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

Percentage Accurate: 79.0% → 92.0%

Time: 16.8s

Alternatives: 18

Speedup: 0.7×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.0% 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: 92.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 6.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{elif}\;c\_m \leq 3 \cdot 10^{+279}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m} + \frac{\frac{b}{c\_m} - \frac{y}{c\_m} \cdot \left(x \cdot -9\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c\_m \cdot z} - b \cdot \left(4 \cdot \frac{a \cdot t}{c\_m \cdot b} + \frac{-1}{c\_m \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 6.2e-49)
    (/ (- (+ (* 9.0 (/ (* x y) z)) (/ b z)) (* 4.0 (* a t))) c_m)
    (if (<= c_m 3e+279)
      (+ (* a (/ (* t -4.0) c_m)) (/ (- (/ b c_m) (* (/ y c_m) (* x -9.0))) z))
      (-
       (/ (* 9.0 (* x y)) (* c_m z))
       (* b (+ (* 4.0 (/ (* a t) (* c_m b))) (/ -1.0 (* c_m z)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 6.2e-49) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else if (c_m <= 3e+279) {
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	} else {
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (b * ((4.0 * ((a * t) / (c_m * b))) + (-1.0 / (c_m * z))));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (c_m <= 6.2d-49) then
        tmp = (((9.0d0 * ((x * y) / z)) + (b / z)) - (4.0d0 * (a * t))) / c_m
    else if (c_m <= 3d+279) then
        tmp = (a * ((t * (-4.0d0)) / c_m)) + (((b / c_m) - ((y / c_m) * (x * (-9.0d0)))) / z)
    else
        tmp = ((9.0d0 * (x * y)) / (c_m * z)) - (b * ((4.0d0 * ((a * t) / (c_m * b))) + ((-1.0d0) / (c_m * z))))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 6.2e-49) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else if (c_m <= 3e+279) {
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	} else {
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (b * ((4.0 * ((a * t) / (c_m * b))) + (-1.0 / (c_m * z))));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 6.2e-49:
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m
	elif c_m <= 3e+279:
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z)
	else:
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (b * ((4.0 * ((a * t) / (c_m * b))) + (-1.0 / (c_m * z))))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 6.2e-49)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z)) - Float64(4.0 * Float64(a * t))) / c_m);
	elseif (c_m <= 3e+279)
		tmp = Float64(Float64(a * Float64(Float64(t * -4.0) / c_m)) + Float64(Float64(Float64(b / c_m) - Float64(Float64(y / c_m) * Float64(x * -9.0))) / z));
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) / Float64(c_m * z)) - Float64(b * Float64(Float64(4.0 * Float64(Float64(a * t) / Float64(c_m * b))) + Float64(-1.0 / Float64(c_m * z)))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 6.2e-49)
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	elseif (c_m <= 3e+279)
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	else
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (b * ((4.0 * ((a * t) / (c_m * b))) + (-1.0 / (c_m * z))));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 6.2e-49], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[c$95$m, 3e+279], N[(N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c$95$m), $MachinePrecision] - N[(N[(y / c$95$m), $MachinePrecision] * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(4.0 * N[(N[(a * t), $MachinePrecision] / N[(c$95$m * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if c < 6.2e-49

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 86.4%

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

      8. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. associate-+l- 86.4%

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

      2. div-sub 77.4%

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

      3. associate-*r* 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-*l* 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-*l* 77.4%

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

   6. Applied egg-rr 77.4%

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

   7. Taylor expanded in c around 0 89.1%

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

   if 6.2e-49 < c < 2.9999999999999998e279

   1. Initial program 71.1%

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

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-+l- 75.8%

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

      6. associate-*l* 75.9%

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

      7. associate-*l* 74.3%

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

      8. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in x around 0 80.8%

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

      1. associate--l+ 80.8%

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

      2. fma-define 80.7%

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

      3. associate-/r* 82.3%

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

      4. associate-/l* 84.0%

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

      5. cancel-sign-sub-inv 84.0%

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

      6. metadata-eval 84.0%

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

      7. +-commutative 84.0%

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

      8. *-commutative 84.0%

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

      9. fma-define 84.0%

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

      10. associate-/l* 88.4%

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

      11. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in z around -inf 85.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 85.5%

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

      2. sub-neg 85.5%

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

      3. sub-neg 85.5%

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

      4. mul-1-neg 85.5%

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

      5. mul-1-neg 85.5%

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

      6. sub-neg 85.5%

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

      7. mul-1-neg 85.5%

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

      8. unsub-neg 85.5%

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

   10. Simplified 91.6%

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

   if 2.9999999999999998e279 < c

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

   3. Simplified 86.1%

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

      1. associate-+l- 86.1%

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

      2. div-sub 86.3%

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

      3. associate-*r* 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-*l* 86.3%

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

      6. *-commutative 86.3%

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

      7. associate-*l* 86.3%

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

   6. Applied egg-rr 86.3%

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

   7. Taylor expanded in b around inf 99.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 6.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+279}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c} + \frac{\frac{b}{c} - \frac{y}{c} \cdot \left(x \cdot -9\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z} - b \cdot \left(4 \cdot \frac{a \cdot t}{c \cdot b} + \frac{-1}{c \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c_m z)))
        (t_2 (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -1e-170)
      t_2
      (if (<= t_1 0.0)
        (/ (- (/ b z) (* 4.0 (* a t))) c_m)
        (if (<= t_1 INFINITY) t_2 (* a (/ (* t -4.0) c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double t_2 = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	double tmp;
	if (t_1 <= -1e-170) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double t_2 = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	double tmp;
	if (t_1 <= -1e-170) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z)
	t_2 = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	tmp = 0
	if t_1 <= -1e-170:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = ((b / z) - (4.0 * (a * t))) / c_m
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	t_2 = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -1e-170)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c_m);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	t_2 = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	tmp = 0.0;
	if (t_1 <= -1e-170)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = a * ((t * -4.0) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e-170], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -9.99999999999999983e-171 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 88.0%

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

      1. associate-+l- 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

      6. associate-*l* 91.7%

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

      7. associate-*l* 91.7%

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

      8. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   if -9.99999999999999983e-171 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 39.3%

