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

Percentage Accurate: 79.1% → 90.5%

Time: 16.2s

Alternatives: 18

Speedup: 0.9×

• 37.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.1% 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: 90.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\\ t_3 := x \cdot \left(y \cdot 9\right)\\ t_4 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - t\_2\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_4 \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t\_1 + \frac{b + t\_3}{z}}{c\_m}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{b + \left(t\_3 - t\_2\right)}{z \cdot c\_m}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\frac{1}{c\_m} \cdot \left(t\_1 + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c\_m}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \end{array} \]

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.
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 (* t (* a -4.0)))
        (t_2 (* a (* t (* z 4.0))))
        (t_3 (* x (* y 9.0)))
        (t_4 (/ (+ b (- (* y (* 9.0 x)) t_2)) (* z c_m))))
   (*
    c_s
    (if (<= t_4 5e+42)
      (/ (+ t_1 (/ (+ b t_3) z)) c_m)
      (if (<= t_4 2e+285)
        (/ (+ b (- t_3 t_2)) (* z c_m))
        (if (<= t_4 INFINITY)
          (* (/ 1.0 c_m) (+ t_1 (/ (+ b (* 9.0 (* y x))) z)))
          (+ (/ x (/ c_m (/ (* y 9.0) z))) (/ a (/ c_m (* t -4.0))))))))))

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);
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 = t * (a * -4.0);
	double t_2 = a * (t * (z * 4.0));
	double t_3 = x * (y * 9.0);
	double t_4 = (b + ((y * (9.0 * x)) - t_2)) / (z * c_m);
	double tmp;
	if (t_4 <= 5e+42) {
		tmp = (t_1 + ((b + t_3) / z)) / c_m;
	} else if (t_4 <= 2e+285) {
		tmp = (b + (t_3 - t_2)) / (z * c_m);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (1.0 / c_m) * (t_1 + ((b + (9.0 * (y * x))) / z));
	} else {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	}
	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;
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 = t * (a * -4.0);
	double t_2 = a * (t * (z * 4.0));
	double t_3 = x * (y * 9.0);
	double t_4 = (b + ((y * (9.0 * x)) - t_2)) / (z * c_m);
	double tmp;
	if (t_4 <= 5e+42) {
		tmp = (t_1 + ((b + t_3) / z)) / c_m;
	} else if (t_4 <= 2e+285) {
		tmp = (b + (t_3 - t_2)) / (z * c_m);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / c_m) * (t_1 + ((b + (9.0 * (y * x))) / z));
	} else {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	}
	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])
[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 = t * (a * -4.0)
	t_2 = a * (t * (z * 4.0))
	t_3 = x * (y * 9.0)
	t_4 = (b + ((y * (9.0 * x)) - t_2)) / (z * c_m)
	tmp = 0
	if t_4 <= 5e+42:
		tmp = (t_1 + ((b + t_3) / z)) / c_m
	elif t_4 <= 2e+285:
		tmp = (b + (t_3 - t_2)) / (z * c_m)
	elif t_4 <= math.inf:
		tmp = (1.0 / c_m) * (t_1 + ((b + (9.0 * (y * x))) / z))
	else:
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)))
	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])
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(t * Float64(a * -4.0))
	t_2 = Float64(a * Float64(t * Float64(z * 4.0)))
	t_3 = Float64(x * Float64(y * 9.0))
	t_4 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - t_2)) / Float64(z * c_m))
	tmp = 0.0
	if (t_4 <= 5e+42)
		tmp = Float64(Float64(t_1 + Float64(Float64(b + t_3) / z)) / c_m);
	elseif (t_4 <= 2e+285)
		tmp = Float64(Float64(b + Float64(t_3 - t_2)) / Float64(z * c_m));
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(1.0 / c_m) * Float64(t_1 + Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z)));
	else
		tmp = Float64(Float64(x / Float64(c_m / Float64(Float64(y * 9.0) / z))) + Float64(a / Float64(c_m / Float64(t * -4.0))));
	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])){:}
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 = t * (a * -4.0);
	t_2 = a * (t * (z * 4.0));
	t_3 = x * (y * 9.0);
	t_4 = (b + ((y * (9.0 * x)) - t_2)) / (z * c_m);
	tmp = 0.0;
	if (t_4 <= 5e+42)
		tmp = (t_1 + ((b + t_3) / z)) / c_m;
	elseif (t_4 <= 2e+285)
		tmp = (b + (t_3 - t_2)) / (z * c_m);
	elseif (t_4 <= Inf)
		tmp = (1.0 / c_m) * (t_1 + ((b + (9.0 * (y * x))) / z));
	else
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	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.
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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$4, 5e+42], N[(N[(t$95$1 + N[(N[(b + t$95$3), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$4, 2e+285], N[(N[(b + N[(t$95$3 - t$95$2), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(1.0 / c$95$m), $MachinePrecision] * N[(t$95$1 + N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(c$95$m / N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 5.00000000000000007e42

   1. Initial program 87.7%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 94.3%

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

   if 5.00000000000000007e42 < (/.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)) < 2e285

   1. Initial program 97.7%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 97.7%

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

   4. Applied egg-rr 97.7%

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

   if 2e285 < (/.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 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-/r* N/A

