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

Percentage Accurate: 78.9% → 91.9%

Time: 14.9s

Alternatives: 15

Speedup: 0.7×

• 37.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 78.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+32} \lor \neg \left(z \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, 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 -1.6e+32) (not (<= z 1.95e+18)))
   (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.6e+32) || !(z <= 1.95e+18)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.6d+32)) .or. (.not. (z <= 1.95d+18))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.6e+32) || !(z <= 1.95e+18)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.6e+32) or not (z <= 1.95e+18):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.6e+32) || !(z <= 1.95e+18))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.6e+32) || ~((z <= 1.95e+18)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.6e+32], N[Not[LessEqual[z, 1.95e+18]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5999999999999999e32 or 1.95e18 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. associate-+r- 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-*r* 66.0%

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

      5. *-commutative 66.0%

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

      6. associate-+r- 66.0%

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

      7. +-commutative 66.0%

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

      8. associate-*l* 66.0%

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

      9. associate-*l* 70.4%

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

      10. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in z around inf 70.5%

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

   6. Taylor expanded in z around inf 79.7%

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

      1. +-commutative 79.7%

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

      2. metadata-eval 79.7%

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

      3. cancel-sign-sub-inv 79.7%

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

      4. +-commutative 79.7%

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

      5. *-commutative 79.7%

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

      6. associate-/l* 82.3%

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

      7. *-commutative 82.3%

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

      8. associate--l+ 82.3%

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

      9. *-commutative 82.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in c around 0 87.7%

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

   if -1.5999999999999999e32 < z < 1.95e18

   1. Initial program 97.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+32} \lor \neg \left(z \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-138}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \end{array} \]

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 -2.9e-8)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= y -2.25e-138)
     (/ b (* z c))
     (if (<= y 2.5e-81)
       (* -4.0 (/ (* a t) c))
       (if (<= y 3.4e-27)
         (* b (/ 1.0 (* z c)))
         (if (<= y 6.8e+156)
           (* a (/ (* -4.0 t) c))
           (* 9.0 (/ y (* z (/ c x))))))))))

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 <= -2.9e-8) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (y <= -2.25e-138) {
		tmp = b / (z * c);
	} else if (y <= 2.5e-81) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= 3.4e-27) {
		tmp = b * (1.0 / (z * c));
	} else if (y <= 6.8e+156) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	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 <= (-2.9d-8)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (y <= (-2.25d-138)) then
        tmp = b / (z * c)
    else if (y <= 2.5d-81) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (y <= 3.4d-27) then
        tmp = b * (1.0d0 / (z * c))
    else if (y <= 6.8d+156) then
        tmp = a * (((-4.0d0) * t) / c)
    else
        tmp = 9.0d0 * (y / (z * (c / x)))
    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 <= -2.9e-8) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (y <= -2.25e-138) {
		tmp = b / (z * c);
	} else if (y <= 2.5e-81) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= 3.4e-27) {
		tmp = b * (1.0 / (z * c));
	} else if (y <= 6.8e+156) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	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 <= -2.9e-8:
		tmp = 9.0 * ((y / z) * (x / c))
	elif y <= -2.25e-138:
		tmp = b / (z * c)
	elif y <= 2.5e-81:
		tmp = -4.0 * ((a * t) / c)
	elif y <= 3.4e-27:
		tmp = b * (1.0 / (z * c))
	elif y <= 6.8e+156:
		tmp = a * ((-4.0 * t) / c)
	else:
		tmp = 9.0 * (y / (z * (c / x)))
	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 <= -2.9e-8)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (y <= -2.25e-138)
		tmp = Float64(b / Float64(z * c));
	elseif (y <= 2.5e-81)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (y <= 3.4e-27)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (y <= 6.8e+156)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	else
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	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 <= -2.9e-8)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (y <= -2.25e-138)
		tmp = b / (z * c);
	elseif (y <= 2.5e-81)
		tmp = -4.0 * ((a * t) / c);
	elseif (y <= 3.4e-27)
		tmp = b * (1.0 / (z * c));
	elseif (y <= 6.8e+156)
		tmp = a * ((-4.0 * t) / c);
	else
		tmp = 9.0 * (y / (z * (c / x)));
	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, -2.9e-8], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.25e-138], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-81], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-27], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+156], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.9000000000000002e-8