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

      1. associate-+l- 39.3%

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

      2. *-commutative 39.3%

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

      3. associate-*r* 31.6%

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

      4. *-commutative 31.6%

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

      5. associate-+l- 31.6%

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

      6. associate-*l* 31.6%

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

      7. associate-*l* 39.3%

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

      8. *-commutative 39.3%

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

   3. Simplified 39.3%

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

      1. associate-+l- 39.3%

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

      2. div-sub 39.3%

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

      3. associate-*r* 39.3%

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

      4. *-commutative 39.3%

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

      5. associate-*l* 39.3%

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

      6. *-commutative 39.3%

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

      7. associate-*l* 39.3%

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

   6. Applied egg-rr 39.3%

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

   7. Taylor expanded in c around 0 99.9%

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

   8. Taylor expanded in x around 0 86.8%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 7.1%

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

      4. *-commutative 7.1%

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

      5. associate-+l- 7.1%

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

      6. associate-*l* 7.1%

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

      7. associate-*l* 7.1%

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

      8. *-commutative 7.1%

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

   3. Simplified 7.1%

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

   5. Taylor expanded in z around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/l* 87.2%

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

      3. associate-*r* 87.2%

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

      4. associate-*l/ 87.2%

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

   7. Simplified 87.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -1 \cdot 10^{-170}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.35 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{elif}\;c\_m \leq 3 \cdot 10^{+279}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m} + \frac{\frac{b}{c\_m} - \frac{y}{c\_m} \cdot \left(x \cdot -9\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c\_m \cdot z} - \frac{4 \cdot \left(z \cdot \left(a \cdot t\right)\right) - b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.35e-48)
    (/ (- (+ (* 9.0 (/ (* x y) z)) (/ b z)) (* 4.0 (* a t))) c_m)
    (if (<= c_m 3e+279)
      (+ (* a (/ (* t -4.0) c_m)) (/ (- (/ b c_m) (* (/ y c_m) (* x -9.0))) z))
      (-
       (/ (* 9.0 (* x y)) (* c_m z))
       (/ (- (* 4.0 (* z (* a t))) b) (* c_m z)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.35e-48) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else if (c_m <= 3e+279) {
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	} else {
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (((4.0 * (z * (a * t))) - b) / (c_m * z));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (c_m <= 1.35d-48) then
        tmp = (((9.0d0 * ((x * y) / z)) + (b / z)) - (4.0d0 * (a * t))) / c_m
    else if (c_m <= 3d+279) then
        tmp = (a * ((t * (-4.0d0)) / c_m)) + (((b / c_m) - ((y / c_m) * (x * (-9.0d0)))) / z)
    else
        tmp = ((9.0d0 * (x * y)) / (c_m * z)) - (((4.0d0 * (z * (a * t))) - b) / (c_m * z))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.35e-48) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else if (c_m <= 3e+279) {
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	} else {
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (((4.0 * (z * (a * t))) - b) / (c_m * z));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 1.35e-48:
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m
	elif c_m <= 3e+279:
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z)
	else:
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (((4.0 * (z * (a * t))) - b) / (c_m * z))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.35e-48)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z)) - Float64(4.0 * Float64(a * t))) / c_m);
	elseif (c_m <= 3e+279)
		tmp = Float64(Float64(a * Float64(Float64(t * -4.0) / c_m)) + Float64(Float64(Float64(b / c_m) - Float64(Float64(y / c_m) * Float64(x * -9.0))) / z));
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) / Float64(c_m * z)) - Float64(Float64(Float64(4.0 * Float64(z * Float64(a * t))) - b) / Float64(c_m * z)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 1.35e-48)
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	elseif (c_m <= 3e+279)
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	else
		tmp = ((9.0 * (x * y)) / (c_m * z)) - (((4.0 * (z * (a * t))) - b) / (c_m * z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.35e-48], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[c$95$m, 3e+279], N[(N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c$95$m), $MachinePrecision] - N[(N[(y / c$95$m), $MachinePrecision] * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if c < 1.35000000000000006e-48

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 86.4%

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

      8. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. associate-+l- 86.4%

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

      2. div-sub 77.4%

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

      3. associate-*r* 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-*l* 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-*l* 77.4%

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

   6. Applied egg-rr 77.4%

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

   7. Taylor expanded in c around 0 89.1%

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

   if 1.35000000000000006e-48 < c < 2.9999999999999998e279

   1. Initial program 71.1%

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

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-+l- 75.8%

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

      6. associate-*l* 75.9%

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

      7. associate-*l* 74.3%

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

      8. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in x around 0 80.8%

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

      1. associate--l+ 80.8%

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

      2. fma-define 80.7%

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

      3. associate-/r* 82.3%

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

      4. associate-/l* 84.0%

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

      5. cancel-sign-sub-inv 84.0%

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

      6. metadata-eval 84.0%

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

      7. +-commutative 84.0%

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

      8. *-commutative 84.0%

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

      9. fma-define 84.0%

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

      10. associate-/l* 88.4%

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

      11. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in z around -inf 85.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 85.5%