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

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

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

   3. Simplified 90.4%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

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

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

      7. associate-*r* N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

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

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

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

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

      14. *-lowering-*.f64 90.4%

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

   6. Applied egg-rr 90.4%

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

   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-/r* N/A

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

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

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

   3. Simplified 32.8%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 66.6%

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

   10. Simplified 66.6%

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

   12. Applied egg-rr 99.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right) + t \cdot \left(a \cdot -4\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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
         (/ (+ (* y (+ (/ (* 9.0 x) z) (/ b (* z y)))) (* t (* a -4.0))) c_m)))
   (*
    c_s
    (if (<= z -1.2e+24)
      t_1
      (if (<= z 3.4e+56)
        (/ (+ b (- (* y (* 9.0 x)) (* t (* a (* z 4.0))))) (* z c_m))
        t_1)))))

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);
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 = ((y * (((9.0 * x) / z) + (b / (z * y)))) + (t * (a * -4.0))) / c_m;
	double tmp;
	if (z <= -1.2e+24) {
		tmp = t_1;
	} else if (z <= 3.4e+56) {
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c_m);
	} else {
		tmp = t_1;
	}
	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.
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) :: tmp
    t_1 = ((y * (((9.0d0 * x) / z) + (b / (z * y)))) + (t * (a * (-4.0d0)))) / c_m
    if (z <= (-1.2d+24)) then
        tmp = t_1
    else if (z <= 3.4d+56) then
        tmp = (b + ((y * (9.0d0 * x)) - (t * (a * (z * 4.0d0))))) / (z * c_m)
    else
        tmp = t_1
    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;
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 = ((y * (((9.0 * x) / z) + (b / (z * y)))) + (t * (a * -4.0))) / c_m;
	double tmp;
	if (z <= -1.2e+24) {
		tmp = t_1;
	} else if (z <= 3.4e+56) {
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c_m);
	} else {
		tmp = t_1;
	}
	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])
[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 = ((y * (((9.0 * x) / z) + (b / (z * y)))) + (t * (a * -4.0))) / c_m
	tmp = 0
	if z <= -1.2e+24:
		tmp = t_1
	elif z <= 3.4e+56:
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c_m)
	else:
		tmp = t_1
	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])
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(Float64(y * Float64(Float64(Float64(9.0 * x) / z) + Float64(b / Float64(z * y)))) + Float64(t * Float64(a * -4.0))) / c_m)
	tmp = 0.0
	if (z <= -1.2e+24)
		tmp = t_1;
	elseif (z <= 3.4e+56)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(z * c_m));
	else
		tmp = t_1;
	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])){:}
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 = ((y * (((9.0 * x) / z) + (b / (z * y)))) + (t * (a * -4.0))) / c_m;
	tmp = 0.0;
	if (z <= -1.2e+24)
		tmp = t_1;
	elseif (z <= 3.4e+56)
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c_m);
	else
		tmp = t_1;
	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.
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[(N[(y * N[(N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.2e+24], t$95$1, If[LessEqual[z, 3.4e+56], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e24 or 3.40000000000000001e56 < z

   1. Initial program 64.1%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 86.3%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 89.5%

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

   7. Simplified 89.5%

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

   if -1.2e24 < z < 3.40000000000000001e56

   1. Initial program 95.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 96.5%

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

   4. Applied egg-rr 96.5%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\frac{c\_m}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c\_m}{t \cdot -4}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \frac{9 \cdot x}{z}}{c\_m}\\ \end{array} \end{array} \]

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.
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 -1e+97)
    (+ (/ x (/ c_m (/ (* y 9.0) z))) (/ a (/ c_m (* t -4.0))))
    (if (<= z 3.5e-62)
      (/ (+ b (* 9.0 (* y x))) (* z c_m))
      (/ (+ (* t (* a -4.0)) (* y (/ (* 9.0 x) 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);
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 <= -1e+97) {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	} else if (z <= 3.5e-62) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = ((t * (a * -4.0)) + (y * ((9.0 * x) / 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.
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 <= (-1d+97)) then
        tmp = (x / (c_m / ((y * 9.0d0) / z))) + (a / (c_m / (t * (-4.0d0))))
    else if (z <= 3.5d-62) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c_m)
    else
        tmp = ((t * (a * (-4.0d0))) + (y * ((9.0d0 * x) / 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;
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 <= -1e+97) {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	} else if (z <= 3.5e-62) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = ((t * (a * -4.0)) + (y * ((9.0 * x) / 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])
[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 <= -1e+97:
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)))
	elif z <= 3.5e-62:
		tmp = (b + (9.0 * (y * x))) / (z * c_m)
	else:
		tmp = ((t * (a * -4.0)) + (y * ((9.0 * x) / 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])
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 <= -1e+97)
		tmp = Float64(Float64(x / Float64(c_m / Float64(Float64(y * 9.0) / z))) + Float64(a / Float64(c_m / Float64(t * -4.0))));
	elseif (z <= 3.5e-62)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(y * Float64(Float64(9.0 * x) / 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])){:}
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 <= -1e+97)
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	elseif (z <= 3.5e-62)
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	else
		tmp = ((t * (a * -4.0)) + (y * ((9.0 * x) / 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.
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, -1e+97], N[(N[(x / N[(c$95$m / N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-62], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.0000000000000001e97

