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

Percentage Accurate: 79.4% → 86.5%

Time: 16.0s

Alternatives: 16

Speedup: 0.7×

• 37.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+134} \lor \neg \left(z \leq 7.5 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{c \cdot z}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= z -8.2e+134) (not (<= z 7.5e+19)))
   (*
    y
    (- (/ (fma -4.0 (* a (/ t c)) (/ b (* c z))) y) (* (/ x z) (/ -9.0 c))))
   (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* 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 ((z <= -8.2e+134) || !(z <= 7.5e+19)) {
		tmp = y * ((fma(-4.0, (a * (t / c)), (b / (c * z))) / y) - ((x / z) * (-9.0 / c)));
	} else {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (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 ((z <= -8.2e+134) || !(z <= 7.5e+19))
		tmp = Float64(y * Float64(Float64(fma(-4.0, Float64(a * Float64(t / c)), Float64(b / Float64(c * z))) / y) - Float64(Float64(x / z) * Float64(-9.0 / c))));
	else
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(c * z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -8.2e+134], N[Not[LessEqual[z, 7.5e+19]], $MachinePrecision]], N[(y * N[(N[(N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(-9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000007e134 or 7.5e19 < z

   1. Initial program 50.7%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in y around -inf 73.5%

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

   7. Simplified 77.3%

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

   if -8.2000000000000007e134 < z < 7.5e19

   1. Initial program 93.7%

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

   3. Simplified 93.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+134} \lor \neg \left(z \leq 7.5 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{c \cdot z}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}\\ \end{array} \end{array} \]

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 2.8e+43)
   (/ (- b (- (* (* z 4.0) (* t a)) (* x (* 9.0 y)))) (* c z))
   (/ (fma -4.0 (* a (* t (/ z c))) (fma 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 <= 2.8e+43) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = fma(-4.0, (a * (t * (z / c))), fma(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 <= 2.8e+43)
		tmp = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(t * a)) - Float64(x * Float64(9.0 * y)))) / Float64(c * z));
	else
		tmp = Float64(fma(-4.0, Float64(a * Float64(t * Float64(z / c))), fma(9.0, Float64(x * Float64(y / c)), Float64(b / c))) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 2.8e+43], N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * N[(t * N[(z / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 2.80000000000000019e43

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-+r- 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-*r* 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-+r- 85.3%

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

      7. +-commutative 85.3%

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

      8. associate-*l* 85.3%

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

      9. associate-*l* 86.3%

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

      10. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   if 2.80000000000000019e43 < c

   1. Initial program 68.7%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in z around 0 72.6%

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

      1. fma-define 72.6%

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

      2. associate-/l* 79.4%

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

      3. associate-/l* 77.9%

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

      4. fma-define 77.9%

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

      5. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+20}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\frac{b}{c \cdot z} - 4 \cdot \frac{t \cdot a}{c}}{y} - -9 \cdot \frac{x}{c \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.1e+128)
   (/ (* y (+ (* -4.0 (/ (* t a) y)) (* 9.0 (/ x z)))) c)
   (if (<= z 2.25e+20)
     (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* c z))
     (*
      y
      (-
       (/ (- (/ b (* c z)) (* 4.0 (/ (* t a) c))) y)
       (* -9.0 (/ x (* 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 (z <= -2.1e+128) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	} else if (z <= 2.25e+20) {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (c * z);
	} else {
		tmp = y * ((((b / (c * z)) - (4.0 * ((t * a) / c))) / y) - (-9.0 * (x / (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 (z <= -2.1e+128)
		tmp = Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(9.0 * Float64(x / z)))) / c);
	elseif (z <= 2.25e+20)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(c * z));
	else
		tmp = Float64(y * Float64(Float64(Float64(Float64(b / Float64(c * z)) - Float64(4.0 * Float64(Float64(t * a) / c))) / y) - Float64(-9.0 * Float64(x / Float64(c * z)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.1e+128], N[(N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.25e+20], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(-9.0 * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e128

   1. Initial program 45.2%

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

      1. +-commutative 45.2%

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

      2. associate-+r- 45.2%

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

      3. *-commutative 45.2%

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

      4. associate-*r* 51.2%

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

      5. *-commutative 51.2%

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

      6. associate-+r- 51.2%

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

      7. +-commutative 51.2%

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

      8. associate-*l* 51.2%

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

      9. associate-*l* 56.6%

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

      10. *-commutative 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in y around inf 67.9%

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

   6. Taylor expanded in b around 0 60.2%

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

      1. times-frac 54.7%

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

      2. cancel-sign-sub-inv 54.7%

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

      3. metadata-eval 54.7%

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

      4. times-frac 60.2%

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

      5. times-frac 54.7%

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

      6. associate-*r/ 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in c around 0 78.5%

