		tmp = 1.0 / ((z * c) / b)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -6000000000000.0)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 2.8e+80)
		tmp = Float64(t * Float64(Float64(-4.0 * a) / c));
	else
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -6000000000000.0)
		tmp = (b / c) / z;
	elseif (b <= 2.8e+80)
		tmp = t * ((-4.0 * a) / c);
	else
		tmp = 1.0 / ((z * c) / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -6000000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 2.8e+80], N[(t * N[(N[(-4.0 * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6e12

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.5%

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

   6. Taylor expanded in a around 0 75.8%

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

   7. Taylor expanded in x around 0 63.8%

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

   if -6e12 < b < 2.79999999999999984e80

   1. Initial program 81.2%

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

      1. associate-+l- 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*r* 81.5%

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

      4. *-commutative 81.5%

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

      5. associate-+l- 81.5%

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

      6. associate-*l* 81.5%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in b around 0 72.4%

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

   6. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. metadata-eval 49.4%

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

      3. distribute-lft-neg-in 49.4%

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

      4. associate-*r* 49.4%

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

      5. *-commutative 49.4%

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

      6. distribute-rgt-neg-in 49.4%

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

      7. distribute-lft-neg-in 49.4%

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

      8. metadata-eval 49.4%

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

      9. associate-*r/ 50.5%

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

      10. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   if 2.79999999999999984e80 < b

   1. Initial program 85.1%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   7. Simplified 57.1%

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

      1. *-commutative 57.1%

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

      2. clear-num 57.1%

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

      3. inv-pow 57.1%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

      4. *-commutative 57.1%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot c}}{b}\right)}^{-1} \]

   9. Applied egg-rr 57.1%

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

       1. unpow-1 57.1%

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

       2. associate-/l* 54.7%

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

   11. Simplified 54.7%

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

   12. Taylor expanded in z around 0 57.1%

       \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6000000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3000000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3000000000000.0)
   (/ (/ b c) z)
   (if (<= b 2.6e+80) (* t (/ (* -4.0 a) c)) (/ b (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3000000000000.0) {
		tmp = (b / c) / z;
	} else if (b <= 2.6e+80) {
		tmp = t * ((-4.0 * a) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-3000000000000.0d0)) then
        tmp = (b / c) / z
    else if (b <= 2.6d+80) then
        tmp = t * (((-4.0d0) * a) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3000000000000.0) {
		tmp = (b / c) / z;
	} else if (b <= 2.6e+80) {
		tmp = t * ((-4.0 * a) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3000000000000.0:
		tmp = (b / c) / z
	elif b <= 2.6e+80:
		tmp = t * ((-4.0 * a) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3000000000000.0)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 2.6e+80)
		tmp = Float64(t * Float64(Float64(-4.0 * a) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3000000000000.0)
		tmp = (b / c) / z;
	elseif (b <= 2.6e+80)
		tmp = t * ((-4.0 * a) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3000000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 2.6e+80], N[(t * N[(N[(-4.0 * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3e12

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.5%

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

   6. Taylor expanded in a around 0 75.8%

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

   7. Taylor expanded in x around 0 63.8%

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

   if -3e12 < b < 2.59999999999999982e80

   1. Initial program 81.2%

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

      1. associate-+l- 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*r* 81.5%

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

      4. *-commutative 81.5%

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

      5. associate-+l- 81.5%

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

      6. associate-*l* 81.5%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in b around 0 72.4%

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

   6. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. metadata-eval 49.4%

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

      3. distribute-lft-neg-in 49.4%

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

      4. associate-*r* 49.4%

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

      5. *-commutative 49.4%

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

      6. distribute-rgt-neg-in 49.4%

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

      7. distribute-lft-neg-in 49.4%

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

      8. metadata-eval 49.4%

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

      9. associate-*r/ 50.5%

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

      10. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   if 2.59999999999999982e80 < b

   1. Initial program 85.1%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   7. Simplified 57.1%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3000000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8000000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -8000000000000.0)
   (/ (/ b c) z)
   (if (<= b 3.2e+80) (* -4.0 (/ (* a t) c)) (/ b (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -8000000000000.0) {
		tmp = (b / c) / z;
	} else if (b <= 3.2e+80) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-8000000000000.0d0)) then
        tmp = (b / c) / z
    else if (b <= 3.2d+80) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -8000000000000.0) {
		tmp = (b / c) / z;
	} else if (b <= 3.2e+80) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -8000000000000.0:
		tmp = (b / c) / z
	elif b <= 3.2e+80:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -8000000000000.0)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 3.2e+80)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -8000000000000.0)
		tmp = (b / c) / z;
	elseif (b <= 3.2e+80)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -8000000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 3.2e+80], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8e12

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.5%

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

   6. Taylor expanded in a around 0 75.8%

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

   7. Taylor expanded in x around 0 63.8%

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

   if -8e12 < b < 3.1999999999999999e80

   1. Initial program 81.2%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in t around inf 49.4%

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

   if 3.1999999999999999e80 < b

   1. Initial program 85.1%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 57.1%

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

      1. *-commutative 57.1%

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

   7. Simplified 57.1%

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

Alternative 22: 35.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

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

Derivation

1. Initial program 83.7%

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

3. Simplified 84.3%

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

5. Taylor expanded in b around inf 34.1%

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

   1. *-commutative 34.1%

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

7. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer Target 1: 81.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))