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

      2. sub-neg 85.5%

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

      3. sub-neg 85.5%

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

      4. mul-1-neg 85.5%

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

      5. mul-1-neg 85.5%

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

      6. sub-neg 85.5%

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

      7. mul-1-neg 85.5%

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

      8. unsub-neg 85.5%

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

   10. Simplified 91.6%

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

   if 2.9999999999999998e279 < c

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

   3. Simplified 86.1%

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

      1. associate-+l- 86.1%

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

      2. div-sub 86.3%

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

      3. associate-*r* 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-*l* 86.3%

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

      6. *-commutative 86.3%

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

      7. associate-*l* 86.3%

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

   6. Applied egg-rr 86.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.35 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+279}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c} + \frac{\frac{b}{c} - \frac{y}{c} \cdot \left(x \cdot -9\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z} - \frac{4 \cdot \left(z \cdot \left(a \cdot t\right)\right) - b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + y \cdot \left(9 \cdot x\right)}{c\_m \cdot z}\\ t_2 := \frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -170:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (* y (* 9.0 x))) (* c_m z)))
        (t_2 (/ (- (/ b z) (* 4.0 (* a t))) c_m)))
   (*
    c_s
    (if (<= z -170.0)
      t_2
      (if (<= z 2e-131)
        t_1
        (if (<= z 1.35e-61)
          (/ (- b (* 4.0 (* a (* z t)))) (* c_m z))
          (if (<= z 3e-21) t_1 t_2)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + (y * (9.0 * x))) / (c_m * z);
	double t_2 = ((b / z) - (4.0 * (a * t))) / c_m;
	double tmp;
	if (z <= -170.0) {
		tmp = t_2;
	} else if (z <= 2e-131) {
		tmp = t_1;
	} else if (z <= 1.35e-61) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= 3e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b + (y * (9.0d0 * x))) / (c_m * z)
    t_2 = ((b / z) - (4.0d0 * (a * t))) / c_m
    if (z <= (-170.0d0)) then
        tmp = t_2
    else if (z <= 2d-131) then
        tmp = t_1
    else if (z <= 1.35d-61) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c_m * z)
    else if (z <= 3d-21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + (y * (9.0 * x))) / (c_m * z);
	double t_2 = ((b / z) - (4.0 * (a * t))) / c_m;
	double tmp;
	if (z <= -170.0) {
		tmp = t_2;
	} else if (z <= 2e-131) {
		tmp = t_1;
	} else if (z <= 1.35e-61) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= 3e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + (y * (9.0 * x))) / (c_m * z)
	t_2 = ((b / z) - (4.0 * (a * t))) / c_m
	tmp = 0
	if z <= -170.0:
		tmp = t_2
	elif z <= 2e-131:
		tmp = t_1
	elif z <= 1.35e-61:
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z)
	elif z <= 3e-21:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(c_m * z))
	t_2 = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c_m)
	tmp = 0.0
	if (z <= -170.0)
		tmp = t_2;
	elseif (z <= 2e-131)
		tmp = t_1;
	elseif (z <= 1.35e-61)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c_m * z));
	elseif (z <= 3e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + (y * (9.0 * x))) / (c_m * z);
	t_2 = ((b / z) - (4.0 * (a * t))) / c_m;
	tmp = 0.0;
	if (z <= -170.0)
		tmp = t_2;
	elseif (z <= 2e-131)
		tmp = t_1;
	elseif (z <= 1.35e-61)
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	elseif (z <= 3e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -170.0], t$95$2, If[LessEqual[z, 2e-131], t$95$1, If[LessEqual[z, 1.35e-61], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-21], t$95$1, t$95$2]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -170 or 2.99999999999999991e-21 < z

   1. Initial program 65.4%

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

      1. associate-+l- 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r* 72.0%

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

      4. *-commutative 72.0%

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

      5. associate-+l- 72.0%

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

      6. associate-*l* 72.0%

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

      7. associate-*l* 77.1%

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

      8. *-commutative 77.1%

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

   3. Simplified 77.1%

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

      1. associate-+l- 77.1%

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

      2. div-sub 77.1%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-*l* 77.1%

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

      6. *-commutative 77.1%

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

      7. associate-*l* 77.1%

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

   6. Applied egg-rr 77.1%

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

   7. Taylor expanded in c around 0 92.4%

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

   8. Taylor expanded in x around 0 74.6%

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

   if -170 < z < 2e-131 or 1.34999999999999997e-61 < z < 2.99999999999999991e-21

   1. Initial program 95.5%

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

      1. associate-+l- 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 95.1%

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

      4. *-commutative 95.1%

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

      5. associate-+l- 95.1%

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

      6. associate-*l* 95.1%

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

      7. associate-*l* 90.9%

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

      8. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in x around inf 83.1%

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

      1. associate-*r* 83.1%

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

   7. Simplified 83.1%

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

   if 2e-131 < z < 1.34999999999999997e-61

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*r* 93.7%

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

      4. *-commutative 93.7%

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

      5. associate-+l- 93.7%

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

      6. associate-*l* 93.7%

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

      7. associate-*l* 86.9%

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

      8. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around 0 93.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -170:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-131}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{elif}\;c\_m \leq 3 \cdot 10^{+279}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m} + \frac{\frac{b}{c\_m} - \frac{y}{c\_m} \cdot \left(x \cdot -9\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.5e-48)
    (/ (- (+ (* 9.0 (/ (* x y) z)) (/ b z)) (* 4.0 (* a t))) c_m)
    (if (<= c_m 3e+279)
      (+ (* a (/ (* t -4.0) c_m)) (/ (- (/ b c_m) (* (/ y c_m) (* x -9.0))) z))
      (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* c_m z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.5e-48) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else if (c_m <= 3e+279) {
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (c_m <= 1.5d-48) then
        tmp = (((9.0d0 * ((x * y) / z)) + (b / z)) - (4.0d0 * (a * t))) / c_m
    else if (c_m <= 3d+279) then
        tmp = (a * ((t * (-4.0d0)) / c_m)) + (((b / c_m) - ((y / c_m) * (x * (-9.0d0)))) / z)
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((a * t) * (z * 4.0d0)))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.5e-48) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else if (c_m <= 3e+279) {
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 1.5e-48:
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m
	elif c_m <= 3e+279:
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z)
	else:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.5e-48)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z)) - Float64(4.0 * Float64(a * t))) / c_m);
	elseif (c_m <= 3e+279)
		tmp = Float64(Float64(a * Float64(Float64(t * -4.0) / c_m)) + Float64(Float64(Float64(b / c_m) - Float64(Float64(y / c_m) * Float64(x * -9.0))) / z));
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 1.5e-48)
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	elseif (c_m <= 3e+279)
		tmp = (a * ((t * -4.0) / c_m)) + (((b / c_m) - ((y / c_m) * (x * -9.0))) / z);
	else
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.5e-48], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[c$95$m, 3e+279], N[(N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c$95$m), $MachinePrecision] - N[(N[(y / c$95$m), $MachinePrecision] * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if c < 1.5e-48

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 86.4%

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

      8. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. associate-+l- 86.4%

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

      2. div-sub 77.4%

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

      3. associate-*r* 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-*l* 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-*l* 77.4%

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

   6. Applied egg-rr 77.4%

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

   7. Taylor expanded in c around 0 89.1%

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

   if 1.5e-48 < c < 2.9999999999999998e279

   1. Initial program 71.1%

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

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-+l- 75.8%

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

      6. associate-*l* 75.9%

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

      7. associate-*l* 74.3%

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

      8. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in x around 0 80.8%

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

      1. associate--l+ 80.8%

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

      2. fma-define 80.7%

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

      3. associate-/r* 82.3%

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

      4. associate-/l* 84.0%

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

      5. cancel-sign-sub-inv 84.0%

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

      6. metadata-eval 84.0%

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

      7. +-commutative 84.0%

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

      8. *-commutative 84.0%

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

      9. fma-define 84.0%

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

      10. associate-/l* 88.4%

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

      11. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in z around -inf 85.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 85.5%

