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

Percentage Accurate: 80.0% → 91.1%

Time: 16.5s

Alternatives: 19

Speedup: 1.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{y} - \frac{x \cdot -9}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.25e-82)
   (/ (+ (/ (+ b (* x (* 9.0 y))) z) (* t (* a -4.0))) c)
   (if (<= z 4.4e+24)
     (/ (+ b (- (* y (* x 9.0)) (* t (* a (* z 4.0))))) (* z c))
     (/ (* y (- (/ (- (/ b z) (* 4.0 (* t a))) y) (/ (* x -9.0) z))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.25e-82) {
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c;
	} else if (z <= 4.4e+24) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = (y * ((((b / z) - (4.0 * (t * a))) / y) - ((x * -9.0) / z))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.25d-82)) then
        tmp = (((b + (x * (9.0d0 * y))) / z) + (t * (a * (-4.0d0)))) / c
    else if (z <= 4.4d+24) then
        tmp = (b + ((y * (x * 9.0d0)) - (t * (a * (z * 4.0d0))))) / (z * c)
    else
        tmp = (y * ((((b / z) - (4.0d0 * (t * a))) / y) - ((x * (-9.0d0)) / z))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.25e-82) {
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c;
	} else if (z <= 4.4e+24) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = (y * ((((b / z) - (4.0 * (t * a))) / y) - ((x * -9.0) / z))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.25e-82:
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c
	elif z <= 4.4e+24:
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c)
	else:
		tmp = (y * ((((b / z) - (4.0 * (t * a))) / y) - ((x * -9.0) / z))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.25e-82)
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z) + Float64(t * Float64(a * -4.0))) / c);
	elseif (z <= 4.4e+24)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(y * Float64(Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(t * a))) / y) - Float64(Float64(x * -9.0) / 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-82)
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c;
	elseif (z <= 4.4e+24)
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	else
		tmp = (y * ((((b / z) - (4.0 * (t * a))) / y) - ((x * -9.0) / z))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.25e-82], N[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 4.4e+24], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x * -9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e-82

   1. Initial program 73.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.3%

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

   if -1.25e-82 < z < 4.40000000000000003e24

   1. Initial program 94.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(\left(a \cdot \left(z \cdot 4\right)\right) \cdot t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\left(a \cdot \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 94.9%

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

   if 4.40000000000000003e24 < z

   1. Initial program 68.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.5%

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

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)}, c\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right), c\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(0 - \left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right), c\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \left(-9 \cdot \frac{x}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\left(-9 \cdot \frac{x}{z}\right), \left(-1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\left(\frac{-9 \cdot x}{z}\right), \left(-1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-9 \cdot x\right), z\right), \left(-1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot -9\right), z\right), \left(-1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(-1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(\frac{-1 \cdot \left(-4 \cdot \left(a \cdot t\right) + \frac{b}{z}\right)}{y}\right)\right)\right)\right), c\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(\frac{\mathsf{neg}\left(\left(-4 \cdot \left(a \cdot t\right) + \frac{b}{z}\right)\right)}{y}\right)\right)\right)\right), c\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(\frac{\left(\mathsf{neg}\left(-4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(\frac{b}{z}\right)\right)}{y}\right)\right)\right)\right), c\right) \]

      14. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(\frac{\left(\mathsf{neg}\left(-4\right)\right) \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(\frac{b}{z}\right)\right)}{y}\right)\right)\right)\right), c\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(\frac{4 \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(\frac{b}{z}\right)\right)}{y}\right)\right)\right)\right), c\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \left(\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{y}\right)\right)\right)\right), c\right) \]

      17. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -9\right), z\right), \mathsf{/.f64}\left(\left(4 \cdot \left(a \cdot t\right) - \frac{b}{z}\right), y\right)\right)\right)\right), c\right) \]