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-+r- 84.5%

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

      3. *-commutative 84.5%

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

      4. associate-*r* 83.0%

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

      5. *-commutative 83.0%

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

      6. associate-+r- 83.0%

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

      7. +-commutative 83.0%

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

      8. associate-*l* 83.0%

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

      9. associate-*l* 82.9%

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

      10. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in z around inf 80.1%

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

   6. Taylor expanded in x around inf 49.0%

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

      1. times-frac 54.9%

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

      2. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -2.9000000000000002e-8 < y < -2.25000000000000004e-138

   1. Initial program 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in b around inf 39.8%

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

      1. *-commutative 39.8%

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

   7. Simplified 39.8%

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

   if -2.25000000000000004e-138 < y < 2.4999999999999999e-81

   1. Initial program 84.1%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in t around inf 56.2%

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

   if 2.4999999999999999e-81 < y < 3.3999999999999997e-27

   1. Initial program 99.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in b around inf 58.6%

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

      1. *-commutative 58.6%

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

   7. Simplified 58.6%

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

      1. div-inv 58.6%

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

   9. Applied egg-rr 58.6%

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

   if 3.3999999999999997e-27 < y < 6.8000000000000002e156

   1. Initial program 77.8%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in t around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/l* 48.5%

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

      3. associate-*r* 48.5%

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

      4. *-commutative 48.5%

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

      5. *-commutative 48.5%

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

      6. associate-*l/ 48.5%

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

   7. Simplified 48.5%

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

   if 6.8000000000000002e156 < y

   1. Initial program 76.6%

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

      1. +-commutative 76.6%

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

      2. associate-+r- 76.6%

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

      3. *-commutative 76.6%

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

      4. associate-*r* 76.5%

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

      5. *-commutative 76.5%

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

      6. associate-+r- 76.5%

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

      7. +-commutative 76.5%

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

      8. associate-*l* 76.5%

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

      9. associate-*l* 72.7%

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

      10. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in z around inf 68.8%

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

   6. Taylor expanded in x around inf 59.9%

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

      1. times-frac 60.7%

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

      2. *-commutative 60.7%

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

   8. Simplified 60.7%

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

      1. *-commutative 60.7%

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

      2. clear-num 60.6%

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

      3. frac-times 64.7%

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

      4. *-un-lft-identity 64.7%

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

   10. Applied egg-rr 64.7%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-138}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-32} \lor \neg \left(z \leq 5.5 \cdot 10^{-143}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5e-32) (not (<= z 5.5e-143)))
   (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e-32) || !(z <= 5.5e-143)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-5d-32)) .or. (.not. (z <= 5.5d-143))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((a * t) * (z * 4.0d0)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e-32) || !(z <= 5.5e-143)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5e-32) or not (z <= 5.5e-143):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e-32) || !(z <= 5.5e-143))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5e-32) || ~((z <= 5.5e-143)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5e-32], N[Not[LessEqual[z, 5.5e-143]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e-32 or 5.50000000000000041e-143 < z

   1. Initial program 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-+r- 76.3%

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

      3. *-commutative 76.3%

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

      4. associate-*r* 75.5%

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

      5. *-commutative 75.5%

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

      6. associate-+r- 75.5%

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

      7. +-commutative 75.5%

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

      8. associate-*l* 75.5%

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

      9. associate-*l* 77.4%

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

      10. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in z around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. metadata-eval 80.1%