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

      2. sub-neg 85.5%

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

      3. sub-neg 85.5%

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

      4. mul-1-neg 85.5%

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

      5. mul-1-neg 85.5%

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

      6. sub-neg 85.5%

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

      7. mul-1-neg 85.5%

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

      8. unsub-neg 85.5%

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

   10. Simplified 91.6%

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

   if 2.9999999999999998e279 < c

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

   3. Simplified 86.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+279}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c} + \frac{\frac{b}{c} - \frac{y}{c} \cdot \left(x \cdot -9\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-71} \lor \neg \left(z \leq 10^{-16}\right):\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -2e-71) (not (<= z 1e-16)))
    (/ (- (+ (* 9.0 (/ (* x y) z)) (/ b z)) (* 4.0 (* a t))) c_m)
    (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2e-71) || !(z <= 1e-16)) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-2d-71)) .or. (.not. (z <= 1d-16))) then
        tmp = (((9.0d0 * ((x * y) / z)) + (b / z)) - (4.0d0 * (a * t))) / c_m
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2e-71) || !(z <= 1e-16)) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -2e-71) or not (z <= 1e-16):
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -2e-71) || !(z <= 1e-16))
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z)) - Float64(4.0 * Float64(a * t))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -2e-71) || ~((z <= 1e-16)))
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c_m;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -2e-71], N[Not[LessEqual[z, 1e-16]], $MachinePrecision]], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999998e-71 or 9.9999999999999998e-17 < z

   1. Initial program 69.3%

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

      1. associate-+l- 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-*r* 74.7%

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

      4. *-commutative 74.7%

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

      5. associate-+l- 74.7%

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

      6. associate-*l* 74.7%

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

      7. associate-*l* 79.4%

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

      8. *-commutative 79.4%

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

   3. Simplified 79.4%

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

      1. associate-+l- 79.4%

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

      2. div-sub 76.8%

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

      3. associate-*r* 76.8%

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

      4. *-commutative 76.8%

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

      5. associate-*l* 76.8%

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

      6. *-commutative 76.8%

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

      7. associate-*l* 76.8%

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

   6. Applied egg-rr 76.8%

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

   7. Taylor expanded in c around 0 92.8%

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

   if -1.9999999999999998e-71 < z < 9.9999999999999998e-17

   1. Initial program 95.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-71} \lor \neg \left(z \leq 10^{-16}\right):\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c\_m}}}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right)}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 1300:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -3.1e+204)
    (/ 1.0 (/ z (/ b c_m)))
    (if (<= b -3e-202)
      (* a (/ (* t -4.0) c_m))
      (if (<= b 3.5e-152)
        (/ (* y (* 9.0 x)) (* c_m z))
        (if (<= b 1300.0) (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.1e+204) {
		tmp = 1.0 / (z / (b / c_m));
	} else if (b <= -3e-202) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (b <= 3.5e-152) {
		tmp = (y * (9.0 * x)) / (c_m * z);
	} else if (b <= 1300.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-3.1d+204)) then
        tmp = 1.0d0 / (z / (b / c_m))
    else if (b <= (-3d-202)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (b <= 3.5d-152) then
        tmp = (y * (9.0d0 * x)) / (c_m * z)
    else if (b <= 1300.0d0) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.1e+204) {
		tmp = 1.0 / (z / (b / c_m));
	} else if (b <= -3e-202) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (b <= 3.5e-152) {
		tmp = (y * (9.0 * x)) / (c_m * z);
	} else if (b <= 1300.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -3.1e+204:
		tmp = 1.0 / (z / (b / c_m))
	elif b <= -3e-202:
		tmp = a * ((t * -4.0) / c_m)
	elif b <= 3.5e-152:
		tmp = (y * (9.0 * x)) / (c_m * z)
	elif b <= 1300.0:
		tmp = -4.0 * ((a * t) / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -3.1e+204)
		tmp = Float64(1.0 / Float64(z / Float64(b / c_m)));
	elseif (b <= -3e-202)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (b <= 3.5e-152)
		tmp = Float64(Float64(y * Float64(9.0 * x)) / Float64(c_m * z));
	elseif (b <= 1300.0)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -3.1e+204)
		tmp = 1.0 / (z / (b / c_m));
	elseif (b <= -3e-202)
		tmp = a * ((t * -4.0) / c_m);
	elseif (b <= 3.5e-152)
		tmp = (y * (9.0 * x)) / (c_m * z);
	elseif (b <= 1300.0)
		tmp = -4.0 * ((a * t) / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -3.1e+204], N[(1.0 / N[(z / N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-202], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-152], N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1300.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if b < -3.1000000000000002e204

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-+l- 86.2%

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

      6. associate-*l* 86.2%

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

      7. associate-*l* 86.2%

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

      8. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf 60.3%

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

      1. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

      1. clear-num 68.9%

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

      2. inv-pow 68.9%

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

   9. Applied egg-rr 68.9%

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

       1. unpow-1 68.9%

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

   11. Simplified 68.9%

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

   if -3.1000000000000002e204 < b < -3.00000000000000011e-202

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 74.1%

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

      8. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in z around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-/l* 52.5%

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

      3. associate-*r* 52.5%

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

      4. associate-*l/ 52.5%

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

   7. Simplified 52.5%

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

   if -3.00000000000000011e-202 < b < 3.5000000000000001e-152

   1. Initial program 84.4%

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

      1. associate-+l- 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r* 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-+l- 85.6%

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

      6. associate-*l* 85.5%

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

      7. associate-*l* 87.5%

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

      8. *-commutative 87.5%

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

   3. Simplified 87.5%

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

      1. associate-+l- 87.5%

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

      2. div-sub 84.4%

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

      3. associate-*r* 84.4%

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

      4. *-commutative 84.4%

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

      5. associate-*l* 84.4%

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

      6. *-commutative 84.4%

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

      7. associate-*l* 84.4%

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

   6. Applied egg-rr 84.4%

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

   7. Taylor expanded in c around 0 92.1%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-*r/ 64.6%

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

      2. associate-*r* 64.6%

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

      3. *-commutative 64.6%

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

      4. *-commutative 64.6%

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

   10. Simplified 64.6%

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

   if 3.5000000000000001e-152 < b < 1300

   1. Initial program 81.4%

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

      1. associate-+l- 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*r* 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-+l- 87.4%