   7. Simplified 94.1%

      \[\leadsto \frac{\color{blue}{y \cdot \left(0 - \left(\frac{x \cdot -9}{z} + \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{y}\right)\right)}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(\frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{y} - \frac{x \cdot -9}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t\_1}{c}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + y \cdot \left(\frac{x \cdot 9}{z} + \frac{b}{z \cdot y}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -9e-83)
     (/ (+ (/ (+ b (* x (* 9.0 y))) z) t_1) c)
     (if (<= z 1.9e+20)
       (/ (+ b (- (* y (* x 9.0)) (* t (* a (* z 4.0))))) (* z c))
       (/ (+ t_1 (* y (+ (/ (* x 9.0) z) (/ b (* z y))))) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -9e-83) {
		tmp = (((b + (x * (9.0 * y))) / z) + t_1) / c;
	} else if (z <= 1.9e+20) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (y * (((x * 9.0) / z) + (b / (z * y))))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-9d-83)) then
        tmp = (((b + (x * (9.0d0 * y))) / z) + t_1) / c
    else if (z <= 1.9d+20) then
        tmp = (b + ((y * (x * 9.0d0)) - (t * (a * (z * 4.0d0))))) / (z * c)
    else
        tmp = (t_1 + (y * (((x * 9.0d0) / z) + (b / (z * y))))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -9e-83) {
		tmp = (((b + (x * (9.0 * y))) / z) + t_1) / c;
	} else if (z <= 1.9e+20) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (y * (((x * 9.0) / z) + (b / (z * y))))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -9e-83:
		tmp = (((b + (x * (9.0 * y))) / z) + t_1) / c
	elif z <= 1.9e+20:
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c)
	else:
		tmp = (t_1 + (y * (((x * 9.0) / z) + (b / (z * y))))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -9e-83)
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z) + t_1) / c);
	elseif (z <= 1.9e+20)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(y * Float64(Float64(Float64(x * 9.0) / z) + Float64(b / Float64(z * y))))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -9e-83)
		tmp = (((b + (x * (9.0 * y))) / z) + t_1) / c;
	elseif (z <= 1.9e+20)
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	else
		tmp = (t_1 + (y * (((x * 9.0) / z) + (b / (z * y))))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-83], N[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.9e+20], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(y * N[(N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999995e-83

   1. Initial program 73.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.3%

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

   if -8.99999999999999995e-83 < z < 1.9e20

   1. Initial program 94.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(\left(a \cdot \left(z \cdot 4\right)\right) \cdot t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\left(a \cdot \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 94.9%

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

   if 1.9e20 < z

   1. Initial program 68.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(9 \cdot \frac{x}{z}\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{9 \cdot x}{z}\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot x\right), z\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \mathsf{/.f64}\left(b, \left(y \cdot z\right)\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \mathsf{/.f64}\left(b, \left(z \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. *-lowering-*.f64 95.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, y\right)\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 95.7%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \left(\frac{x \cdot 9}{z} + \frac{b}{z \cdot y}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + a \cdot \left(-4 \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;\frac{t\_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= b -1.65e+41)
     (/ (+ t_1 (/ b z)) c)
     (if (<= b -8.2e-77)
       (/ (+ (* x (* 9.0 y)) (* a (* -4.0 (* z t)))) (* z c))
       (if (<= b 1e-76)
         (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
         (/ (/ (+ b (* y (* x 9.0))) z) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -1.65e+41) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= -8.2e-77) {
		tmp = ((x * (9.0 * y)) + (a * (-4.0 * (z * t)))) / (z * c);
	} else if (b <= 1e-76) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-1.65d+41)) then
        tmp = (t_1 + (b / z)) / c
    else if (b <= (-8.2d-77)) then
        tmp = ((x * (9.0d0 * y)) + (a * ((-4.0d0) * (z * t)))) / (z * c)
    else if (b <= 1d-76) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = ((b + (y * (x * 9.0d0))) / z) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -1.65e+41) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= -8.2e-77) {
		tmp = ((x * (9.0 * y)) + (a * (-4.0 * (z * t)))) / (z * c);
	} else if (b <= 1e-76) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if b <= -1.65e+41:
		tmp = (t_1 + (b / z)) / c
	elif b <= -8.2e-77:
		tmp = ((x * (9.0 * y)) + (a * (-4.0 * (z * t)))) / (z * c)
	elif b <= 1e-76:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = ((b + (y * (x * 9.0))) / z) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (b <= -1.65e+41)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (b <= -8.2e-77)
		tmp = Float64(Float64(Float64(x * Float64(9.0 * y)) + Float64(a * Float64(-4.0 * Float64(z * t)))) / Float64(z * c));
	elseif (b <= 1e-76)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / 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)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -1.65e+41)
		tmp = (t_1 + (b / z)) / c;
	elseif (b <= -8.2e-77)
		tmp = ((x * (9.0 * y)) + (a * (-4.0 * (z * t)))) / (z * c);
	elseif (b <= 1e-76)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+41], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, -8.2e-77], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-76], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.65e41

   1. Initial program 85.7%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 81.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 73.9%

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

   if -1.65e41 < b < -8.19999999999999925e-77

   1. Initial program 87.9%

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

   3. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \color{blue}{\left(c \cdot z\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(c \cdot z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right)\right), \left(c \cdot z\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(z \cdot \color{blue}{c}\right)\right) \]

      15. *-lowering-*.f64 71.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 71.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(y \cdot x\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot y\right) \cdot x\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(9 \cdot y\right), x\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(9, y\right), x\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   7. Applied egg-rr 71.4%

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

   if -8.19999999999999925e-77 < b < 9.99999999999999927e-77

   1. Initial program 82.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \frac{x \cdot y}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(x \cdot y\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 87.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 87.7%