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

   if -2.1e128 < z < 2.25e20

   1. Initial program 94.2%

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

   3. Simplified 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

   if 2.25e20 < z

   1. Initial program 54.8%

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

      1. +-commutative 54.8%

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

      2. associate-+r- 54.8%

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

      3. *-commutative 54.8%

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

      4. associate-*r* 56.8%

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

      5. *-commutative 56.8%

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

      6. associate-+r- 56.8%

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

      7. +-commutative 56.8%

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

      8. associate-*l* 56.7%

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

      9. associate-*l* 59.3%

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

      10. *-commutative 59.3%

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

   3. Simplified 59.3%

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

   5. Taylor expanded in y around -inf 74.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+20}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\frac{b}{c \cdot z} - 4 \cdot \frac{t \cdot a}{c}}{y} - -9 \cdot \frac{x}{c \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-285}:\\ \;\;\;\;b \cdot \frac{9 \cdot \left(x \cdot \frac{y}{b}\right) + 1}{c \cdot z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{-4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z}\\ \end{array} \end{array} \]

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 (<= y -3.4e-12)
   (* x (* (/ y c) (/ 9.0 z)))
   (if (<= y 5e-285)
     (* b (/ (+ (* 9.0 (* x (/ y b))) 1.0) (* c z)))
     (if (<= y 3.6e+67)
       (/ (+ (/ b c) (/ (* -4.0 (* z (* t a))) c)) z)
       (/ (/ (+ b (* 9.0 (* x y))) 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 (y <= -3.4e-12) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (y <= 5e-285) {
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z));
	} else if (y <= 3.6e+67) {
		tmp = ((b / c) + ((-4.0 * (z * (t * a))) / c)) / z;
	} else {
		tmp = ((b + (9.0 * (x * y))) / 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 (y <= (-3.4d-12)) then
        tmp = x * ((y / c) * (9.0d0 / z))
    else if (y <= 5d-285) then
        tmp = b * (((9.0d0 * (x * (y / b))) + 1.0d0) / (c * z))
    else if (y <= 3.6d+67) then
        tmp = ((b / c) + (((-4.0d0) * (z * (t * a))) / c)) / z
    else
        tmp = ((b + (9.0d0 * (x * y))) / 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 (y <= -3.4e-12) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (y <= 5e-285) {
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z));
	} else if (y <= 3.6e+67) {
		tmp = ((b / c) + ((-4.0 * (z * (t * a))) / c)) / z;
	} else {
		tmp = ((b + (9.0 * (x * y))) / 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 y <= -3.4e-12:
		tmp = x * ((y / c) * (9.0 / z))
	elif y <= 5e-285:
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z))
	elif y <= 3.6e+67:
		tmp = ((b / c) + ((-4.0 * (z * (t * a))) / c)) / z
	else:
		tmp = ((b + (9.0 * (x * y))) / 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 (y <= -3.4e-12)
		tmp = Float64(x * Float64(Float64(y / c) * Float64(9.0 / z)));
	elseif (y <= 5e-285)
		tmp = Float64(b * Float64(Float64(Float64(9.0 * Float64(x * Float64(y / b))) + 1.0) / Float64(c * z)));
	elseif (y <= 3.6e+67)
		tmp = Float64(Float64(Float64(b / c) + Float64(Float64(-4.0 * Float64(z * Float64(t * a))) / c)) / z);
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / 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 (y <= -3.4e-12)
		tmp = x * ((y / c) * (9.0 / z));
	elseif (y <= 5e-285)
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z));
	elseif (y <= 3.6e+67)
		tmp = ((b / c) + ((-4.0 * (z * (t * a))) / c)) / z;
	else
		tmp = ((b + (9.0 * (x * y))) / 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[y, -3.4e-12], N[(x * N[(N[(y / c), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-285], N[(b * N[(N[(N[(9.0 * N[(x * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+67], N[(N[(N[(b / c), $MachinePrecision] + N[(N[(-4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4000000000000001e-12

   1. Initial program 66.0%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in x around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-commutative 40.2%

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

      3. *-commutative 40.2%

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

      4. times-frac 51.6%

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

   7. Simplified 51.6%

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

   8. Taylor expanded in y around 0 40.2%

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

      1. associate-/l* 48.2%

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

      2. associate-*r* 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*r* 48.2%

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

      5. associate-*r/ 48.2%

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

      6. *-commutative 48.2%

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

      7. times-frac 51.2%

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

   10. Simplified 51.2%

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

   if -3.4000000000000001e-12 < y < 5.00000000000000018e-285

   1. Initial program 85.6%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in b around inf 79.6%

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

   6. Taylor expanded in a around 0 64.1%

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

      1. associate-/l* 65.5%

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

      2. associate-*r/ 65.5%

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

   8. Simplified 65.5%

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

   if 5.00000000000000018e-285 < y < 3.5999999999999999e67

   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 83.9%

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

   5. Taylor expanded in z around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. associate-*r* 82.7%

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

   7. Applied egg-rr 82.7%

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

   8. Taylor expanded in x around 0 71.0%

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

   if 3.5999999999999999e67 < y

   1. Initial program 86.3%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 84.0%

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

   6. Taylor expanded in a around 0 84.0%

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

   7. Taylor expanded in c around 0 84.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-285}:\\ \;\;\;\;b \cdot \frac{9 \cdot \left(x \cdot \frac{y}{b}\right) + 1}{c \cdot z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{-4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+134}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+205}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{c \cdot z} + -4 \cdot \frac{t \cdot \frac{a}{c}}{y}\right)\\ \end{array} \end{array} \]