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

      6. associate-*l* 87.4%

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

      7. associate-*l* 87.5%

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

      8. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   if 1300 < b

   1. Initial program 86.5%

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

      1. associate-+l- 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-+l- 89.4%

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

      6. associate-*l* 89.4%

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

      7. associate-*l* 87.8%

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

      8. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf 54.9%

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

      1. associate-/r* 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 1300:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c\_m}}}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-153}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 2650:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -3.1e+204)
    (/ 1.0 (/ z (/ b c_m)))
    (if (<= b -1.7e-202)
      (* a (/ (* t -4.0) c_m))
      (if (<= b 4e-153)
        (* 9.0 (/ (* x y) (* c_m z)))
        (if (<= b 2650.0) (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.1e+204) {
		tmp = 1.0 / (z / (b / c_m));
	} else if (b <= -1.7e-202) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (b <= 4e-153) {
		tmp = 9.0 * ((x * y) / (c_m * z));
	} else if (b <= 2650.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-3.1d+204)) then
        tmp = 1.0d0 / (z / (b / c_m))
    else if (b <= (-1.7d-202)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (b <= 4d-153) then
        tmp = 9.0d0 * ((x * y) / (c_m * z))
    else if (b <= 2650.0d0) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.1e+204) {
		tmp = 1.0 / (z / (b / c_m));
	} else if (b <= -1.7e-202) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (b <= 4e-153) {
		tmp = 9.0 * ((x * y) / (c_m * z));
	} else if (b <= 2650.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -3.1e+204:
		tmp = 1.0 / (z / (b / c_m))
	elif b <= -1.7e-202:
		tmp = a * ((t * -4.0) / c_m)
	elif b <= 4e-153:
		tmp = 9.0 * ((x * y) / (c_m * z))
	elif b <= 2650.0:
		tmp = -4.0 * ((a * t) / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -3.1e+204)
		tmp = Float64(1.0 / Float64(z / Float64(b / c_m)));
	elseif (b <= -1.7e-202)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (b <= 4e-153)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z)));
	elseif (b <= 2650.0)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -3.1e+204)
		tmp = 1.0 / (z / (b / c_m));
	elseif (b <= -1.7e-202)
		tmp = a * ((t * -4.0) / c_m);
	elseif (b <= 4e-153)
		tmp = 9.0 * ((x * y) / (c_m * z));
	elseif (b <= 2650.0)
		tmp = -4.0 * ((a * t) / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -3.1e+204], N[(1.0 / N[(z / N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-202], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-153], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2650.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if b < -3.1000000000000002e204

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-+l- 86.2%

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

      6. associate-*l* 86.2%

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

      7. associate-*l* 86.2%

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

      8. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf 60.3%

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

      1. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

      1. clear-num 68.9%

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

      2. inv-pow 68.9%

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

   9. Applied egg-rr 68.9%

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

       1. unpow-1 68.9%

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

   11. Simplified 68.9%

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

   if -3.1000000000000002e204 < b < -1.70000000000000006e-202

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 74.1%

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

      8. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in z around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-/l* 52.5%

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

      3. associate-*r* 52.5%

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

      4. associate-*l/ 52.5%

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

   7. Simplified 52.5%

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

   if -1.70000000000000006e-202 < b < 4.00000000000000016e-153

   1. Initial program 84.4%

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

      1. associate-+l- 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r* 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-+l- 85.6%

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

      6. associate-*l* 85.5%

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

      7. associate-*l* 87.5%

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

      8. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in x around inf 64.6%

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

   if 4.00000000000000016e-153 < b < 2650

   1. Initial program 81.4%

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

      1. associate-+l- 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*r* 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-+l- 87.4%

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

      6. associate-*l* 87.4%

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

      7. associate-*l* 87.5%

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

      8. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   if 2650 < b

   1. Initial program 86.5%

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

      1. associate-+l- 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-+l- 89.4%

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

      6. associate-*l* 89.4%

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

      7. associate-*l* 87.8%

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

      8. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf 54.9%

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

      1. associate-/r* 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-153}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;b \leq 2650:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c\_m}}}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-152}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \mathbf{elif}\;b \leq 580:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -3.1e+204)
    (/ 1.0 (/ z (/ b c_m)))
    (if (<= b -1.4e-253)
      (* a (/ (* t -4.0) c_m))
      (if (<= b 2.2e-152)
        (* 9.0 (* x (/ (/ y c_m) z)))
        (if (<= b 580.0) (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.1e+204) {
		tmp = 1.0 / (z / (b / c_m));
	} else if (b <= -1.4e-253) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (b <= 2.2e-152) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else if (b <= 580.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-3.1d+204)) then
        tmp = 1.0d0 / (z / (b / c_m))
    else if (b <= (-1.4d-253)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (b <= 2.2d-152) then
        tmp = 9.0d0 * (x * ((y / c_m) / z))
    else if (b <= 580.0d0) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.1e+204) {
		tmp = 1.0 / (z / (b / c_m));
	} else if (b <= -1.4e-253) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (b <= 2.2e-152) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else if (b <= 580.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -3.1e+204:
		tmp = 1.0 / (z / (b / c_m))
	elif b <= -1.4e-253:
		tmp = a * ((t * -4.0) / c_m)
	elif b <= 2.2e-152:
		tmp = 9.0 * (x * ((y / c_m) / z))
	elif b <= 580.0:
		tmp = -4.0 * ((a * t) / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -3.1e+204)
		tmp = Float64(1.0 / Float64(z / Float64(b / c_m)));
	elseif (b <= -1.4e-253)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (b <= 2.2e-152)
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c_m) / z)));
	elseif (b <= 580.0)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -3.1e+204)
		tmp = 1.0 / (z / (b / c_m));
	elseif (b <= -1.4e-253)
		tmp = a * ((t * -4.0) / c_m);
	elseif (b <= 2.2e-152)
		tmp = 9.0 * (x * ((y / c_m) / z));
	elseif (b <= 580.0)
		tmp = -4.0 * ((a * t) / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -3.1e+204], N[(1.0 / N[(z / N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.4e-253], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-152], N[(9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 580.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if b < -3.1000000000000002e204