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

   if 9.99999999999999927e-77 < b

   1. Initial program 77.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 86.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 86.7%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \color{blue}{z}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right)\right) \]

      4. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right)\right) \]

   9. Simplified 73.6%

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

       1. *-commutative N/A

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

       2. div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right), \color{blue}{c}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\left(9 \cdot x\right) \cdot y\right)\right), z\right), c\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(y \cdot \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       9. *-lowering-*.f64 73.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right)\right), z\right), c\right) \]

   11. Applied egg-rr 73.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + a \cdot \left(-4 \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot \left(z \cdot t\right)\right) + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;\frac{t\_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= b -1.55e+41)
     (/ (+ t_1 (/ b z)) c)
     (if (<= b -8.2e-76)
       (/ (+ (* a (* -4.0 (* z t))) (* 9.0 (* x y))) (* z c))
       (if (<= b 1e-76)
         (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
         (/ (/ (+ b (* y (* x 9.0))) z) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -1.55e+41) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= -8.2e-76) {
		tmp = ((a * (-4.0 * (z * t))) + (9.0 * (x * y))) / (z * c);
	} else if (b <= 1e-76) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-1.55d+41)) then
        tmp = (t_1 + (b / z)) / c
    else if (b <= (-8.2d-76)) then
        tmp = ((a * ((-4.0d0) * (z * t))) + (9.0d0 * (x * y))) / (z * c)
    else if (b <= 1d-76) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = ((b + (y * (x * 9.0d0))) / z) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -1.55e+41) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= -8.2e-76) {
		tmp = ((a * (-4.0 * (z * t))) + (9.0 * (x * y))) / (z * c);
	} else if (b <= 1e-76) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if b <= -1.55e+41:
		tmp = (t_1 + (b / z)) / c
	elif b <= -8.2e-76:
		tmp = ((a * (-4.0 * (z * t))) + (9.0 * (x * y))) / (z * c)
	elif b <= 1e-76:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = ((b + (y * (x * 9.0))) / z) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (b <= -1.55e+41)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (b <= -8.2e-76)
		tmp = Float64(Float64(Float64(a * Float64(-4.0 * Float64(z * t))) + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (b <= 1e-76)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / 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)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -1.55e+41)
		tmp = (t_1 + (b / z)) / c;
	elseif (b <= -8.2e-76)
		tmp = ((a * (-4.0 * (z * t))) + (9.0 * (x * y))) / (z * c);
	elseif (b <= 1e-76)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+41], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, -8.2e-76], N[(N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-76], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55e41

   1. Initial program 85.7%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 81.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 73.9%

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

   if -1.55e41 < b < -8.1999999999999996e-76

   1. Initial program 87.9%

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

   3. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \color{blue}{\left(c \cdot z\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(c \cdot z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right)\right), \left(c \cdot z\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(z \cdot \color{blue}{c}\right)\right) \]

      15. *-lowering-*.f64 71.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 71.3%

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

   if -8.1999999999999996e-76 < b < 9.99999999999999927e-77

   1. Initial program 82.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \frac{x \cdot y}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(x \cdot y\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 87.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 87.7%

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

   if 9.99999999999999927e-77 < b

   1. Initial program 77.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 86.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 86.7%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \color{blue}{z}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right)\right) \]

      4. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right)\right) \]

   9. Simplified 73.6%

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

       1. *-commutative N/A

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

       2. div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right), \color{blue}{c}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\left(9 \cdot x\right) \cdot y\right)\right), z\right), c\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(y \cdot \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       9. *-lowering-*.f64 73.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right)\right), z\right), c\right) \]

   11. Applied egg-rr 73.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot \left(z \cdot t\right)\right) + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-8}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (+ (/ (+ b (* x (* 9.0 y))) z) (* t (* a -4.0))) c)))
   (if (<= z -1.25e-82)
     t_1
     (if (<= z 1e-8)
       (/ (+ b (- (* y (* x 9.0)) (* t (* a (* z 4.0))))) (* 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 = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1.25e-82) {
		tmp = t_1;
	} else if (z <= 1e-8) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (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 = (((b + (x * (9.0d0 * y))) / z) + (t * (a * (-4.0d0)))) / c
    if (z <= (-1.25d-82)) then
        tmp = t_1
    else if (z <= 1d-8) then
        tmp = (b + ((y * (x * 9.0d0)) - (t * (a * (z * 4.0d0))))) / (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 = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1.25e-82) {
		tmp = t_1;
	} else if (z <= 1e-8) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (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 = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c
	tmp = 0
	if z <= -1.25e-82:
		tmp = t_1
	elif z <= 1e-8:
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (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(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (z <= -1.25e-82)
		tmp = t_1;
	elseif (z <= 1e-8)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(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 = (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / c;
	tmp = 0.0;
	if (z <= -1.25e-82)
		tmp = t_1;
	elseif (z <= 1e-8)
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (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[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.25e-82], t$95$1, If[LessEqual[z, 1e-8], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e-82 or 1e-8 < z