   1. Initial program 58.7%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 79.0%

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

   10. Simplified 79.0%

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

   12. Applied egg-rr 85.5%

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

   if -1.0000000000000001e97 < z < 3.5000000000000001e-62

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 87.7%

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

   5. Simplified 87.7%

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

   if 3.5000000000000001e-62 < z

   1. Initial program 74.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 78.6%

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

   10. Simplified 78.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\frac{c}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c}{t \cdot -4}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \frac{9 \cdot x}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + y \cdot \frac{9 \cdot x}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (+ (* t (* a -4.0)) (* y (/ (* 9.0 x) z))) c_m)))
   (*
    c_s
    (if (<= z -3.4e+96)
      t_1
      (if (<= z 8.9e-63) (/ (+ b (* 9.0 (* y x))) (* z c_m)) t_1)))))

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);
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 = ((t * (a * -4.0)) + (y * ((9.0 * x) / z))) / c_m;
	double tmp;
	if (z <= -3.4e+96) {
		tmp = t_1;
	} else if (z <= 8.9e-63) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = t_1;
	}
	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.
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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (y * ((9.0d0 * x) / z))) / c_m
    if (z <= (-3.4d+96)) then
        tmp = t_1
    else if (z <= 8.9d-63) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c_m)
    else
        tmp = t_1
    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;
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 = ((t * (a * -4.0)) + (y * ((9.0 * x) / z))) / c_m;
	double tmp;
	if (z <= -3.4e+96) {
		tmp = t_1;
	} else if (z <= 8.9e-63) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = t_1;
	}
	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])
[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 = ((t * (a * -4.0)) + (y * ((9.0 * x) / z))) / c_m
	tmp = 0
	if z <= -3.4e+96:
		tmp = t_1
	elif z <= 8.9e-63:
		tmp = (b + (9.0 * (y * x))) / (z * c_m)
	else:
		tmp = t_1
	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])
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(Float64(t * Float64(a * -4.0)) + Float64(y * Float64(Float64(9.0 * x) / z))) / c_m)
	tmp = 0.0
	if (z <= -3.4e+96)
		tmp = t_1;
	elseif (z <= 8.9e-63)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c_m));
	else
		tmp = t_1;
	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])){:}
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 = ((t * (a * -4.0)) + (y * ((9.0 * x) / z))) / c_m;
	tmp = 0.0;
	if (z <= -3.4e+96)
		tmp = t_1;
	elseif (z <= 8.9e-63)
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	else
		tmp = t_1;
	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.
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[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -3.4e+96], t$95$1, If[LessEqual[z, 8.9e-63], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e96 or 8.89999999999999988e-63 < z

   1. Initial program 67.2%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 78.7%

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

   10. Simplified 78.7%

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

   if -3.4000000000000001e96 < z < 8.89999999999999988e-63

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \frac{9 \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 8.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \frac{9 \cdot x}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.3 \cdot 10^{+201}:\\ \;\;\;\;\frac{1}{c\_m} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c\_m}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 1.3e+201)
    (* (/ 1.0 c_m) (+ (* t (* a -4.0)) (/ (+ b (* 9.0 (* y x))) z)))
    (+ (/ x (/ c_m (/ (* y 9.0) z))) (/ a (/ c_m (* t -4.0)))))))

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);
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 <= 1.3e+201) {
		tmp = (1.0 / c_m) * ((t * (a * -4.0)) + ((b + (9.0 * (y * x))) / z));
	} else {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	}
	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.
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 <= 1.3d+201) then
        tmp = (1.0d0 / c_m) * ((t * (a * (-4.0d0))) + ((b + (9.0d0 * (y * x))) / z))
    else
        tmp = (x / (c_m / ((y * 9.0d0) / z))) + (a / (c_m / (t * (-4.0d0))))
    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;
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 <= 1.3e+201) {
		tmp = (1.0 / c_m) * ((t * (a * -4.0)) + ((b + (9.0 * (y * x))) / z));
	} else {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	}
	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])
[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 <= 1.3e+201:
		tmp = (1.0 / c_m) * ((t * (a * -4.0)) + ((b + (9.0 * (y * x))) / z))
	else:
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)))
	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])
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 <= 1.3e+201)
		tmp = Float64(Float64(1.0 / c_m) * Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z)));
	else
		tmp = Float64(Float64(x / Float64(c_m / Float64(Float64(y * 9.0) / z))) + Float64(a / Float64(c_m / Float64(t * -4.0))));
	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])){:}
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 <= 1.3e+201)
		tmp = (1.0 / c_m) * ((t * (a * -4.0)) + ((b + (9.0 * (y * x))) / z));
	else
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	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.
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, 1.3e+201], N[(N[(1.0 / c$95$m), $MachinePrecision] * N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(c$95$m / N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.29999999999999993e201

   1. Initial program 81.8%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 87.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

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

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

      7. associate-*r* N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

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

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

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

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

      14. *-lowering-*.f64 87.8%

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

   6. Applied egg-rr 87.8%

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

   if 1.29999999999999993e201 < c

   1. Initial program 63.4%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 58.3%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 52.2%

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

   10. Simplified 52.2%

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

   12. Applied egg-rr 51.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.3 \cdot 10^{+201}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-78}:\\ \;\;\;\;\frac{y \cdot \frac{9 \cdot x}{z}}{c\_m}\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 -1.65e+132)
    (* (* t -4.0) (/ a c_m))
    (if (<= z -1.66e-78)
      (/ (* y (/ (* 9.0 x) z)) c_m)
      (if (<= z 1.05) (/ b (* z c_m)) (/ a (/ c_m (* t -4.0))))))))