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

      3. cancel-sign-sub-inv 80.1%

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

      4. +-commutative 80.1%

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

      5. *-commutative 80.1%

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

      6. associate-/l* 82.4%

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

      7. *-commutative 82.4%

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

      8. associate--l+ 82.4%

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

      9. *-commutative 82.4%

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

   8. Simplified 86.0%

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

   9. Taylor expanded in c around 0 89.3%

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

   if -5e-32 < z < 5.50000000000000041e-143

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-+r- 98.7%

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

      3. *-commutative 98.7%

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

      4. associate-*r* 98.7%

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

      5. *-commutative 98.7%

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

      6. associate-+r- 98.7%

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

      7. +-commutative 98.7%

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

      8. associate-*l* 98.7%

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

      9. associate-*l* 95.5%

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

      10. *-commutative 95.5%

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

   3. Simplified 95.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-32} \lor \neg \left(z \leq 5.5 \cdot 10^{-143}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-127} \lor \neg \left(z \leq 5.2 \cdot 10^{-154}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5e-127) (not (<= z 5.2e-154)))
   (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e-127) || !(z <= 5.2e-154)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-5d-127)) .or. (.not. (z <= 5.2d-154))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e-127) || !(z <= 5.2e-154)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5e-127) or not (z <= 5.2e-154):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e-127) || !(z <= 5.2e-154))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5e-127) || ~((z <= 5.2e-154)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5e-127], N[Not[LessEqual[z, 5.2e-154]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999997e-127 or 5.2e-154 < z

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-+r- 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r* 77.7%

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

      5. *-commutative 77.7%

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

      6. associate-+r- 77.7%

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

      7. +-commutative 77.7%

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

      8. associate-*l* 77.7%

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

      9. associate-*l* 78.9%

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

      10. *-commutative 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in z around inf 78.4%

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

   6. Taylor expanded in z around inf 79.1%

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

      1. +-commutative 79.1%

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

      2. metadata-eval 79.1%

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

      3. cancel-sign-sub-inv 79.1%

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

      4. +-commutative 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-/l* 81.2%

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

      7. *-commutative 81.2%

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

      8. associate--l+ 81.2%

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

      9. *-commutative 81.2%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in c around 0 89.1%

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

   if -4.9999999999999997e-127 < z < 5.2e-154

   1. Initial program 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. *-commutative 93.3%

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

   7. Simplified 93.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-127} \lor \neg \left(z \leq 5.2 \cdot 10^{-154}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-308}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* -4.0 t) c))))
   (if (<= t -1.1e+135)
     t_1
     (if (<= t -1.6e-308)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= t 2.3e-30) (/ (/ b z) c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -1.1e+135) {
		tmp = t_1;
	} else if (t <= -1.6e-308) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (t <= 2.3e-30) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((-4.0d0) * t) / c)
    if (t <= (-1.1d+135)) then
        tmp = t_1
    else if (t <= (-1.6d-308)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (t <= 2.3d-30) then
        tmp = (b / z) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -1.1e+135) {
		tmp = t_1;
	} else if (t <= -1.6e-308) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (t <= 2.3e-30) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((-4.0 * t) / c)
	tmp = 0
	if t <= -1.1e+135:
		tmp = t_1
	elif t <= -1.6e-308:
		tmp = 9.0 * ((y / z) * (x / c))
	elif t <= 2.3e-30:
		tmp = (b / z) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(-4.0 * t) / c))
	tmp = 0.0
	if (t <= -1.1e+135)
		tmp = t_1;
	elseif (t <= -1.6e-308)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (t <= 2.3e-30)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((-4.0 * t) / c);
	tmp = 0.0;
	if (t <= -1.1e+135)
		tmp = t_1;
	elseif (t <= -1.6e-308)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (t <= 2.3e-30)
		tmp = (b / z) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+135], t$95$1, If[LessEqual[t, -1.6e-308], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-30], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e135 or 2.29999999999999984e-30 < t

   1. Initial program 80.0%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 60.3%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

      6. associate-*l/ 60.3%

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

   7. Simplified 60.3%

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

   if -1.1e135 < t < -1.6000000000000001e-308

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. associate-+r- 85.5%

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

      3. *-commutative 85.5%

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

      4. associate-*r* 83.3%

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

      5. *-commutative 83.3%

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

      6. associate-+r- 83.3%

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

      7. +-commutative 83.3%

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

      8. associate-*l* 83.3%

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

      9. associate-*l* 85.4%

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

      10. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in z around inf 83.3%

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

   6. Taylor expanded in x around inf 37.3%

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

      1. times-frac 41.8%

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

      2. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   if -1.6000000000000001e-308 < t < 2.29999999999999984e-30