   1. Initial program 71.9%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.6%

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

   if -1.25e-82 < z < 1e-8

   1. Initial program 95.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(\left(a \cdot \left(z \cdot 4\right)\right) \cdot t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\left(a \cdot \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. *-lowering-*.f64 95.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 95.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-8}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := \frac{\frac{b + t\_1}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{b + \left(t\_1 - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* x (* 9.0 y))) (t_2 (/ (+ (/ (+ b t_1) z) (* t (* a -4.0))) c)))
   (if (<= z -1.25e-82)
     t_2
     (if (<= z 6.8e-93) (/ (+ b (- t_1 (* a (* t (* z 4.0))))) (* z c)) t_2))))

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 = x * (9.0 * y);
	double t_2 = (((b + t_1) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1.25e-82) {
		tmp = t_2;
	} else if (z <= 6.8e-93) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * (9.0d0 * y)
    t_2 = (((b + t_1) / z) + (t * (a * (-4.0d0)))) / c
    if (z <= (-1.25d-82)) then
        tmp = t_2
    else if (z <= 6.8d-93) then
        tmp = (b + (t_1 - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = t_2
    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 = x * (9.0 * y);
	double t_2 = (((b + t_1) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1.25e-82) {
		tmp = t_2;
	} else if (z <= 6.8e-93) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_2;
	}
	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 = x * (9.0 * y)
	t_2 = (((b + t_1) / z) + (t * (a * -4.0))) / c
	tmp = 0
	if z <= -1.25e-82:
		tmp = t_2
	elif z <= 6.8e-93:
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = t_2
	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(x * Float64(9.0 * y))
	t_2 = Float64(Float64(Float64(Float64(b + t_1) / z) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (z <= -1.25e-82)
		tmp = t_2;
	elseif (z <= 6.8e-93)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = t_2;
	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 = x * (9.0 * y);
	t_2 = (((b + t_1) / z) + (t * (a * -4.0))) / c;
	tmp = 0.0;
	if (z <= -1.25e-82)
		tmp = t_2;
	elseif (z <= 6.8e-93)
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = t_2;
	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[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(b + t$95$1), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.25e-82], t$95$2, If[LessEqual[z, 6.8e-93], N[(N[(b + N[(t$95$1 - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e-82 or 6.80000000000000002e-93 < z

   1. Initial program 74.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.0%

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

   if -1.25e-82 < z < 6.80000000000000002e-93

   1. Initial program 95.7%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \left(9 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(\left(9 \cdot y\right) \cdot x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(9 \cdot y\right), x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(9, y\right), x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 95.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{-53}:\\ \;\;\;\;\frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{t\_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= b -2e-53)
     (/ (+ t_1 (/ b z)) c)
     (if (<= b 8.2e-77)
       (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
       (/ (/ (+ b (* y (* x 9.0))) z) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -2e-53) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= 8.2e-77) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-2d-53)) then
        tmp = (t_1 + (b / z)) / c
    else if (b <= 8.2d-77) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = ((b + (y * (x * 9.0d0))) / z) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -2e-53) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= 8.2e-77) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if b <= -2e-53:
		tmp = (t_1 + (b / z)) / c
	elif b <= 8.2e-77:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = ((b + (y * (x * 9.0))) / z) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (b <= -2e-53)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (b <= 8.2e-77)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / 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)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -2e-53)
		tmp = (t_1 + (b / z)) / c;
	elseif (b <= 8.2e-77)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = ((b + (y * (x * 9.0))) / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e-53], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 8.2e-77], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.00000000000000006e-53

   1. Initial program 85.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 81.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 71.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 71.3%

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

   if -2.00000000000000006e-53 < b < 8.19999999999999925e-77

   1. Initial program 83.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \frac{x \cdot y}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(x \cdot y\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 85.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 85.2%

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

   if 8.19999999999999925e-77 < b

   1. Initial program 77.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 86.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 86.7%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \color{blue}{z}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right)\right) \]

      4. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right)\right) \]

   9. Simplified 73.6%

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

       1. *-commutative N/A

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

       2. div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right), \color{blue}{c}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\left(9 \cdot x\right) \cdot y\right)\right), z\right), c\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(y \cdot \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       9. *-lowering-*.f64 73.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right)\right), z\right), c\right) \]