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);
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 <= -1.65e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -1.66e-78) {
		tmp = (y * ((9.0 * x) / z)) / c_m;
	} else if (z <= 1.05) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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.
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 <= (-1.65d+132)) then
        tmp = (t * (-4.0d0)) * (a / c_m)
    else if (z <= (-1.66d-78)) then
        tmp = (y * ((9.0d0 * x) / z)) / c_m
    else if (z <= 1.05d0) then
        tmp = b / (z * c_m)
    else
        tmp = a / (c_m / (t * (-4.0d0)))
    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;
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 <= -1.65e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -1.66e-78) {
		tmp = (y * ((9.0 * x) / z)) / c_m;
	} else if (z <= 1.05) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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])
[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 <= -1.65e+132:
		tmp = (t * -4.0) * (a / c_m)
	elif z <= -1.66e-78:
		tmp = (y * ((9.0 * x) / z)) / c_m
	elif z <= 1.05:
		tmp = b / (z * c_m)
	else:
		tmp = a / (c_m / (t * -4.0))
	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])
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 <= -1.65e+132)
		tmp = Float64(Float64(t * -4.0) * Float64(a / c_m));
	elseif (z <= -1.66e-78)
		tmp = Float64(Float64(y * Float64(Float64(9.0 * x) / z)) / c_m);
	elseif (z <= 1.05)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(a / Float64(c_m / Float64(t * -4.0)));
	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])){:}
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 <= -1.65e+132)
		tmp = (t * -4.0) * (a / c_m);
	elseif (z <= -1.66e-78)
		tmp = (y * ((9.0 * x) / z)) / c_m;
	elseif (z <= 1.05)
		tmp = b / (z * c_m);
	else
		tmp = a / (c_m / (t * -4.0));
	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.
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, -1.65e+132], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.66e-78], N[(N[(y * N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[z, 1.05], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -1.65000000000000015e132

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 34.6%

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

   5. Simplified 34.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 46.1%

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

   7. Applied egg-rr 46.1%

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

      1. *-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. *-lowering-*.f64 65.9%

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

   9. Applied egg-rr 65.9%

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

   if -1.65000000000000015e132 < z < -1.6600000000000001e-78

   1. Initial program 89.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

      12. associate-*l* N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

      6. *-lowering-*.f64 54.6%

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

   7. Simplified 54.6%

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

      1. *-commutative N/A

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

      2. un-div-inv N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

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

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

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

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

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

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

      8. /-lowering-/.f64 51.6%

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

   9. Applied egg-rr 51.6%

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

       1. associate-*r/ N/A

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

       2. associate-*l/ N/A

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

       3. associate-*r* N/A

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

       4. associate-*r/ N/A

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

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

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

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

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

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

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

       8. *-lowering-*.f64 61.6%

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

   11. Applied egg-rr 61.6%

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

   if -1.6600000000000001e-78 < z < 1.05000000000000004

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 56.6%

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

   5. Simplified 56.6%

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

   if 1.05000000000000004 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 44.6%

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

   5. Simplified 44.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 59.1%

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

   7. Applied egg-rr 59.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. *-rgt-identity N/A

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

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

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot 1}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot \color{blue}{\left(-4 \cdot 1\right)}}\right)\right) \]

      12. metadata-eval N/A

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

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

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

      14. *-lowering-*.f64 63.5%

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

   9. Applied egg-rr 63.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-78}:\\ \;\;\;\;\frac{y \cdot \frac{9 \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{\frac{c\_m}{\frac{y \cdot 9}{z}}}\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 -2.5e+132)
    (* (* t -4.0) (/ a c_m))
    (if (<= z -2.9e-75)
      (/ x (/ c_m (/ (* y 9.0) z)))
      (if (<= z 0.6) (/ b (* z c_m)) (/ a (/ c_m (* t -4.0))))))))

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);
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+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -2.9e-75) {
		tmp = x / (c_m / ((y * 9.0) / z));
	} else if (z <= 0.6) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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.
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+132)) then
        tmp = (t * (-4.0d0)) * (a / c_m)
    else if (z <= (-2.9d-75)) then
        tmp = x / (c_m / ((y * 9.0d0) / z))
    else if (z <= 0.6d0) then
        tmp = b / (z * c_m)
    else
        tmp = a / (c_m / (t * (-4.0d0)))
    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;
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+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -2.9e-75) {
		tmp = x / (c_m / ((y * 9.0) / z));
	} else if (z <= 0.6) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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])
[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+132:
		tmp = (t * -4.0) * (a / c_m)
	elif z <= -2.9e-75:
		tmp = x / (c_m / ((y * 9.0) / z))
	elif z <= 0.6:
		tmp = b / (z * c_m)
	else:
		tmp = a / (c_m / (t * -4.0))
	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])
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+132)
		tmp = Float64(Float64(t * -4.0) * Float64(a / c_m));
	elseif (z <= -2.9e-75)
		tmp = Float64(x / Float64(c_m / Float64(Float64(y * 9.0) / z)));
	elseif (z <= 0.6)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(a / Float64(c_m / Float64(t * -4.0)));
	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])){:}
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+132)
		tmp = (t * -4.0) * (a / c_m);
	elseif (z <= -2.9e-75)
		tmp = x / (c_m / ((y * 9.0) / z));
	elseif (z <= 0.6)
		tmp = b / (z * c_m);
	else
		tmp = a / (c_m / (t * -4.0));
	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.
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, -2.5e+132], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-75], N[(x / N[(c$95$m / N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -2.5000000000000001e132