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 -6.4e+134)
   (/ (* y (+ (* -4.0 (/ (* t a) y)) (* 9.0 (/ x z)))) c)
   (if (<= z 8e+205)
     (/ (+ b (- (* y (* x 9.0)) (* a (* (* z 4.0) t)))) (* c z))
     (* y (+ (* 9.0 (/ x (* c z))) (* -4.0 (/ (* t (/ a c)) y)))))))

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 <= -6.4e+134) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	} else if (z <= 8e+205) {
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c * z);
	} else {
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)));
	}
	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 <= (-6.4d+134)) then
        tmp = (y * (((-4.0d0) * ((t * a) / y)) + (9.0d0 * (x / z)))) / c
    else if (z <= 8d+205) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * ((z * 4.0d0) * t)))) / (c * z)
    else
        tmp = y * ((9.0d0 * (x / (c * z))) + ((-4.0d0) * ((t * (a / c)) / y)))
    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 <= -6.4e+134) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	} else if (z <= 8e+205) {
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c * z);
	} else {
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)));
	}
	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 <= -6.4e+134:
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c
	elif z <= 8e+205:
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c * z)
	else:
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)))
	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 <= -6.4e+134)
		tmp = Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(9.0 * Float64(x / z)))) / c);
	elseif (z <= 8e+205)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(Float64(z * 4.0) * t)))) / Float64(c * z));
	else
		tmp = Float64(y * Float64(Float64(9.0 * Float64(x / Float64(c * z))) + Float64(-4.0 * Float64(Float64(t * Float64(a / c)) / y))));
	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 <= -6.4e+134)
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	elseif (z <= 8e+205)
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c * z);
	else
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)));
	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, -6.4e+134], N[(N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 8e+205], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(9.0 * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4000000000000001e134

   1. Initial program 45.0%

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

      1. +-commutative 45.0%

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

      2. associate-+r- 45.0%

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

      3. *-commutative 45.0%

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

      4. associate-*r* 51.1%

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

      5. *-commutative 51.1%

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

      6. associate-+r- 51.1%

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

      7. +-commutative 51.1%

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

      8. associate-*l* 51.1%

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

      9. associate-*l* 56.8%

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

      10. *-commutative 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around inf 69.0%

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

   6. Taylor expanded in b around 0 60.8%

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

      1. times-frac 58.0%

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

      2. cancel-sign-sub-inv 58.0%

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

      3. metadata-eval 58.0%

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

      4. times-frac 60.8%

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

      5. times-frac 58.0%

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

      6. associate-*r/ 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in c around 0 80.2%

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

   if -6.4000000000000001e134 < z < 8.00000000000000013e205

   1. Initial program 90.5%

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

   if 8.00000000000000013e205 < z

   1. Initial program 25.3%

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

      1. +-commutative 25.3%

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

      2. associate-+r- 25.3%

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

      3. *-commutative 25.3%

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

      4. associate-*r* 31.0%

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

      5. *-commutative 31.0%

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

      6. associate-+r- 31.0%

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

      7. +-commutative 31.0%

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

      8. associate-*l* 31.0%

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

      9. associate-*l* 31.3%

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

      10. *-commutative 31.3%

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

   3. Simplified 31.3%

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

   5. Taylor expanded in y around inf 70.4%

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

   6. Taylor expanded in b around 0 53.5%

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

      1. times-frac 70.3%

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

      2. cancel-sign-sub-inv 70.3%

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

      3. metadata-eval 70.3%

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

      4. times-frac 53.5%

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

      5. times-frac 70.3%

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

      6. associate-*r/ 70.3%

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

   8. Simplified 70.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+134}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+205}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{c \cdot z} + -4 \cdot \frac{t \cdot \frac{a}{c}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+205}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{c \cdot z} + -4 \cdot \frac{t \cdot \frac{a}{c}}{y}\right)\\ \end{array} \end{array} \]

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 -8.2e+135)
   (/ (* y (+ (* -4.0 (/ (* t a) y)) (* 9.0 (/ x z)))) c)
   (if (<= z 2.2e+205)
     (/ (- b (- (* (* z 4.0) (* t a)) (* x (* 9.0 y)))) (* c z))
     (* y (+ (* 9.0 (/ x (* c z))) (* -4.0 (/ (* t (/ a c)) y)))))))