   11. Applied egg-rr 73.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0105:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-133}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -0.0105)
   (/ b (* z c))
   (if (<= b -2e-133)
     (/ (* y (* x 9.0)) (* z c))
     (if (<= b 1e-76) (/ (* a (* t -4.0)) c) (/ (/ b c) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -0.0105) {
		tmp = b / (z * c);
	} else if (b <= -2e-133) {
		tmp = (y * (x * 9.0)) / (z * c);
	} else if (b <= 1e-76) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-0.0105d0)) then
        tmp = b / (z * c)
    else if (b <= (-2d-133)) then
        tmp = (y * (x * 9.0d0)) / (z * c)
    else if (b <= 1d-76) then
        tmp = (a * (t * (-4.0d0))) / c
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -0.0105) {
		tmp = b / (z * c);
	} else if (b <= -2e-133) {
		tmp = (y * (x * 9.0)) / (z * c);
	} else if (b <= 1e-76) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -0.0105:
		tmp = b / (z * c)
	elif b <= -2e-133:
		tmp = (y * (x * 9.0)) / (z * c)
	elif b <= 1e-76:
		tmp = (a * (t * -4.0)) / c
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -0.0105)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -2e-133)
		tmp = Float64(Float64(y * Float64(x * 9.0)) / Float64(z * c));
	elseif (b <= 1e-76)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -0.0105)
		tmp = b / (z * c);
	elseif (b <= -2e-133)
		tmp = (y * (x * 9.0)) / (z * c);
	elseif (b <= 1e-76)
		tmp = (a * (t * -4.0)) / c;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -0.0105], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-133], N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-76], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.0105000000000000007

   1. Initial program 86.0%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 61.0%

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

   if -0.0105000000000000007 < b < -2.0000000000000001e-133

   1. Initial program 90.4%

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

      1. div-inv N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, c\right), \mathsf{/.f64}\left(1, z\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), c\right), \mathsf{/.f64}\left(1, z\right)\right) \]

      2. *-lowering-*.f64 52.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), c\right), \mathsf{/.f64}\left(1, z\right)\right) \]

   7. Simplified 52.2%

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

      1. un-div-inv N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), \color{blue}{\left(c \cdot z\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(9 \cdot x\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(9 \cdot x\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right), \left(c \cdot z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right), \left(z \cdot \color{blue}{c}\right)\right) \]

      9. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   9. Applied egg-rr 58.3%

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

   if -2.0000000000000001e-133 < b < 9.99999999999999927e-77

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 55.9%

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

   if 9.99999999999999927e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0105:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-133}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0077:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-133}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -0.0077)
   (/ b (* z c))
   (if (<= b -1.05e-133)
     (/ (* 9.0 (* x y)) (* z c))
     (if (<= b 8.2e-77) (/ (* a (* t -4.0)) c) (/ (/ b c) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -0.0077) {
		tmp = b / (z * c);
	} else if (b <= -1.05e-133) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (b <= 8.2e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-0.0077d0)) then
        tmp = b / (z * c)
    else if (b <= (-1.05d-133)) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else if (b <= 8.2d-77) then
        tmp = (a * (t * (-4.0d0))) / c
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -0.0077) {
		tmp = b / (z * c);
	} else if (b <= -1.05e-133) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (b <= 8.2e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -0.0077:
		tmp = b / (z * c)
	elif b <= -1.05e-133:
		tmp = (9.0 * (x * y)) / (z * c)
	elif b <= 8.2e-77:
		tmp = (a * (t * -4.0)) / c
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -0.0077)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -1.05e-133)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	elseif (b <= 8.2e-77)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -0.0077)
		tmp = b / (z * c);
	elseif (b <= -1.05e-133)
		tmp = (9.0 * (x * y)) / (z * c);
	elseif (b <= 8.2e-77)
		tmp = (a * (t * -4.0)) / c;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -0.0077], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-133], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-77], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.0077000000000000002