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 34.6%

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

   5. Simplified 34.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 46.1%

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

   7. Applied egg-rr 46.1%

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

      1. *-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. *-lowering-*.f64 65.9%

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

   9. Applied egg-rr 65.9%

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

   if -2.5000000000000001e132 < z < -2.9000000000000002e-75

   1. Initial program 89.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

      12. associate-*l* N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

      6. *-lowering-*.f64 54.6%

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

   7. Simplified 54.6%

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

      1. *-commutative N/A

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

      2. un-div-inv N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

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

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

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

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

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

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

      8. /-lowering-/.f64 51.6%

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

   9. Applied egg-rr 51.6%

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

       1. *-commutative N/A

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

       2. clear-num N/A

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

       3. frac-times N/A

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

       4. *-rgt-identity N/A

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

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

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

       6. clear-num N/A

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

       7. un-div-inv N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. *-lowering-*.f64 60.6%

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

   11. Applied egg-rr 60.6%

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

   if -2.9000000000000002e-75 < z < 0.599999999999999978

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 56.6%

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

   5. Simplified 56.6%

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

   if 0.599999999999999978 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 44.6%

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

   5. Simplified 44.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 59.1%

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

   7. Applied egg-rr 59.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. *-rgt-identity N/A

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

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

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot 1}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot \color{blue}{\left(-4 \cdot 1\right)}}\right)\right) \]

      12. metadata-eval N/A

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

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

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

      14. *-lowering-*.f64 63.5%

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

   9. Applied egg-rr 63.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{\frac{c}{\frac{y \cdot 9}{z}}}\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-76}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{x}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 0.37:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 -1.75e+132)
    (* (* t -4.0) (/ a c_m))
    (if (<= z -1.5e-76)
      (* (* y 9.0) (/ x (* z c_m)))
      (if (<= z 0.37) (/ b (* z c_m)) (/ a (/ c_m (* t -4.0))))))))

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);
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 <= -1.75e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -1.5e-76) {
		tmp = (y * 9.0) * (x / (z * c_m));
	} else if (z <= 0.37) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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.
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 <= (-1.75d+132)) then
        tmp = (t * (-4.0d0)) * (a / c_m)
    else if (z <= (-1.5d-76)) then
        tmp = (y * 9.0d0) * (x / (z * c_m))
    else if (z <= 0.37d0) then
        tmp = b / (z * c_m)
    else
        tmp = a / (c_m / (t * (-4.0d0)))
    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;
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 <= -1.75e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -1.5e-76) {
		tmp = (y * 9.0) * (x / (z * c_m));
	} else if (z <= 0.37) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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])
[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 <= -1.75e+132:
		tmp = (t * -4.0) * (a / c_m)
	elif z <= -1.5e-76:
		tmp = (y * 9.0) * (x / (z * c_m))
	elif z <= 0.37:
		tmp = b / (z * c_m)
	else:
		tmp = a / (c_m / (t * -4.0))
	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])
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 <= -1.75e+132)
		tmp = Float64(Float64(t * -4.0) * Float64(a / c_m));
	elseif (z <= -1.5e-76)
		tmp = Float64(Float64(y * 9.0) * Float64(x / Float64(z * c_m)));
	elseif (z <= 0.37)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(a / Float64(c_m / Float64(t * -4.0)));
	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])){:}
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 <= -1.75e+132)
		tmp = (t * -4.0) * (a / c_m);
	elseif (z <= -1.5e-76)
		tmp = (y * 9.0) * (x / (z * c_m));
	elseif (z <= 0.37)
		tmp = b / (z * c_m);
	else
		tmp = a / (c_m / (t * -4.0));
	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.
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, -1.75e+132], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-76], N[(N[(y * 9.0), $MachinePrecision] * N[(x / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.37], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -1.7500000000000001e132

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 34.6%

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

   5. Simplified 34.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 46.1%

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

   7. Applied egg-rr 46.1%

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

      1. *-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. *-lowering-*.f64 65.9%

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

   9. Applied egg-rr 65.9%

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

   if -1.7500000000000001e132 < z < -1.50000000000000012e-76

   1. Initial program 89.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

      12. associate-*l* N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

      6. *-lowering-*.f64 54.6%

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

   7. Simplified 54.6%

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

      1. *-commutative N/A

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

      2. un-div-inv N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

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

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

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

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

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

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

      8. /-lowering-/.f64 51.6%

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

   9. Applied egg-rr 51.6%

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

       1. *-commutative N/A

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

       2. clear-num N/A

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

       3. associate-/r/ N/A

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

       4. associate-*r* N/A

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

       5. div-inv N/A

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

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

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

       7. clear-num N/A

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

       8. un-div-inv N/A

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

       9. clear-num N/A

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

       10. associate-*r/ N/A

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

       11. clear-num N/A

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

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

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

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

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

       14. *-lowering-*.f64 58.4%

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

   11. Applied egg-rr 58.4%

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

   if -1.50000000000000012e-76 < z < 0.37

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 56.6%

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

   5. Simplified 56.6%

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

   if 0.37 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 44.6%

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

   5. Simplified 44.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 59.1%

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

   7. Applied egg-rr 59.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. *-rgt-identity N/A

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

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

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot 1}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot \color{blue}{\left(-4 \cdot 1\right)}}\right)\right) \]