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r* 84.7%

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

      5. *-commutative 84.7%

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

      6. associate-+r- 84.7%

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

      7. +-commutative 84.7%

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

      8. associate-*l* 84.7%

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

      9. associate-*l* 89.4%

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

      10. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 88.0%

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

   6. Taylor expanded in z around 0 83.4%

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

      1. associate-*r* 83.4%

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

   8. Simplified 83.4%

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

   9. Taylor expanded in x around 0 47.6%

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

       1. *-commutative 47.6%

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

       2. associate-/r* 49.9%

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

   11. Simplified 49.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-308}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-246}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* -4.0 t) c))))
   (if (<= t -4.5e+134)
     t_1
     (if (<= t -1.6e-246)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (<= t 7.4e-28) (/ (/ b z) c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -4.5e+134) {
		tmp = t_1;
	} else if (t <= -1.6e-246) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (t <= 7.4e-28) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((-4.0d0) * t) / c)
    if (t <= (-4.5d+134)) then
        tmp = t_1
    else if (t <= (-1.6d-246)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (t <= 7.4d-28) then
        tmp = (b / z) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -4.5e+134) {
		tmp = t_1;
	} else if (t <= -1.6e-246) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (t <= 7.4e-28) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((-4.0 * t) / c)
	tmp = 0
	if t <= -4.5e+134:
		tmp = t_1
	elif t <= -1.6e-246:
		tmp = 9.0 * ((y / c) * (x / z))
	elif t <= 7.4e-28:
		tmp = (b / z) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(-4.0 * t) / c))
	tmp = 0.0
	if (t <= -4.5e+134)
		tmp = t_1;
	elseif (t <= -1.6e-246)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (t <= 7.4e-28)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((-4.0 * t) / c);
	tmp = 0.0;
	if (t <= -4.5e+134)
		tmp = t_1;
	elseif (t <= -1.6e-246)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (t <= 7.4e-28)
		tmp = (b / z) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+134], t$95$1, If[LessEqual[t, -1.6e-246], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e-28], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4999999999999997e134 or 7.40000000000000039e-28 < t

   1. Initial program 80.0%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 60.3%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

      6. associate-*l/ 60.3%

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

   7. Simplified 60.3%

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

   if -4.4999999999999997e134 < t < -1.6e-246

   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 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 x around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. *-commutative 40.3%

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

      3. *-commutative 40.3%

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

      4. times-frac 43.9%

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

   7. Simplified 43.9%

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

   if -1.6e-246 < t < 7.40000000000000039e-28

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-+r- 90.7%

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

      3. *-commutative 90.7%

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

      4. associate-*r* 86.6%

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

      5. *-commutative 86.6%

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

      6. associate-+r- 86.6%

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

      7. +-commutative 86.6%

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

      8. associate-*l* 86.7%

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

      9. associate-*l* 89.5%

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

      10. *-commutative 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in z around inf 88.3%

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

   6. Taylor expanded in z around 0 81.8%

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

      1. associate-*r* 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in x around 0 50.8%

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

       1. *-commutative 50.8%

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

       2. associate-/r* 51.5%

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

   11. Simplified 51.5%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+134}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-246}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+57} \lor \neg \left(z \leq 5 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -7.6e+57) (not (<= z 5e-125)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.6e+57) || !(z <= 5e-125)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-7.6d+57)) .or. (.not. (z <= 5d-125))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.6e+57) || !(z <= 5e-125)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7.6e+57) or not (z <= 5e-125):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7.6e+57) || !(z <= 5e-125))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -7.6e+57) || ~((z <= 5e-125)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -7.6e+57], N[Not[LessEqual[z, 5e-125]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999997e57 or 4.99999999999999967e-125 < z