   1. Initial program 86.0%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 61.0%

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

   if -0.0077000000000000002 < b < -1.05e-133

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 58.2%

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

   if -1.05e-133 < b < 8.19999999999999925e-77

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 55.9%

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

   if 8.19999999999999925e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

Alternative 10: 47.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-137}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -7.2e-53)
   (/ b (* z c))
   (if (<= b -4.8e-137)
     (* (/ (* 9.0 y) z) (/ x c))
     (if (<= b 9.8e-77) (/ (* a (* t -4.0)) c) (/ (/ b c) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -7.2e-53) {
		tmp = b / (z * c);
	} else if (b <= -4.8e-137) {
		tmp = ((9.0 * y) / z) * (x / c);
	} else if (b <= 9.8e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-7.2d-53)) then
        tmp = b / (z * c)
    else if (b <= (-4.8d-137)) then
        tmp = ((9.0d0 * y) / z) * (x / c)
    else if (b <= 9.8d-77) then
        tmp = (a * (t * (-4.0d0))) / c
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -7.2e-53) {
		tmp = b / (z * c);
	} else if (b <= -4.8e-137) {
		tmp = ((9.0 * y) / z) * (x / c);
	} else if (b <= 9.8e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -7.2e-53:
		tmp = b / (z * c)
	elif b <= -4.8e-137:
		tmp = ((9.0 * y) / z) * (x / c)
	elif b <= 9.8e-77:
		tmp = (a * (t * -4.0)) / c
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -7.2e-53)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -4.8e-137)
		tmp = Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c));
	elseif (b <= 9.8e-77)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -7.2e-53)
		tmp = b / (z * c);
	elseif (b <= -4.8e-137)
		tmp = ((9.0 * y) / z) * (x / c);
	elseif (b <= 9.8e-77)
		tmp = (a * (t * -4.0)) / c;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -7.2e-53], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-137], N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-77], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.1999999999999998e-53

   1. Initial program 85.1%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 56.5%

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

   if -7.1999999999999998e-53 < b < -4.8000000000000001e-137

   1. Initial program 91.3%

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

      1. div-inv N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

   4. Applied egg-rr 75.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, c\right), \mathsf{/.f64}\left(1, z\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), c\right), \mathsf{/.f64}\left(1, z\right)\right) \]

      2. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), c\right), \mathsf{/.f64}\left(1, z\right)\right) \]

   7. Simplified 56.9%

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

      1. un-div-inv N/A

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

      2. associate-/l/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{9 \cdot y}{z}\right), \color{blue}{\left(\frac{x}{c}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot y\right), z\right), \left(\frac{\color{blue}{x}}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{x}{c}\right)\right) \]

      9. /-lowering-/.f64 52.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(x, \color{blue}{c}\right)\right) \]

   9. Applied egg-rr 52.7%

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

   if -4.8000000000000001e-137 < b < 9.7999999999999994e-77

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 56.5%

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

   if 9.7999999999999994e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

Alternative 11: 47.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-134}:\\ \;\;\;\;9 \cdot \frac{\frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -7.5e-53)
   (/ b (* z c))
   (if (<= b -7.8e-134)
     (* 9.0 (/ (/ (* x y) z) c))
     (if (<= b 4.8e-77) (/ (* a (* t -4.0)) c) (/ (/ b c) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-53) {
		tmp = b / (z * c);
	} else if (b <= -7.8e-134) {
		tmp = 9.0 * (((x * y) / z) / c);
	} else if (b <= 4.8e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-7.5d-53)) then
        tmp = b / (z * c)
    else if (b <= (-7.8d-134)) then
        tmp = 9.0d0 * (((x * y) / z) / c)
    else if (b <= 4.8d-77) then
        tmp = (a * (t * (-4.0d0))) / c
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -7.5e-53) {
		tmp = b / (z * c);
	} else if (b <= -7.8e-134) {
		tmp = 9.0 * (((x * y) / z) / c);
	} else if (b <= 4.8e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -7.5e-53:
		tmp = b / (z * c)
	elif b <= -7.8e-134:
		tmp = 9.0 * (((x * y) / z) / c)
	elif b <= 4.8e-77:
		tmp = (a * (t * -4.0)) / c
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -7.5e-53)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -7.8e-134)
		tmp = Float64(9.0 * Float64(Float64(Float64(x * y) / z) / c));
	elseif (b <= 4.8e-77)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -7.5e-53)
		tmp = b / (z * c);
	elseif (b <= -7.8e-134)
		tmp = 9.0 * (((x * y) / z) / c);
	elseif (b <= 4.8e-77)
		tmp = (a * (t * -4.0)) / c;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -7.5e-53], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.8e-134], N[(9.0 * N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e-77], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.5000000000000001e-53

   1. Initial program 85.1%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 56.5%

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

   if -7.5000000000000001e-53 < b < -7.8000000000000002e-134

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z \cdot \color{blue}{c}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{\frac{x \cdot y}{z}}{\color{blue}{c}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{c}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), c\right)\right) \]

      6. *-lowering-*.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), c\right)\right) \]