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-+l- 86.2%

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

      6. associate-*l* 86.2%

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

      7. associate-*l* 86.2%

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

      8. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf 60.3%

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

      1. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

      1. clear-num 68.9%

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

      2. inv-pow 68.9%

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

   9. Applied egg-rr 68.9%

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

       1. unpow-1 68.9%

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

   11. Simplified 68.9%

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

   if -3.1000000000000002e204 < b < -1.40000000000000003e-253

   1. Initial program 70.0%

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

      1. associate-+l- 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-+l- 75.1%

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

      6. associate-*l* 75.1%

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

      7. associate-*l* 76.6%

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

      8. *-commutative 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in z around inf 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-/l* 50.1%

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

      3. associate-*r* 50.1%

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

      4. associate-*l/ 50.1%

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

   7. Simplified 50.1%

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

   if -1.40000000000000003e-253 < b < 2.19999999999999985e-152

   1. Initial program 84.5%

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

      1. associate-+l- 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-*r* 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-+l- 84.8%

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

      6. associate-*l* 84.8%

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

      7. associate-*l* 86.5%

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

      8. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 71.3%

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

      1. associate-/l* 69.6%

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

      2. associate-/r* 63.2%

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

   7. Simplified 63.2%

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

   if 2.19999999999999985e-152 < b < 580

   1. Initial program 81.4%

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

      1. associate-+l- 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*r* 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-+l- 87.4%

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

      6. associate-*l* 87.4%

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

      7. associate-*l* 87.5%

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

      8. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   if 580 < b

   1. Initial program 86.5%

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

      1. associate-+l- 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-+l- 89.4%

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

      6. associate-*l* 89.4%

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

      7. associate-*l* 87.8%

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

      8. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf 54.9%

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

      1. associate-/r* 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-152}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;b \leq 580:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{elif}\;b \leq 28:\\ \;\;\;\;\frac{\frac{y \cdot \left(9 \cdot x\right)}{z} - t \cdot \left(4 \cdot a\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -3.6e+42)
    (/ (- (/ b z) (* 4.0 (* a t))) c_m)
    (if (<= b 28.0)
      (/ (- (/ (* y (* 9.0 x)) z) (* t (* 4.0 a))) c_m)
      (/ (+ (/ b c_m) (* 9.0 (/ (* x y) c_m))) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.6e+42) {
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	} else if (b <= 28.0) {
		tmp = (((y * (9.0 * x)) / z) - (t * (4.0 * a))) / c_m;
	} else {
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-3.6d+42)) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c_m
    else if (b <= 28.0d0) then
        tmp = (((y * (9.0d0 * x)) / z) - (t * (4.0d0 * a))) / c_m
    else
        tmp = ((b / c_m) + (9.0d0 * ((x * y) / c_m))) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -3.6e+42) {
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	} else if (b <= 28.0) {
		tmp = (((y * (9.0 * x)) / z) - (t * (4.0 * a))) / c_m;
	} else {
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -3.6e+42:
		tmp = ((b / z) - (4.0 * (a * t))) / c_m
	elif b <= 28.0:
		tmp = (((y * (9.0 * x)) / z) - (t * (4.0 * a))) / c_m
	else:
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -3.6e+42)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c_m);
	elseif (b <= 28.0)
		tmp = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) / z) - Float64(t * Float64(4.0 * a))) / c_m);
	else
		tmp = Float64(Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / c_m))) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -3.6e+42)
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	elseif (b <= 28.0)
		tmp = (((y * (9.0 * x)) / z) - (t * (4.0 * a))) / c_m;
	else
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -3.6e+42], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[b, 28.0], N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -3.6000000000000001e42