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-+r- 72.6%

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

      3. *-commutative 72.6%

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

      4. associate-*r* 71.8%

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

      5. *-commutative 71.8%

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

      6. associate-+r- 71.8%

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

      7. +-commutative 71.8%

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

      8. associate-*l* 71.7%

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

      9. associate-*l* 74.0%

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

      10. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in z around inf 74.0%

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

   6. Taylor expanded in z around inf 78.6%

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

      1. +-commutative 78.6%

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

      2. metadata-eval 78.6%

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

      3. cancel-sign-sub-inv 78.6%

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

      4. +-commutative 78.6%

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

      5. *-commutative 78.6%

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

      6. associate-/l* 82.0%

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

      7. *-commutative 82.0%

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

      8. associate--l+ 82.0%

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

      9. *-commutative 82.0%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in c around 0 88.0%

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

   10. Taylor expanded in x around 0 71.7%

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

   if -7.5999999999999997e57 < z < 4.99999999999999967e-125

   1. Initial program 98.0%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. *-commutative 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+57} \lor \neg \left(z \leq 5 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+25}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-125}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6e+25)
   (/ (- (* 9.0 (/ (* x y) z)) (* (* a t) 4.0)) c)
   (if (<= z 5e-125)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (/ (+ (* -4.0 (* a t)) (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6e+25) {
		tmp = ((9.0 * ((x * y) / z)) - ((a * t) * 4.0)) / c;
	} else if (z <= 5e-125) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-6d+25)) then
        tmp = ((9.0d0 * ((x * y) / z)) - ((a * t) * 4.0d0)) / c
    else if (z <= 5d-125) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6e+25) {
		tmp = ((9.0 * ((x * y) / z)) - ((a * t) * 4.0)) / c;
	} else if (z <= 5e-125) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -6e+25:
		tmp = ((9.0 * ((x * y) / z)) - ((a * t) * 4.0)) / c
	elif z <= 5e-125:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6e+25)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(Float64(a * t) * 4.0)) / c);
	elseif (z <= 5e-125)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -6e+25)
		tmp = ((9.0 * ((x * y) / z)) - ((a * t) * 4.0)) / c;
	elseif (z <= 5e-125)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6e+25], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 5e-125], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.00000000000000011e25

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-+r- 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*r* 76.7%

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

      5. *-commutative 76.7%

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

      6. associate-+r- 76.7%

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

      7. +-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. associate-*l* 76.9%

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

      10. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around inf 77.0%

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

   6. Taylor expanded in b around 0 75.6%

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

   if -6.00000000000000011e25 < z < 4.99999999999999967e-125

   1. Initial program 98.8%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. *-commutative 86.2%

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

   7. Simplified 86.2%

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

   if 4.99999999999999967e-125 < z

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-+r- 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-*r* 69.8%

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

      5. *-commutative 69.8%

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

      6. associate-+r- 69.8%

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

      7. +-commutative 69.8%

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

      8. associate-*l* 69.8%

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

      9. associate-*l* 73.5%

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

      10. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in z around inf 73.5%

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

   6. Taylor expanded in z around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. metadata-eval 75.4%

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

      3. cancel-sign-sub-inv 75.4%

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

      4. +-commutative 75.4%

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

      5. *-commutative 75.4%

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

      6. associate-/l* 78.8%

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

      7. *-commutative 78.8%

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

      8. associate--l+ 78.8%

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

      9. *-commutative 78.8%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in c around 0 86.8%

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

   10. Taylor expanded in x around 0 71.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+25}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-125}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.35e-5)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= y 7.5e+174)
     (/ (+ (* -4.0 (* a t)) (/ b z)) c)
     (* 9.0 (/ y (* z (/ c x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.35e-5) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (y <= 7.5e+174) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-1.35d-5)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (y <= 7.5d+174) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = 9.0d0 * (y / (z * (c / x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.35e-5) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (y <= 7.5e+174) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.35e-5:
		tmp = 9.0 * ((y / z) * (x / c))
	elif y <= 7.5e+174:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = 9.0 * (y / (z * (c / x)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.35e-5)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (y <= 7.5e+174)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -1.35e-5)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (y <= 7.5e+174)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = 9.0 * (y / (z * (c / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.35e-5], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+174], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e-5