      12. metadata-eval N/A

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

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

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

      14. *-lowering-*.f64 63.5%

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

   9. Applied egg-rr 63.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-76}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.37:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-80}:\\ \;\;\;\;9 \cdot \frac{\frac{y \cdot x}{z}}{c\_m}\\ \mathbf{elif}\;z \leq 74:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 -1.65e+132)
    (* (* t -4.0) (/ a c_m))
    (if (<= z -5.3e-80)
      (* 9.0 (/ (/ (* y x) z) c_m))
      (if (<= z 74.0) (/ b (* z c_m)) (/ a (/ c_m (* t -4.0))))))))

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);
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 <= -1.65e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -5.3e-80) {
		tmp = 9.0 * (((y * x) / z) / c_m);
	} else if (z <= 74.0) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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.
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 <= (-1.65d+132)) then
        tmp = (t * (-4.0d0)) * (a / c_m)
    else if (z <= (-5.3d-80)) then
        tmp = 9.0d0 * (((y * x) / z) / c_m)
    else if (z <= 74.0d0) then
        tmp = b / (z * c_m)
    else
        tmp = a / (c_m / (t * (-4.0d0)))
    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;
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 <= -1.65e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= -5.3e-80) {
		tmp = 9.0 * (((y * x) / z) / c_m);
	} else if (z <= 74.0) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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])
[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 <= -1.65e+132:
		tmp = (t * -4.0) * (a / c_m)
	elif z <= -5.3e-80:
		tmp = 9.0 * (((y * x) / z) / c_m)
	elif z <= 74.0:
		tmp = b / (z * c_m)
	else:
		tmp = a / (c_m / (t * -4.0))
	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])
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 <= -1.65e+132)
		tmp = Float64(Float64(t * -4.0) * Float64(a / c_m));
	elseif (z <= -5.3e-80)
		tmp = Float64(9.0 * Float64(Float64(Float64(y * x) / z) / c_m));
	elseif (z <= 74.0)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(a / Float64(c_m / Float64(t * -4.0)));
	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])){:}
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 <= -1.65e+132)
		tmp = (t * -4.0) * (a / c_m);
	elseif (z <= -5.3e-80)
		tmp = 9.0 * (((y * x) / z) / c_m);
	elseif (z <= 74.0)
		tmp = b / (z * c_m);
	else
		tmp = a / (c_m / (t * -4.0));
	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.
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, -1.65e+132], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-80], N[(9.0 * N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 74.0], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -1.65000000000000015e132

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 34.6%

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

   5. Simplified 34.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 46.1%

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

   7. Applied egg-rr 46.1%

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

      1. *-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. *-lowering-*.f64 65.9%

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

   9. Applied egg-rr 65.9%

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

   if -1.65000000000000015e132 < z < -5.30000000000000026e-80

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

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

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

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

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

      6. *-lowering-*.f64 54.7%

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

   5. Simplified 54.7%

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

   if -5.30000000000000026e-80 < z < 74

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 56.6%

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

   5. Simplified 56.6%

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

   if 74 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 44.6%

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

   5. Simplified 44.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 59.1%

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

   7. Applied egg-rr 59.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. *-rgt-identity N/A

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

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

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\frac{\left(t \cdot -4\right) \cdot z}{z}}\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot \color{blue}{\frac{z}{z}}}\right)\right) \]

      10. *-inverses N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot 1}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot \color{blue}{\left(-4 \cdot 1\right)}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot -4}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \color{blue}{\left(t \cdot -4\right)}\right)\right) \]

      14. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right)\right) \]

   9. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t \cdot -4}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-80}:\\ \;\;\;\;9 \cdot \frac{\frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 74:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 8 \cdot 10^{+202}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c\_m}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 8e+202)
    (/ (+ (* t (* a -4.0)) (/ (+ b (* x (* y 9.0))) z)) c_m)
    (+ (/ x (/ c_m (/ (* y 9.0) z))) (/ a (/ c_m (* t -4.0)))))))

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);
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 <= 8e+202) {
		tmp = ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	}
	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.
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 <= 8d+202) then
        tmp = ((t * (a * (-4.0d0))) + ((b + (x * (y * 9.0d0))) / z)) / c_m
    else
        tmp = (x / (c_m / ((y * 9.0d0) / z))) + (a / (c_m / (t * (-4.0d0))))
    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;
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 <= 8e+202) {
		tmp = ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	}
	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])
[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 <= 8e+202:
		tmp = ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / z)) / c_m
	else:
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)))
	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])
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 <= 8e+202)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(x * Float64(y * 9.0))) / z)) / c_m);
	else
		tmp = Float64(Float64(x / Float64(c_m / Float64(Float64(y * 9.0) / z))) + Float64(a / Float64(c_m / Float64(t * -4.0))));
	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])){:}
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 <= 8e+202)
		tmp = ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	else
		tmp = (x / (c_m / ((y * 9.0) / z))) + (a / (c_m / (t * -4.0)));
	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.
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, 8e+202], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(x / N[(c$95$m / N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 7.9999999999999992e202

   1. Initial program 81.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   if 7.9999999999999992e202 < c

   1. Initial program 60.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 55.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(9 \cdot \frac{x}{z}\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{9 \cdot x}{z}\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot x\right), z\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \left(\frac{b}{y \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \mathsf{/.f64}\left(b, \left(y \cdot z\right)\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \mathsf{/.f64}\left(b, \left(z \cdot y\right)\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. *-lowering-*.f64 55.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right), \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, y\right)\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 55.1%