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 <= -8.2e+135) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	} else if (z <= 2.2e+205) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)));
	}
	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 <= (-8.2d+135)) then
        tmp = (y * (((-4.0d0) * ((t * a) / y)) + (9.0d0 * (x / z)))) / c
    else if (z <= 2.2d+205) then
        tmp = (b - (((z * 4.0d0) * (t * a)) - (x * (9.0d0 * y)))) / (c * z)
    else
        tmp = y * ((9.0d0 * (x / (c * z))) + ((-4.0d0) * ((t * (a / c)) / y)))
    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 <= -8.2e+135) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	} else if (z <= 2.2e+205) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)));
	}
	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 <= -8.2e+135:
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c
	elif z <= 2.2e+205:
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z)
	else:
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)))
	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 <= -8.2e+135)
		tmp = Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(9.0 * Float64(x / z)))) / c);
	elseif (z <= 2.2e+205)
		tmp = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(t * a)) - Float64(x * Float64(9.0 * y)))) / Float64(c * z));
	else
		tmp = Float64(y * Float64(Float64(9.0 * Float64(x / Float64(c * z))) + Float64(-4.0 * Float64(Float64(t * Float64(a / c)) / y))));
	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 <= -8.2e+135)
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / z)))) / c;
	elseif (z <= 2.2e+205)
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	else
		tmp = y * ((9.0 * (x / (c * z))) + (-4.0 * ((t * (a / c)) / y)));
	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, -8.2e+135], N[(N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.2e+205], N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(9.0 * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e135

   1. Initial program 45.0%

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

      1. +-commutative 45.0%

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

      2. associate-+r- 45.0%

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

      3. *-commutative 45.0%

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

      4. associate-*r* 51.1%

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

      5. *-commutative 51.1%

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

      6. associate-+r- 51.1%

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

      7. +-commutative 51.1%

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

      8. associate-*l* 51.1%

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

      9. associate-*l* 56.8%

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

      10. *-commutative 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around inf 69.0%

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

   6. Taylor expanded in b around 0 60.8%

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

      1. times-frac 58.0%

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

      2. cancel-sign-sub-inv 58.0%

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

      3. metadata-eval 58.0%

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

      4. times-frac 60.8%

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

      5. times-frac 58.0%

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

      6. associate-*r/ 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in c around 0 80.2%

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

   if -8.2e135 < z < 2.1999999999999998e205

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-+r- 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*r* 90.0%

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

      5. *-commutative 90.0%

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

      6. associate-+r- 90.0%

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

      7. +-commutative 90.0%

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

      8. associate-*l* 90.5%

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

      9. associate-*l* 90.5%

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

      10. *-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

   if 2.1999999999999998e205 < z

   1. Initial program 25.3%

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

      1. +-commutative 25.3%

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

      2. associate-+r- 25.3%

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

      3. *-commutative 25.3%

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

      4. associate-*r* 31.0%

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

      5. *-commutative 31.0%

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

      6. associate-+r- 31.0%

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

      7. +-commutative 31.0%

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

      8. associate-*l* 31.0%

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

      9. associate-*l* 31.3%

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

      10. *-commutative 31.3%

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

   3. Simplified 31.3%

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

   5. Taylor expanded in y around inf 70.4%

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

   6. Taylor expanded in b around 0 53.5%

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

      1. times-frac 70.3%

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

      2. cancel-sign-sub-inv 70.3%

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

      3. metadata-eval 70.3%

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

      4. times-frac 53.5%

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

      5. times-frac 70.3%

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

      6. associate-*r/ 70.3%

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

   8. Simplified 70.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+205}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{c \cdot z} + -4 \cdot \frac{t \cdot \frac{a}{c}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)\right)}{z}\\ \end{array} \end{array} \]

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 6.2e+42)
   (/ (- b (- (* (* z 4.0) (* t a)) (* x (* 9.0 y)))) (* c z))
   (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (/ b c) (* 9.0 (* x (/ y 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 <= 6.2e+42) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((b / c) + (9.0 * (x * (y / 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 <= 6.2d+42) then
        tmp = (b - (((z * 4.0d0) * (t * a)) - (x * (9.0d0 * y)))) / (c * z)
    else
        tmp = (((-4.0d0) * ((a * (z * t)) / c)) + ((b / c) + (9.0d0 * (x * (y / 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 <= 6.2e+42) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((b / c) + (9.0 * (x * (y / 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 <= 6.2e+42:
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z)
	else:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((b / c) + (9.0 * (x * (y / 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 <= 6.2e+42)
		tmp = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(t * a)) - Float64(x * Float64(9.0 * y)))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(b / c) + Float64(9.0 * Float64(x * Float64(y / 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 <= 6.2e+42)
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c * z);
	else
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((b / c) + (9.0 * (x * (y / 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, 6.2e+42], N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 6.2000000000000003e42