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-+r- 84.5%

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

      3. *-commutative 84.5%

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

      4. associate-*r* 83.0%

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

      5. *-commutative 83.0%

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

      6. associate-+r- 83.0%

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

      7. +-commutative 83.0%

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

      8. associate-*l* 83.0%

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

      9. associate-*l* 82.9%

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

      10. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in z around inf 80.1%

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

   6. Taylor expanded in x around inf 49.0%

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

      1. times-frac 54.9%

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

      2. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -1.3499999999999999e-5 < y < 7.5000000000000004e174

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. associate-+r- 85.5%

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

      3. *-commutative 85.5%

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

      4. associate-*r* 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-+r- 85.4%

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

      7. +-commutative 85.4%

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

      8. associate-*l* 85.4%

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

      9. associate-*l* 86.0%

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

      10. *-commutative 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in z around inf 84.3%

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

   6. Taylor expanded in z around inf 83.4%

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

      1. +-commutative 83.4%

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

      2. metadata-eval 83.4%

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

      3. cancel-sign-sub-inv 83.4%

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

      4. +-commutative 83.4%

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

      5. *-commutative 83.4%

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

      6. associate-/l* 84.0%

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

      7. *-commutative 84.0%

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

      8. associate--l+ 84.0%

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

      9. *-commutative 84.0%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in c around 0 89.7%

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

   10. Taylor expanded in x around 0 74.5%

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

   if 7.5000000000000004e174 < y

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-+r- 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-*r* 74.5%

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

      5. *-commutative 74.5%

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

      6. associate-+r- 74.5%

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

      7. +-commutative 74.5%

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

      8. associate-*l* 74.4%

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

      9. associate-*l* 70.3%

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

      10. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 66.0%

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

   6. Taylor expanded in x around inf 56.4%

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

      1. times-frac 61.3%

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

      2. *-commutative 61.3%

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

   8. Simplified 61.3%

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

      1. *-commutative 61.3%

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

      2. clear-num 61.1%

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

      3. frac-times 61.7%

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

      4. *-un-lft-identity 61.7%

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

   10. Applied egg-rr 61.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+25} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -7e+25) (not (<= z 2.15e-152)))
   (* a (/ (* -4.0 t) c))
   (* b (/ 1.0 (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7e+25) || !(z <= 2.15e-152)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-7d+25)) .or. (.not. (z <= 2.15d-152))) then
        tmp = a * (((-4.0d0) * t) / c)
    else
        tmp = b * (1.0d0 / (z * c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7e+25) || !(z <= 2.15e-152)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7e+25) or not (z <= 2.15e-152):
		tmp = a * ((-4.0 * t) / c)
	else:
		tmp = b * (1.0 / (z * c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7e+25) || !(z <= 2.15e-152))
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	else
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -7e+25) || ~((z <= 2.15e-152)))
		tmp = a * ((-4.0 * t) / c);
	else
		tmp = b * (1.0 / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -7e+25], N[Not[LessEqual[z, 2.15e-152]], $MachinePrecision]], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999999e25 or 2.1499999999999999e-152 < z

   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 74.5%

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

   5. Taylor expanded in t around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 55.8%

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

      3. associate-*r* 55.8%

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

      4. *-commutative 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-*l/ 55.8%

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

   7. Simplified 55.8%

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

   if -6.99999999999999999e25 < z < 2.1499999999999999e-152

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

      1. div-inv 53.6%

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

   9. Applied egg-rr 53.6%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+25} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+23} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.25e+23) (not (<= z 2.15e-152)))
   (* a (/ (* -4.0 t) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.25e+23) || !(z <= 2.15e-152)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.25d+23)) .or. (.not. (z <= 2.15d-152))) then
        tmp = a * (((-4.0d0) * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.25e+23) || !(z <= 2.15e-152)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.25e+23) or not (z <= 2.15e-152):
		tmp = a * ((-4.0 * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.25e+23) || !(z <= 2.15e-152))
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.25e+23) || ~((z <= 2.15e-152)))
		tmp = a * ((-4.0 * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.25e+23], N[Not[LessEqual[z, 2.15e-152]], $MachinePrecision]], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e23 or 2.1499999999999999e-152 < z