   5. Simplified 60.5%

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

   if -7.8000000000000002e-134 < b < 4.7999999999999998e-77

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 55.9%

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

   if 4.7999999999999998e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

Alternative 12: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= a -1.3e-192)
     t_1
     (if (<= a 1.26e+94) (/ (/ (+ b (* y (* x 9.0))) 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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (a <= -1.3e-192) {
		tmp = t_1;
	} else if (a <= 1.26e+94) {
		tmp = ((b + (y * (x * 9.0))) / 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 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (a <= (-1.3d-192)) then
        tmp = t_1
    else if (a <= 1.26d+94) then
        tmp = ((b + (y * (x * 9.0d0))) / 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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (a <= -1.3e-192) {
		tmp = t_1;
	} else if (a <= 1.26e+94) {
		tmp = ((b + (y * (x * 9.0))) / 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 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if a <= -1.3e-192:
		tmp = t_1
	elif a <= 1.26e+94:
		tmp = ((b + (y * (x * 9.0))) / 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(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (a <= -1.3e-192)
		tmp = t_1;
	elseif (a <= 1.26e+94)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(x * 9.0))) / 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 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (a <= -1.3e-192)
		tmp = t_1;
	elseif (a <= 1.26e+94)
		tmp = ((b + (y * (x * 9.0))) / 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[a, -1.3e-192], t$95$1, If[LessEqual[a, 1.26e+94], N[(N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3000000000000001e-192 or 1.25999999999999997e94 < a

   1. Initial program 80.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 82.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 72.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 72.5%

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

   if -1.3000000000000001e-192 < a < 1.25999999999999997e94

   1. Initial program 84.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 93.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 92.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \color{blue}{z}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right)\right) \]

      4. *-lowering-*.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right)\right) \]

   9. Simplified 79.9%

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

       1. *-commutative N/A

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

       2. div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right), \color{blue}{c}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\left(9 \cdot x\right) \cdot y\right)\right), z\right), c\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(y \cdot \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(9 \cdot x\right)\right)\right), z\right), c\right) \]

       9. *-lowering-*.f64 80.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, x\right)\right)\right), z\right), c\right) \]

   11. Applied egg-rr 80.0%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= a -1.3e-192)
     t_1
     (if (<= a 1.56e+94) (/ (/ (+ b (* 9.0 (* x y))) 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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (a <= -1.3e-192) {
		tmp = t_1;
	} else if (a <= 1.56e+94) {
		tmp = ((b + (9.0 * (x * y))) / 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 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (a <= (-1.3d-192)) then
        tmp = t_1
    else if (a <= 1.56d+94) then
        tmp = ((b + (9.0d0 * (x * y))) / 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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (a <= -1.3e-192) {
		tmp = t_1;
	} else if (a <= 1.56e+94) {
		tmp = ((b + (9.0 * (x * y))) / 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 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if a <= -1.3e-192:
		tmp = t_1
	elif a <= 1.56e+94:
		tmp = ((b + (9.0 * (x * y))) / 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(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (a <= -1.3e-192)
		tmp = t_1;
	elseif (a <= 1.56e+94)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / 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 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (a <= -1.3e-192)
		tmp = t_1;
	elseif (a <= 1.56e+94)
		tmp = ((b + (9.0 * (x * y))) / 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[a, -1.3e-192], t$95$1, If[LessEqual[a, 1.56e+94], N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3000000000000001e-192 or 1.5600000000000001e94 < a

   1. Initial program 80.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 82.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 72.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 72.5%

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

   if -1.3000000000000001e-192 < a < 1.5600000000000001e94

   1. Initial program 84.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}, c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      4. *-lowering-*.f64 80.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right), c\right) \]

   7. Simplified 80.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.55e+45)
   (/ b (* z c))
   (if (<= b 1e-76) (* a (/ (* t -4.0) c)) (/ (/ b c) z))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.55e+45) {
		tmp = b / (z * c);
	} else if (b <= 1e-76) {
		tmp = a * ((t * -4.0) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.55d+45)) then
        tmp = b / (z * c)
    else if (b <= 1d-76) then
        tmp = a * ((t * (-4.0d0)) / c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.55e+45) {
		tmp = b / (z * c);
	} else if (b <= 1e-76) {
		tmp = a * ((t * -4.0) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.55e+45:
		tmp = b / (z * c)
	elif b <= 1e-76:
		tmp = a * ((t * -4.0) / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.55e+45)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 1e-76)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.55e+45)
		tmp = b / (z * c);
	elseif (b <= 1e-76)
		tmp = a * ((t * -4.0) / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.55e+45], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-76], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.54999999999999994e45

   1. Initial program 87.1%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 66.5%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 66.5%

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

   if -1.54999999999999994e45 < b < 9.99999999999999927e-77

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 49.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 49.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t \cdot -4}{c}\right), \color{blue}{a}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t \cdot -4\right), c\right), a\right) \]

      5. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(t, -4\right), c\right), a\right) \]

   7. Applied egg-rr 48.2%

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

   if 9.99999999999999927e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-77}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4e+45)
   (/ b (* z c))
   (if (<= b 9e-77) (* (* t a) (/ -4.0 c)) (/ (/ b c) z))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e+45) {
		tmp = b / (z * c);
	} else if (b <= 9e-77) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4d+45)) then
        tmp = b / (z * c)
    else if (b <= 9d-77) then
        tmp = (t * a) * ((-4.0d0) / c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e+45) {
		tmp = b / (z * c);
	} else if (b <= 9e-77) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4e+45:
		tmp = b / (z * c)
	elif b <= 9e-77:
		tmp = (t * a) * (-4.0 / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4e+45)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 9e-77)
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4e+45)
		tmp = b / (z * c);
	elseif (b <= 9e-77)
		tmp = (t * a) * (-4.0 / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4e+45], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-77], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.9999999999999997e45