   1. Initial program 78.7%

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

      1. associate-+l- 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-*r* 84.3%

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

      4. *-commutative 84.3%

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

      5. associate-+l- 84.3%

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

      6. associate-*l* 84.3%

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

      7. associate-*l* 82.3%

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

      8. *-commutative 82.3%

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

   3. Simplified 82.3%

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

      1. associate-+l- 82.3%

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

      2. div-sub 76.3%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-*l* 76.3%

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

      6. *-commutative 76.3%

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

      7. associate-*l* 76.3%

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

   6. Applied egg-rr 76.3%

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

   7. Taylor expanded in c around 0 84.4%

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

   8. Taylor expanded in x around 0 82.6%

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

   if -3.6000000000000001e42 < b < 28

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 80.3%

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

      4. *-commutative 80.3%

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

      5. associate-+l- 80.3%

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

      6. associate-*l* 80.3%

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

      7. associate-*l* 82.6%

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

      8. *-commutative 82.6%

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

   3. Simplified 82.6%

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

      1. associate-+l- 82.6%

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

      2. div-sub 76.1%

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

      3. associate-*r* 76.1%

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

      4. *-commutative 76.1%

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

      5. associate-*l* 76.1%

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

      6. *-commutative 76.1%

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

      7. associate-*l* 76.1%

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

   6. Applied egg-rr 76.1%

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

   7. Taylor expanded in c around 0 89.6%

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

   8. Taylor expanded in b around 0 82.0%

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

      1. associate-*r/ 81.9%

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

      2. associate-*r* 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-*r* 81.9%

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

      5. *-commutative 81.9%

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

   10. Simplified 81.9%

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

   if 28 < b

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-+l- 88.1%

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

      6. associate-*l* 88.1%

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

      7. associate-*l* 86.5%

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

      8. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 75.8%

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

      1. associate--l+ 75.8%

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

      2. fma-define 75.8%

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

      3. associate-/r* 77.5%

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

      4. associate-/l* 76.3%

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

      5. cancel-sign-sub-inv 76.3%

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

      6. metadata-eval 76.3%

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

      7. +-commutative 76.3%

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

      8. *-commutative 76.3%

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

      9. fma-define 76.3%

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

      10. associate-/l* 77.5%

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

      11. *-commutative 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in z around 0 72.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;b \leq 28:\\ \;\;\;\;\frac{\frac{y \cdot \left(9 \cdot x\right)}{z} - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1750 \lor \neg \left(z \leq 4.4 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -1750.0) (not (<= z 4.4e-85)))
    (/ (- (/ b z) (* 4.0 (* a t))) c_m)
    (/ (+ b (* y (* 9.0 x))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1750.0) || !(z <= 4.4e-85)) {
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = (b + (y * (9.0 * x))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-1750.0d0)) .or. (.not. (z <= 4.4d-85))) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c_m
    else
        tmp = (b + (y * (9.0d0 * x))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1750.0) || !(z <= 4.4e-85)) {
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = (b + (y * (9.0 * x))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -1750.0) or not (z <= 4.4e-85):
		tmp = ((b / z) - (4.0 * (a * t))) / c_m
	else:
		tmp = (b + (y * (9.0 * x))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -1750.0) || !(z <= 4.4e-85))
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -1750.0) || ~((z <= 4.4e-85)))
		tmp = ((b / z) - (4.0 * (a * t))) / c_m;
	else
		tmp = (b + (y * (9.0 * x))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -1750.0], N[Not[LessEqual[z, 4.4e-85]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1750 or 4.4e-85 < z

   1. Initial program 68.0%

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

      1. associate-+l- 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-*r* 74.0%

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

      4. *-commutative 74.0%

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

      5. associate-+l- 74.0%

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

      6. associate-*l* 74.0%

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

      7. associate-*l* 78.6%

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

      8. *-commutative 78.6%

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

   3. Simplified 78.6%

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

      1. associate-+l- 78.6%

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

      2. div-sub 77.9%

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

      3. associate-*r* 77.9%

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

      4. *-commutative 77.9%

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

      5. associate-*l* 77.9%

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

      6. *-commutative 77.9%

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

      7. associate-*l* 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in c around 0 91.8%

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

   8. Taylor expanded in x around 0 73.8%

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

   if -1750 < z < 4.4e-85

   1. Initial program 95.5%

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

      1. associate-+l- 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 95.2%

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

      4. *-commutative 95.2%

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

      5. associate-+l- 95.2%

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

      6. associate-*l* 95.2%

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

      7. associate-*l* 90.2%

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

      8. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around inf 82.7%

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

      1. associate-*r* 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1750 \lor \neg \left(z \leq 4.4 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+151} \lor \neg \left(t \leq 1.15 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= t -8.1e+151) (not (<= t 1.15e-50)))
    (* a (/ (* t -4.0) c_m))
    (/ (+ b (* y (* 9.0 x))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((t <= -8.1e+151) || !(t <= 1.15e-50)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = (b + (y * (9.0 * x))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((t <= (-8.1d+151)) .or. (.not. (t <= 1.15d-50))) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else
        tmp = (b + (y * (9.0d0 * x))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((t <= -8.1e+151) || !(t <= 1.15e-50)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = (b + (y * (9.0 * x))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (t <= -8.1e+151) or not (t <= 1.15e-50):
		tmp = a * ((t * -4.0) / c_m)
	else:
		tmp = (b + (y * (9.0 * x))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((t <= -8.1e+151) || !(t <= 1.15e-50))
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	else
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((t <= -8.1e+151) || ~((t <= 1.15e-50)))
		tmp = a * ((t * -4.0) / c_m);
	else
		tmp = (b + (y * (9.0 * x))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[t, -8.1e+151], N[Not[LessEqual[t, 1.15e-50]], $MachinePrecision]], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -8.1000000000000004e151 or 1.1500000000000001e-50 < t

   1. Initial program 71.4%

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

      1. associate-+l- 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-*r* 81.1%

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

      4. *-commutative 81.1%

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

      5. associate-+l- 81.1%

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

      6. associate-*l* 81.1%

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

      7. associate-*l* 77.1%

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

      8. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-/l* 59.5%

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

      3. associate-*r* 59.5%

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

      4. associate-*l/ 59.5%

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

   7. Simplified 59.5%

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

   if -8.1000000000000004e151 < t < 1.1500000000000001e-50

   1. Initial program 86.8%

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

      1. associate-+l- 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*r* 84.7%

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

      4. *-commutative 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. associate-*l* 88.8%

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

      8. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 74.8%

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

      1. associate-*r* 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+151} \lor \neg \left(t \leq 1.15 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-30} \lor \neg \left(z \leq 1.05 \cdot 10^{-19}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -2.4e-30) (not (<= z 1.05e-19)))
    (* a (/ (* t -4.0) c_m))
    (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.4e-30) || !(z <= 1.05e-19)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-2.4d-30)) .or. (.not. (z <= 1.05d-19))) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.4e-30) || !(z <= 1.05e-19)) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -2.4e-30) or not (z <= 1.05e-19):
		tmp = a * ((t * -4.0) / c_m)
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -2.4e-30) || !(z <= 1.05e-19))
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -2.4e-30) || ~((z <= 1.05e-19)))
		tmp = a * ((t * -4.0) / c_m);
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -2.4e-30], N[Not[LessEqual[z, 1.05e-19]], $MachinePrecision]], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999985e-30 or 1.0499999999999999e-19 < z

   1. Initial program 67.6%

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

      1. associate-+l- 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

      6. associate-*l* 73.8%

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

      7. associate-*l* 78.5%

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

      8. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in z around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. associate-/l* 58.5%

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

      3. associate-*r* 58.5%

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

      4. associate-*l/ 58.5%

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

   7. Simplified 58.5%

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

   if -2.39999999999999985e-30 < z < 1.0499999999999999e-19

   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. Step-by-step derivation

      1. associate-+l- 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r* 94.5%

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

      4. *-commutative 94.5%

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

      5. associate-+l- 94.5%

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

      6. associate-*l* 94.5%

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

      7. associate-*l* 89.7%

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

      8. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in b around inf 49.5%

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

      1. *-commutative 49.5%

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

   7. Simplified 49.5%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-30} \lor \neg \left(z \leq 1.05 \cdot 10^{-19}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-29} \lor \neg \left(z \leq 6 \cdot 10^{-20}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -2.5e-29) (not (<= z 6e-20)))
    (* a (* t (/ -4.0 c_m)))
    (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.5e-29) || !(z <= 6e-20)) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-2.5d-29)) .or. (.not. (z <= 6d-20))) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.5e-29) || !(z <= 6e-20)) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -2.5e-29) or not (z <= 6e-20):
		tmp = a * (t * (-4.0 / c_m))
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -2.5e-29) || !(z <= 6e-20))
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -2.5e-29) || ~((z <= 6e-20)))
		tmp = a * (t * (-4.0 / c_m));
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -2.5e-29], N[Not[LessEqual[z, 6e-20]], $MachinePrecision]], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999993e-29 or 6.00000000000000057e-20 < z