      \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(9 \cdot \frac{x}{z}\right)}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{9 \cdot x}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(9 \cdot x\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, x\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   10. Simplified 49.0%

       \[\leadsto \frac{y \cdot \color{blue}{\frac{9 \cdot x}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   12. Applied egg-rr 48.5%

       \[\leadsto \color{blue}{\frac{x}{\frac{c}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c}{t \cdot -4}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 8 \cdot 10^{+202}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c}{\frac{y \cdot 9}{z}}} + \frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(\frac{a \cdot -4}{c\_m} + \frac{\frac{b}{z}}{t \cdot c\_m}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

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.
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 -1.65e+132)
    (* t (+ (/ (* a -4.0) c_m) (/ (/ b z) (* t c_m))))
    (if (<= z 4.1e-66)
      (/ (+ b (* 9.0 (* y x))) (* z c_m))
      (/ (+ (* t (* a -4.0)) (/ 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);
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 <= -1.65e+132) {
		tmp = t * (((a * -4.0) / c_m) + ((b / z) / (t * c_m)));
	} else if (z <= 4.1e-66) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = ((t * (a * -4.0)) + (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.
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 <= (-1.65d+132)) then
        tmp = t * (((a * (-4.0d0)) / c_m) + ((b / z) / (t * c_m)))
    else if (z <= 4.1d-66) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c_m)
    else
        tmp = ((t * (a * (-4.0d0))) + (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;
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 <= -1.65e+132) {
		tmp = t * (((a * -4.0) / c_m) + ((b / z) / (t * c_m)));
	} else if (z <= 4.1e-66) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = ((t * (a * -4.0)) + (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])
[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 <= -1.65e+132:
		tmp = t * (((a * -4.0) / c_m) + ((b / z) / (t * c_m)))
	elif z <= 4.1e-66:
		tmp = (b + (9.0 * (y * x))) / (z * c_m)
	else:
		tmp = ((t * (a * -4.0)) + (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])
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 <= -1.65e+132)
		tmp = Float64(t * Float64(Float64(Float64(a * -4.0) / c_m) + Float64(Float64(b / z) / Float64(t * c_m))));
	elseif (z <= 4.1e-66)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + 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])){:}
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 <= -1.65e+132)
		tmp = t * (((a * -4.0) / c_m) + ((b / z) / (t * c_m)));
	elseif (z <= 4.1e-66)
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	else
		tmp = ((t * (a * -4.0)) + (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.
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, -1.65e+132], N[(t * N[(N[(N[(a * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] / N[(t * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-66], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000015e132

   1. Initial program 57.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{c} \cdot \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 83.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 83.6%

      \[\leadsto \color{blue}{\frac{1}{c} \cdot \left(\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 68.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(a, -4\right)\right)\right)\right) \]

   9. Simplified 68.3%

      \[\leadsto \frac{1}{c} \cdot \left(\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)\right) \]

   10. Taylor expanded in t around inf

       \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]
   11. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot \frac{a}{c}\right), \color{blue}{\left(\frac{b}{c \cdot \left(t \cdot z\right)}\right)}\right)\right) \]

       3. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-4 \cdot a}{c}\right), \left(\frac{\color{blue}{b}}{c \cdot \left(t \cdot z\right)}\right)\right)\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-4 \cdot a\right), c\right), \left(\frac{\color{blue}{b}}{c \cdot \left(t \cdot z\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \left(\frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \left(\frac{b}{\left(c \cdot t\right) \cdot \color{blue}{z}}\right)\right)\right) \]

       7. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \left(\frac{\frac{b}{c \cdot t}}{\color{blue}{z}}\right)\right)\right) \]

       8. associate-/l/ N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \left(\frac{b}{\color{blue}{z \cdot \left(c \cdot t\right)}}\right)\right)\right) \]

       9. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \left(\frac{\frac{b}{z}}{\color{blue}{c \cdot t}}\right)\right)\right) \]

       10. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \mathsf{/.f64}\left(\left(\frac{b}{z}\right), \color{blue}{\left(c \cdot t\right)}\right)\right)\right) \]

       11. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(\color{blue}{c} \cdot t\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(t \cdot \color{blue}{c}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 72.5%

           \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, a\right), c\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \color{blue}{c}\right)\right)\right)\right) \]

   12. Simplified 72.5%

       \[\leadsto \color{blue}{t \cdot \left(\frac{-4 \cdot a}{c} + \frac{\frac{b}{z}}{t \cdot c}\right)} \]

   if -1.65000000000000015e132 < z < 4.09999999999999998e-66

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 85.9%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 4.09999999999999998e-66 < z

   1. Initial program 74.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 75.0%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(\frac{a \cdot -4}{c} + \frac{\frac{b}{z}}{t \cdot c}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + \frac{b}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+132}:\\ \;\;\;\;\frac{1}{c\_m} \cdot t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{c\_m}\\ \end{array} \end{array} \end{array} \]