   1. Initial program 87.1%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 66.5%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 66.5%

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

   if -3.9999999999999997e45 < b < 9.0000000000000001e-77

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 49.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 49.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot a\right), \color{blue}{\left(\frac{-4}{c}\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\frac{\color{blue}{-4}}{c}\right)\right) \]

      6. /-lowering-/.f64 49.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 49.3%

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

   if 9.0000000000000001e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

Alternative 16: 49.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.6e+45)
   (/ b (* z c))
   (if (<= b 1e-76) (* t (/ (* a -4.0) c)) (/ (/ b c) z))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.6e+45) {
		tmp = b / (z * c);
	} else if (b <= 1e-76) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.6d+45)) then
        tmp = b / (z * c)
    else if (b <= 1d-76) then
        tmp = t * ((a * (-4.0d0)) / c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.6e+45) {
		tmp = b / (z * c);
	} else if (b <= 1e-76) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.6e+45:
		tmp = b / (z * c)
	elif b <= 1e-76:
		tmp = t * ((a * -4.0) / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.6e+45)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 1e-76)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.6e+45)
		tmp = b / (z * c);
	elseif (b <= 1e-76)
		tmp = t * ((a * -4.0) / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.6e+45], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-76], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.60000000000000007e45

   1. Initial program 87.1%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 66.5%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 66.5%

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

   if -2.60000000000000007e45 < b < 9.99999999999999927e-77

   1. Initial program 82.6%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 90.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 90.8%

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

   7. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot \frac{a}{c}\right)}\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\frac{-4 \cdot a}{\color{blue}{c}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(-4 \cdot a\right), \color{blue}{c}\right)\right) \]

      9. *-lowering-*.f64 50.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right)\right) \]

   9. Simplified 50.1%

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

   if 9.99999999999999927e-77 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.8%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 10^{-76}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 85.7% accurate, 1.1× speedup

Math

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

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 (* x (* 9.0 y))) z) (* t (* a -4.0))) c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((b + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / 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 + (x * (9.0d0 * y))) / z) + (t * (a * (-4.0d0)))) / 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 + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / 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 + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / 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(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z) + Float64(t * Float64(a * -4.0))) / 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 + (x * (9.0 * y))) / z) + (t * (a * -4.0))) / 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[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]

Derivation

1. Initial program 82.0%

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

   1. associate-/r* N/A

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

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

3. Simplified 87.2%

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

5. Final simplification 87.2%

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

Alternative 18: 65.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+249}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x \cdot 9}}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 1.05e+249)
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (/ y (/ z (* x 9.0))) c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.05e+249) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (y / (z / (x * 9.0))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= 1.05d+249) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (y / (z / (x * 9.0d0))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.05e+249) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (y / (z / (x * 9.0))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 1.05e+249:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (y / (z / (x * 9.0))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 1.05e+249)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(y / Float64(z / Float64(x * 9.0))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 1.05e+249)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (y / (z / (x * 9.0))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 1.05e+249], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(y / N[(z / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.0499999999999999e249

   1. Initial program 82.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 68.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 68.1%

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

   if 1.0499999999999999e249 < y

   1. Initial program 82.9%

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

      1. div-inv N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

   4. Applied egg-rr 91.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, c\right), \mathsf{/.f64}\left(1, z\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), c\right), \mathsf{/.f64}\left(1, z\right)\right) \]

      2. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), c\right), \mathsf{/.f64}\left(1, z\right)\right) \]

   7. Simplified 74.9%

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

      1. associate-*l/ N/A

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

      2. un-div-inv N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. *-commutative N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{9 \cdot x}{z}\right), \color{blue}{c}\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{\frac{z}{9 \cdot x}}\right), c\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{\frac{z}{9 \cdot x}}\right), c\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{z}{9 \cdot x}\right)\right), c\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \left(9 \cdot x\right)\right)\right), c\right) \]

      11. *-lowering-*.f64 74.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(9, x\right)\right)\right), c\right) \]

   9. Applied egg-rr 74.4%

      \[\leadsto \color{blue}{\frac{\frac{y}{\frac{z}{9 \cdot x}}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+249}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x \cdot 9}}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.3% 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 82.0%

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

3. Taylor expanded in b around inf

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

   3. *-lowering-*.f64 39.3%

      \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

5. Simplified 39.3%

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

Developer Target 1: 80.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024158 
(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)))