   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 74.5%

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

   5. Taylor expanded in t around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 55.8%

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

      3. associate-*r* 55.8%

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

      4. *-commutative 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-*l/ 55.8%

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

   7. Simplified 55.8%

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

   if -1.25e23 < z < 2.1499999999999999e-152

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+23} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+21} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5.4e+21) (not (<= z 2.15e-152)))
   (* a (* t (/ -4.0 c)))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.4e+21) || !(z <= 2.15e-152)) {
		tmp = a * (t * (-4.0 / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-5.4d+21)) .or. (.not. (z <= 2.15d-152))) then
        tmp = a * (t * ((-4.0d0) / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.4e+21) || !(z <= 2.15e-152)) {
		tmp = a * (t * (-4.0 / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5.4e+21) or not (z <= 2.15e-152):
		tmp = a * (t * (-4.0 / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5.4e+21) || !(z <= 2.15e-152))
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5.4e+21) || ~((z <= 2.15e-152)))
		tmp = a * (t * (-4.0 / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5.4e+21], N[Not[LessEqual[z, 2.15e-152]], $MachinePrecision]], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e21 or 2.1499999999999999e-152 < z

   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 74.5%

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

   5. Taylor expanded in t around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 55.8%

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

      3. associate-*r* 55.8%

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

      4. *-commutative 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-*l/ 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in a around 0 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*l/ 51.5%

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

      3. associate-*r/ 51.4%

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

      4. associate-*r* 55.7%

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

   10. Simplified 55.7%

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

   if -5.4e21 < z < 2.1499999999999999e-152

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+21} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+22} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.5e+22) (not (<= z 2.15e-152)))
   (* -4.0 (/ (* a t) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.5e+22) || !(z <= 2.15e-152)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.5d+22)) .or. (.not. (z <= 2.15d-152))) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.5e+22) || !(z <= 2.15e-152)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.5e+22) or not (z <= 2.15e-152):
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.5e+22) || !(z <= 2.15e-152))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.5e+22) || ~((z <= 2.15e-152)))
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.5e+22], N[Not[LessEqual[z, 2.15e-152]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e22 or 2.1499999999999999e-152 < z

   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 74.5%

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

   5. Taylor expanded in t around inf 51.5%

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

   if -3.5e22 < z < 2.1499999999999999e-152

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+22} \lor \neg \left(z \leq 2.15 \cdot 10^{-152}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.6e+20)
   (* a (/ (* -4.0 t) c))
   (if (<= z 1.52e-152) (* b (/ 1.0 (* z c))) (* t (* -4.0 (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.6e+20) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 1.52e-152) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-7.6d+20)) then
        tmp = a * (((-4.0d0) * t) / c)
    else if (z <= 1.52d-152) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t * ((-4.0d0) * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.6e+20) {
		tmp = a * ((-4.0 * t) / c);
	} else if (z <= 1.52e-152) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t * (-4.0 * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7.6e+20:
		tmp = a * ((-4.0 * t) / c)
	elif z <= 1.52e-152:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t * (-4.0 * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.6e+20)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	elseif (z <= 1.52e-152)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7.6e+20)
		tmp = a * ((-4.0 * t) / c);
	elseif (z <= 1.52e-152)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t * (-4.0 * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.6e+20], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e-152], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6e20

   1. Initial program 74.1%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in t around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-/l* 59.8%

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

      3. associate-*r* 59.8%

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

      4. *-commutative 59.8%

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

      5. *-commutative 59.8%

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

      6. associate-*l/ 59.8%

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

   7. Simplified 59.8%

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

   if -7.6e20 < z < 1.52000000000000009e-152

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

      1. div-inv 53.6%

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

   9. Applied egg-rr 53.6%

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

   if 1.52000000000000009e-152 < z

   1. Initial program 75.0%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in t around inf 72.6%

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

   6. Taylor expanded in x around 0 64.9%

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

   7. Taylor expanded in a around inf 50.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.8% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

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

Derivation

1. Initial program 84.2%

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

3. Simplified 84.2%

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

5. Taylor expanded in b around inf 34.6%

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

   1. *-commutative 34.6%

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

7. Simplified 34.6%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer Target 1: 80.1% 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 2024133 
(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)))