   1. Initial program 67.6%

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

      1. associate-+l- 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

      6. associate-*l* 73.8%

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

      7. associate-*l* 78.5%

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

      8. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in y around inf 73.0%

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

   6. Taylor expanded in c around 0 72.0%

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

   7. Taylor expanded in z around inf 57.5%

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

      1. associate-*r/ 58.5%

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

      2. associate-*r* 58.5%

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

      3. *-commutative 58.5%

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

      4. associate-*r* 58.5%

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

      5. associate-*r/ 58.5%

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

      6. *-commutative 58.5%

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

      7. associate-/l* 58.4%

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

   9. Simplified 58.4%

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

   if -2.49999999999999993e-29 < z < 6.00000000000000057e-20

   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. Step-by-step derivation

      1. associate-+l- 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r* 94.5%

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

      4. *-commutative 94.5%

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

      5. associate-+l- 94.5%

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

      6. associate-*l* 94.5%

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

      7. associate-*l* 89.7%

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

      8. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in b around inf 49.5%

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

      1. *-commutative 49.5%

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

   7. Simplified 49.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-29} \lor \neg \left(z \leq 6 \cdot 10^{-20}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2800000:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -2800000.0)
    (* -4.0 (/ (* a t) c_m))
    (if (<= z 4.2e-20) (/ b (* c_m z)) (* a (/ (* t -4.0) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2800000.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else if (z <= 4.2e-20) {
		tmp = b / (c_m * z);
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (z <= (-2800000.0d0)) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else if (z <= 4.2d-20) then
        tmp = b / (c_m * z)
    else
        tmp = a * ((t * (-4.0d0)) / c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2800000.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else if (z <= 4.2e-20) {
		tmp = b / (c_m * z);
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -2800000.0:
		tmp = -4.0 * ((a * t) / c_m)
	elif z <= 4.2e-20:
		tmp = b / (c_m * z)
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -2800000.0)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	elseif (z <= 4.2e-20)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -2800000.0)
		tmp = -4.0 * ((a * t) / c_m);
	elseif (z <= 4.2e-20)
		tmp = b / (c_m * z);
	else
		tmp = a * ((t * -4.0) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -2800000.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-20], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e6

   1. Initial program 60.6%

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

      1. associate-+l- 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-*r* 68.7%

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

      4. *-commutative 68.7%

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

      5. associate-+l- 68.7%

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

      6. associate-*l* 68.7%

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

      7. associate-*l* 72.3%

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

      8. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

   7. Simplified 62.0%

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

   if -2.8e6 < z < 4.1999999999999998e-20

   1. Initial program 94.6%

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

      1. associate-+l- 94.6%

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

      2. *-commutative 94.6%

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

      3. associate-*r* 94.3%

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

      4. *-commutative 94.3%

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

      5. associate-+l- 94.3%

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

      6. associate-*l* 94.3%

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

      7. associate-*l* 90.0%

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

      8. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

   7. Simplified 47.8%

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

   if 4.1999999999999998e-20 < z

   1. Initial program 69.0%

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

      1. associate-+l- 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*r* 74.5%

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

      4. *-commutative 74.5%

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

      5. associate-+l- 74.5%

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

      6. associate-*l* 74.5%

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

      7. associate-*l* 81.2%

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

      8. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-/l* 59.2%

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

      3. associate-*r* 59.2%

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

      4. associate-*l/ 59.2%

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

   7. Simplified 59.2%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (* c_s (if (<= t -9e-70) (/ (/ b c_m) z) (/ (/ b z) c_m))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -9e-70) {
		tmp = (b / c_m) / z;
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-9d-70)) then
        tmp = (b / c_m) / z
    else
        tmp = (b / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -9e-70) {
		tmp = (b / c_m) / z;
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -9e-70:
		tmp = (b / c_m) / z
	else:
		tmp = (b / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -9e-70)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = Float64(Float64(b / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -9e-70)
		tmp = (b / c_m) / z;
	else
		tmp = (b / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -9e-70], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000044e-70

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 79.8%

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

      4. *-commutative 79.8%

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

      5. associate-+l- 79.8%

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

      6. associate-*l* 79.8%

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

      7. associate-*l* 78.5%

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

      8. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in b around inf 32.2%

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

      1. associate-/r* 39.1%

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

   7. Simplified 39.1%

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

   if -9.00000000000000044e-70 < t

   1. Initial program 83.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 84.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 84.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 84.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 84.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 85.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 80.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. associate-*r* 80.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. *-commutative 80.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right)} \cdot y}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 80.2%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      6. *-commutative 80.2%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{z \cdot c} - \frac{\color{blue}{\left(4 \cdot z\right)} \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      7. associate-*l* 80.2%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{z \cdot c} - \frac{\color{blue}{4 \cdot \left(z \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

   6. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c} - \frac{4 \cdot \left(z \cdot \left(t \cdot a\right)\right) - b}{z \cdot c}} \]

   7. Taylor expanded in c around 0 89.2%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   8. Taylor expanded in b around inf 32.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 35.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-56}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (* c_s (if (<= t -4.2e-56) (/ (/ b c_m) z) (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -4.2e-56) {
		tmp = (b / c_m) / z;
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-4.2d-56)) then
        tmp = (b / c_m) / z
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -4.2e-56) {
		tmp = (b / c_m) / z;
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -4.2e-56:
		tmp = (b / c_m) / z
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -4.2e-56)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -4.2e-56)
		tmp = (b / c_m) / z;
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -4.2e-56], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000012e-56

   1. Initial program 71.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 31.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 38.5%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 38.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -4.20000000000000012e-56 < t

   1. Initial program 83.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 84.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 84.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 84.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 84.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 33.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 33.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 33.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-56}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 79.9%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 79.9%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 83.1%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 83.1%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 83.1%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 83.1%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 83.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 83.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 83.5%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 32.6%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 32.6%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 32.6%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 32.6%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer target: 79.9% 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 2024089 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))