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-+r- 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-*r* 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-+r- 85.3%

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

      7. +-commutative 85.3%

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

      8. associate-*l* 85.3%

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

      9. associate-*l* 86.3%

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

      10. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   if 6.2000000000000003e42 < c

   1. Initial program 68.7%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in z around 0 72.6%

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

      1. associate-/l* 75.8%

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

   7. Applied egg-rr 75.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-30} \lor \neg \left(b \leq 2.8 \cdot 10^{-54}\right):\\ \;\;\;\;b \cdot \frac{9 \cdot \left(x \cdot \frac{y}{b}\right) + 1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \end{array} \end{array} \]

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 (or (<= b -4.5e-30) (not (<= b 2.8e-54)))
   (* b (/ (+ (* 9.0 (* x (/ y b))) 1.0) (* c z)))
   (/ (* y (+ (* -4.0 (/ (* t a) y)) (* 9.0 (/ x 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 <= -4.5e-30) || !(b <= 2.8e-54)) {
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z));
	} else {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / 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 <= (-4.5d-30)) .or. (.not. (b <= 2.8d-54))) then
        tmp = b * (((9.0d0 * (x * (y / b))) + 1.0d0) / (c * z))
    else
        tmp = (y * (((-4.0d0) * ((t * a) / y)) + (9.0d0 * (x / 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 <= -4.5e-30) || !(b <= 2.8e-54)) {
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z));
	} else {
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / 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 <= -4.5e-30) or not (b <= 2.8e-54):
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z))
	else:
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / 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 <= -4.5e-30) || !(b <= 2.8e-54))
		tmp = Float64(b * Float64(Float64(Float64(9.0 * Float64(x * Float64(y / b))) + 1.0) / Float64(c * z)));
	else
		tmp = Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(9.0 * Float64(x / 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 <= -4.5e-30) || ~((b <= 2.8e-54)))
		tmp = b * (((9.0 * (x * (y / b))) + 1.0) / (c * z));
	else
		tmp = (y * ((-4.0 * ((t * a) / y)) + (9.0 * (x / 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[b, -4.5e-30], N[Not[LessEqual[b, 2.8e-54]], $MachinePrecision]], N[(b * N[(N[(N[(9.0 * N[(x * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.49999999999999967e-30 or 2.8000000000000002e-54 < b

   1. Initial program 83.0%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 83.6%

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

   6. Taylor expanded in a around 0 78.5%

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

      1. associate-/l* 78.4%

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

      2. associate-*r/ 81.0%

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

   8. Simplified 81.0%

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

   if -4.49999999999999967e-30 < b < 2.8000000000000002e-54

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. associate-+r- 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-*r* 75.3%

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

      5. *-commutative 75.3%

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

      6. associate-+r- 75.3%

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

      7. +-commutative 75.3%

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

      8. associate-*l* 75.3%

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

      9. associate-*l* 78.1%

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

      10. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in y around inf 69.0%

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

   6. Taylor expanded in b around 0 69.8%

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

      1. times-frac 67.7%

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

      2. cancel-sign-sub-inv 67.7%

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

      3. metadata-eval 67.7%

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

      4. times-frac 69.8%

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

      5. times-frac 67.7%

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

      6. associate-*r/ 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in c around 0 80.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-30} \lor \neg \left(b \leq 2.8 \cdot 10^{-54}\right):\\ \;\;\;\;b \cdot \frac{9 \cdot \left(x \cdot \frac{y}{b}\right) + 1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 9 \cdot \frac{x}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-233}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-97}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= b -1.4e-23)
   (/ 1.0 (* z (/ c b)))
   (if (<= b 3.7e-233)
     (* -4.0 (* t (/ a c)))
     (if (<= b 1.3e-97) (/ (* y (* x 9.0)) (* c z)) (/ 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 (b <= -1.4e-23) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 3.7e-233) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 1.3e-97) {
		tmp = (y * (x * 9.0)) / (c * z);
	} 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 (b <= (-1.4d-23)) then
        tmp = 1.0d0 / (z * (c / b))
    else if (b <= 3.7d-233) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 1.3d-97) then
        tmp = (y * (x * 9.0d0)) / (c * z)
    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 (b <= -1.4e-23) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 3.7e-233) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 1.3e-97) {
		tmp = (y * (x * 9.0)) / (c * z);
	} 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 b <= -1.4e-23:
		tmp = 1.0 / (z * (c / b))
	elif b <= 3.7e-233:
		tmp = -4.0 * (t * (a / c))
	elif b <= 1.3e-97:
		tmp = (y * (x * 9.0)) / (c * z)
	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 (b <= -1.4e-23)
		tmp = Float64(1.0 / Float64(z * Float64(c / b)));
	elseif (b <= 3.7e-233)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 1.3e-97)
		tmp = Float64(Float64(y * Float64(x * 9.0)) / Float64(c * z));
	else
		tmp = Float64(b / Float64(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 (b <= -1.4e-23)
		tmp = 1.0 / (z * (c / b));
	elseif (b <= 3.7e-233)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 1.3e-97)
		tmp = (y * (x * 9.0)) / (c * z);
	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[LessEqual[b, -1.4e-23], N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-233], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-97], N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.3999999999999999e-23

   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 83.9%

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

   5. Taylor expanded in b around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

      1. clear-num 60.8%

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

      2. inv-pow 60.8%

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

   9. Applied egg-rr 60.8%

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

       1. unpow-1 60.8%

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

       2. associate-/l* 62.3%

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

   11. Simplified 62.3%

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

   if -1.3999999999999999e-23 < b < 3.6999999999999998e-233

   1. Initial program 74.6%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in t around inf 49.2%

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

      1. associate-*l/ 56.8%

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

   7. Applied egg-rr 56.8%

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

   if 3.6999999999999998e-233 < b < 1.30000000000000003e-97

   1. Initial program 86.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in b around inf 72.7%

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

   6. Taylor expanded in x around inf 66.6%

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

      1. associate-*r* 66.6%

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

   8. Simplified 66.6%

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

   if 1.30000000000000003e-97 < b

   1. Initial program 80.9%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in b around inf 66.1%

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

      1. *-commutative 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-233}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-97}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-233}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-107}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= b -9.8e-24)
   (/ 1.0 (* z (/ c b)))
   (if (<= b 3.7e-233)
     (* -4.0 (* t (/ a c)))
     (if (<= b 3.4e-107) (* 9.0 (/ (* x y) (* c z))) (/ 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 (b <= -9.8e-24) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 3.7e-233) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 3.4e-107) {
		tmp = 9.0 * ((x * y) / (c * z));
	} 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 (b <= (-9.8d-24)) then
        tmp = 1.0d0 / (z * (c / b))
    else if (b <= 3.7d-233) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 3.4d-107) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    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 (b <= -9.8e-24) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 3.7e-233) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 3.4e-107) {
		tmp = 9.0 * ((x * y) / (c * z));
	} 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 b <= -9.8e-24:
		tmp = 1.0 / (z * (c / b))
	elif b <= 3.7e-233:
		tmp = -4.0 * (t * (a / c))
	elif b <= 3.4e-107:
		tmp = 9.0 * ((x * y) / (c * z))
	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 (b <= -9.8e-24)
		tmp = Float64(1.0 / Float64(z * Float64(c / b)));
	elseif (b <= 3.7e-233)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 3.4e-107)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	else
		tmp = Float64(b / Float64(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 (b <= -9.8e-24)
		tmp = 1.0 / (z * (c / b));
	elseif (b <= 3.7e-233)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 3.4e-107)
		tmp = 9.0 * ((x * y) / (c * z));
	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[LessEqual[b, -9.8e-24], N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-233], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-107], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.8000000000000002e-24

   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 83.9%

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

   5. Taylor expanded in b around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

      1. clear-num 60.8%

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

      2. inv-pow 60.8%

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

   9. Applied egg-rr 60.8%

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

       1. unpow-1 60.8%

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

       2. associate-/l* 62.3%

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

   11. Simplified 62.3%

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

   if -9.8000000000000002e-24 < b < 3.6999999999999998e-233

   1. Initial program 74.6%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in t around inf 49.2%

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

      1. associate-*l/ 56.8%

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

   7. Applied egg-rr 56.8%

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

   if 3.6999999999999998e-233 < b < 3.39999999999999994e-107

   1. Initial program 86.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in x around inf 66.5%

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

   if 3.39999999999999994e-107 < b

   1. Initial program 80.9%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in b around inf 66.1%

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

      1. *-commutative 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-233}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-107}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-97}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= b -3.6e-24)
   (/ 1.0 (* z (/ c b)))
   (if (<= b 3.8e-233)
     (* -4.0 (* t (/ a c)))
     (if (<= b 1.4e-97) (* 9.0 (* x (/ y (* c z)))) (/ 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 (b <= -3.6e-24) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 3.8e-233) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 1.4e-97) {
		tmp = 9.0 * (x * (y / (c * z)));
	} 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 (b <= (-3.6d-24)) then
        tmp = 1.0d0 / (z * (c / b))
    else if (b <= 3.8d-233) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 1.4d-97) then
        tmp = 9.0d0 * (x * (y / (c * z)))
    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 (b <= -3.6e-24) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 3.8e-233) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 1.4e-97) {
		tmp = 9.0 * (x * (y / (c * z)));
	} 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 b <= -3.6e-24:
		tmp = 1.0 / (z * (c / b))
	elif b <= 3.8e-233:
		tmp = -4.0 * (t * (a / c))
	elif b <= 1.4e-97:
		tmp = 9.0 * (x * (y / (c * z)))
	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 (b <= -3.6e-24)
		tmp = Float64(1.0 / Float64(z * Float64(c / b)));
	elseif (b <= 3.8e-233)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 1.4e-97)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c * z))));
	else
		tmp = Float64(b / Float64(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 (b <= -3.6e-24)
		tmp = 1.0 / (z * (c / b));
	elseif (b <= 3.8e-233)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 1.4e-97)
		tmp = 9.0 * (x * (y / (c * z)));
	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[LessEqual[b, -3.6e-24], N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-233], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-97], N[(9.0 * N[(x * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.6000000000000001e-24

   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 83.9%

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

   5. Taylor expanded in b around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

      1. clear-num 60.8%

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

      2. inv-pow 60.8%

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

   9. Applied egg-rr 60.8%

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

       1. unpow-1 60.8%

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

       2. associate-/l* 62.3%

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

   11. Simplified 62.3%

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

   if -3.6000000000000001e-24 < b < 3.8e-233

   1. Initial program 74.6%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in t around inf 49.2%

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

      1. associate-*l/ 56.8%

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

   7. Applied egg-rr 56.8%

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

   if 3.8e-233 < b < 1.4000000000000001e-97

   1. Initial program 86.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in x around inf 66.5%

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

      1. associate-/l* 63.1%

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

      2. *-commutative 63.1%

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

   7. Simplified 63.1%

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

   if 1.4000000000000001e-97 < b

   1. Initial program 80.9%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in b around inf 66.1%

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

      1. *-commutative 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-97}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z}\\ \end{array} \end{array} \]

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 (<= y -1e-13)
   (* x (* (/ y c) (/ 9.0 z)))
   (if (<= y 2.4e+34)
     (/ (- b (* 4.0 (* a (* z t)))) (* c z))
     (/ (/ (+ b (* 9.0 (* x y))) 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 (y <= -1e-13) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (y <= 2.4e+34) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z);
	} else {
		tmp = ((b + (9.0 * (x * y))) / 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 (y <= (-1d-13)) then
        tmp = x * ((y / c) * (9.0d0 / z))
    else if (y <= 2.4d+34) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c * z)
    else
        tmp = ((b + (9.0d0 * (x * y))) / 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 (y <= -1e-13) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (y <= 2.4e+34) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z);
	} else {
		tmp = ((b + (9.0 * (x * y))) / 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 y <= -1e-13:
		tmp = x * ((y / c) * (9.0 / z))
	elif y <= 2.4e+34:
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z)
	else:
		tmp = ((b + (9.0 * (x * y))) / 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 (y <= -1e-13)
		tmp = Float64(x * Float64(Float64(y / c) * Float64(9.0 / z)));
	elseif (y <= 2.4e+34)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / 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 (y <= -1e-13)
		tmp = x * ((y / c) * (9.0 / z));
	elseif (y <= 2.4e+34)
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z);
	else
		tmp = ((b + (9.0 * (x * y))) / 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[y, -1e-13], N[(x * N[(N[(y / c), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+34], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e-13

   1. Initial program 67.0%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in x around inf 40.5%

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

      1. *-commutative 40.5%

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

      2. *-commutative 40.5%

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

      3. *-commutative 40.5%

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

      4. times-frac 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in y around 0 40.5%

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

      1. associate-/l* 48.2%

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

      2. associate-*r* 48.3%

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

      3. *-commutative 48.3%

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

      4. associate-*r* 48.2%

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

      5. associate-*r/ 48.2%

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

      6. *-commutative 48.2%

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

      7. times-frac 51.2%

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

   10. Simplified 51.2%

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

   if -1e-13 < y < 2.39999999999999987e34

   1. Initial program 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-+r- 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-*r* 82.9%

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

      5. *-commutative 82.9%

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

      6. associate-+r- 82.9%

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

      7. +-commutative 82.9%

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

      8. associate-*l* 83.7%

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

      9. associate-*l* 84.6%

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

      10. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in x around 0 75.3%

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

   if 2.39999999999999987e34 < y

   1. Initial program 86.2%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around 0 84.2%

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

   6. Taylor expanded in a around 0 84.2%

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

   7. Taylor expanded in c around 0 84.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-25} \lor \neg \left(a \leq 1.05 \cdot 10^{+148}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 -1.1e-25) (not (<= a 1.05e+148)))
   (* -4.0 (* t (/ a c)))
   (/ (+ b (* 9.0 (* x y))) (* 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 <= -1.1e-25) || !(a <= 1.05e+148)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b + (9.0 * (x * y))) / (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 <= (-1.1d-25)) .or. (.not. (a <= 1.05d+148))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b + (9.0d0 * (x * y))) / (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 <= -1.1e-25) || !(a <= 1.05e+148)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b + (9.0 * (x * y))) / (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 <= -1.1e-25) or not (a <= 1.05e+148):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b + (9.0 * (x * y))) / (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 <= -1.1e-25) || !(a <= 1.05e+148))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(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 <= -1.1e-25) || ~((a <= 1.05e+148)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b + (9.0 * (x * y))) / (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, -1.1e-25], N[Not[LessEqual[a, 1.05e+148]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1000000000000001e-25 or 1.04999999999999999e148 < a

   1. Initial program 78.5%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in t around inf 46.9%

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

      1. associate-*l/ 58.9%

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

   7. Applied egg-rr 58.9%

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

   if -1.1000000000000001e-25 < a < 1.04999999999999999e148

   1. Initial program 80.9%

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

   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 t around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. *-commutative 73.6%

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

   7. Simplified 73.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-25} \lor \neg \left(a \leq 1.05 \cdot 10^{+148}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-54}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= b -3.8e-26)
   (/ 1.0 (* z (/ c b)))
   (if (<= b 7e-54) (* -4.0 (* t (/ a 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 (b <= -3.8e-26) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 7e-54) {
		tmp = -4.0 * (t * (a / 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 (b <= (-3.8d-26)) then
        tmp = 1.0d0 / (z * (c / b))
    else if (b <= 7d-54) then
        tmp = (-4.0d0) * (t * (a / 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 (b <= -3.8e-26) {
		tmp = 1.0 / (z * (c / b));
	} else if (b <= 7e-54) {
		tmp = -4.0 * (t * (a / 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 b <= -3.8e-26:
		tmp = 1.0 / (z * (c / b))
	elif b <= 7e-54:
		tmp = -4.0 * (t * (a / 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 (b <= -3.8e-26)
		tmp = Float64(1.0 / Float64(z * Float64(c / b)));
	elseif (b <= 7e-54)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(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 (b <= -3.8e-26)
		tmp = 1.0 / (z * (c / b));
	elseif (b <= 7e-54)
		tmp = -4.0 * (t * (a / 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[LessEqual[b, -3.8e-26], N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-54], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000015e-26

   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 83.9%

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

   5. Taylor expanded in b around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

      1. clear-num 60.8%

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

      2. inv-pow 60.8%

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

   9. Applied egg-rr 60.8%

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

       1. unpow-1 60.8%

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

       2. associate-/l* 62.3%

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

   11. Simplified 62.3%

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

   if -3.80000000000000015e-26 < b < 6.99999999999999964e-54

   1. Initial program 76.5%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 48.3%

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

      1. associate-*l/ 52.7%

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

   7. Applied egg-rr 52.7%

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

   if 6.99999999999999964e-54 < b

   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 86.7%

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

   5. Taylor expanded in b around inf 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-54}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= b -5.4e-24)
   (/ (/ b c) z)
   (if (<= b 2.3e-54) (* -4.0 (* t (/ a 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 (b <= -5.4e-24) {
		tmp = (b / c) / z;
	} else if (b <= 2.3e-54) {
		tmp = -4.0 * (t * (a / 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 (b <= (-5.4d-24)) then
        tmp = (b / c) / z
    else if (b <= 2.3d-54) then
        tmp = (-4.0d0) * (t * (a / 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 (b <= -5.4e-24) {
		tmp = (b / c) / z;
	} else if (b <= 2.3e-54) {
		tmp = -4.0 * (t * (a / 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 b <= -5.4e-24:
		tmp = (b / c) / z
	elif b <= 2.3e-54:
		tmp = -4.0 * (t * (a / 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 (b <= -5.4e-24)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 2.3e-54)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(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 (b <= -5.4e-24)
		tmp = (b / c) / z;
	elseif (b <= 2.3e-54)
		tmp = -4.0 * (t * (a / 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[LessEqual[b, -5.4e-24], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 2.3e-54], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.40000000000000014e-24

   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 83.9%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. associate-*r* 75.3%

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

   7. Applied egg-rr 75.3%

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

   8. Taylor expanded in b around inf 60.7%

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

      1. associate-/r* 62.2%

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

   10. Simplified 62.2%

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

   if -5.40000000000000014e-24 < b < 2.2999999999999999e-54

   1. Initial program 76.5%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 48.3%

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

      1. associate-*l/ 52.7%

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

   7. Applied egg-rr 52.7%

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

   if 2.2999999999999999e-54 < b

   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 86.7%

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

   5. Taylor expanded in b around inf 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

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 (* 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) {
	return b / (c * z);
}

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 / (c * z)
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 / (c * z);
}

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 / (c * z)

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(c * z))
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 / (c * z);
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[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.1%

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

3. Simplified 81.3%

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

5. Taylor expanded in b around inf 45.3%

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

   1. *-commutative 45.3%

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

7. Simplified 45.3%

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

8. Final simplification 45.3%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer Target 1: 80.5% 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 2024135 
(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)))