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.
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 (+ (* t (* a -4.0)) (/ b z))))
   (*
    c_s
    (if (<= z -1.75e+132)
      (* (/ 1.0 c_m) t_1)
      (if (<= z 1.02e-64) (/ (+ b (* 9.0 (* y x))) (* z c_m)) (/ t_1 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);
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 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -1.75e+132) {
		tmp = (1.0 / c_m) * t_1;
	} else if (z <= 1.02e-64) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = t_1 / 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.
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) :: tmp
    t_1 = (t * (a * (-4.0d0))) + (b / z)
    if (z <= (-1.75d+132)) then
        tmp = (1.0d0 / c_m) * t_1
    else if (z <= 1.02d-64) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c_m)
    else
        tmp = t_1 / 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;
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 = (t * (a * -4.0)) + (b / z);
	double tmp;
	if (z <= -1.75e+132) {
		tmp = (1.0 / c_m) * t_1;
	} else if (z <= 1.02e-64) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = t_1 / 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])
[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 = (t * (a * -4.0)) + (b / z)
	tmp = 0
	if z <= -1.75e+132:
		tmp = (1.0 / c_m) * t_1
	elif z <= 1.02e-64:
		tmp = (b + (9.0 * (y * x))) / (z * c_m)
	else:
		tmp = t_1 / 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])
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(t * Float64(a * -4.0)) + Float64(b / z))
	tmp = 0.0
	if (z <= -1.75e+132)
		tmp = Float64(Float64(1.0 / c_m) * t_1);
	elseif (z <= 1.02e-64)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c_m));
	else
		tmp = Float64(t_1 / 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])){:}
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 = (t * (a * -4.0)) + (b / z);
	tmp = 0.0;
	if (z <= -1.75e+132)
		tmp = (1.0 / c_m) * t_1;
	elseif (z <= 1.02e-64)
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	else
		tmp = t_1 / 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.
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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.75e+132], N[(N[(1.0 / c$95$m), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[z, 1.02e-64], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / c$95$m), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7500000000000001e132

   1. Initial program 57.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{c} \cdot \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c}\right), \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \left(\color{blue}{\frac{x \cdot \left(9 \cdot y\right) + b}{z}} + t \cdot \left(a \cdot -4\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right) \]

      14. *-lowering-*.f64 83.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right) \]

   6. Applied egg-rr 83.6%

      \[\leadsto \color{blue}{\frac{1}{c} \cdot \left(\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 68.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, c\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(a, -4\right)\right)\right)\right) \]

   9. Simplified 68.3%

      \[\leadsto \frac{1}{c} \cdot \left(\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)\right) \]

   if -1.7500000000000001e132 < z < 1.02e-64

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 85.9%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 1.02e-64 < z

   1. Initial program 74.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 75.0%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+132}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right) + \frac{b}{z}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (+ (* t (* a -4.0)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= z -1.75e+132)
      t_1
      (if (<= z 1.3e-64) (/ (+ b (* 9.0 (* y x))) (* z c_m)) t_1)))))

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);
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 = ((t * (a * -4.0)) + (b / z)) / c_m;
	double tmp;
	if (z <= -1.75e+132) {
		tmp = t_1;
	} else if (z <= 1.3e-64) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = t_1;
	}
	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.
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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c_m
    if (z <= (-1.75d+132)) then
        tmp = t_1
    else if (z <= 1.3d-64) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c_m)
    else
        tmp = t_1
    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;
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 = ((t * (a * -4.0)) + (b / z)) / c_m;
	double tmp;
	if (z <= -1.75e+132) {
		tmp = t_1;
	} else if (z <= 1.3e-64) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = t_1;
	}
	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])
[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 = ((t * (a * -4.0)) + (b / z)) / c_m
	tmp = 0
	if z <= -1.75e+132:
		tmp = t_1
	elif z <= 1.3e-64:
		tmp = (b + (9.0 * (y * x))) / (z * c_m)
	else:
		tmp = t_1
	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])
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(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (z <= -1.75e+132)
		tmp = t_1;
	elseif (z <= 1.3e-64)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c_m));
	else
		tmp = t_1;
	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])){:}
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 = ((t * (a * -4.0)) + (b / z)) / c_m;
	tmp = 0.0;
	if (z <= -1.75e+132)
		tmp = t_1;
	elseif (z <= 1.3e-64)
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	else
		tmp = t_1;
	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.
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[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.75e+132], t$95$1, If[LessEqual[z, 1.3e-64], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e132 or 1.3e-64 < z

   1. Initial program 67.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 72.3%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -1.7500000000000001e132 < z < 1.3e-64

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 85.9%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+132}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq 130:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 -3.1e+132)
    (* (* t -4.0) (/ a c_m))
    (if (<= z 130.0)
      (/ (+ b (* 9.0 (* y x))) (* z c_m))
      (/ a (/ c_m (* t -4.0)))))))

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);
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 <= -3.1e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= 130.0) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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.
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 <= (-3.1d+132)) then
        tmp = (t * (-4.0d0)) * (a / c_m)
    else if (z <= 130.0d0) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c_m)
    else
        tmp = a / (c_m / (t * (-4.0d0)))
    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;
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 <= -3.1e+132) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= 130.0) {
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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])
[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 <= -3.1e+132:
		tmp = (t * -4.0) * (a / c_m)
	elif z <= 130.0:
		tmp = (b + (9.0 * (y * x))) / (z * c_m)
	else:
		tmp = a / (c_m / (t * -4.0))
	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])
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 <= -3.1e+132)
		tmp = Float64(Float64(t * -4.0) * Float64(a / c_m));
	elseif (z <= 130.0)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c_m));
	else
		tmp = Float64(a / Float64(c_m / Float64(t * -4.0)));
	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])){:}
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 <= -3.1e+132)
		tmp = (t * -4.0) * (a / c_m);
	elseif (z <= 130.0)
		tmp = (b + (9.0 * (y * x))) / (z * c_m);
	else
		tmp = a / (c_m / (t * -4.0));
	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.
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, -3.1e+132], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 130.0], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.0999999999999998e132

   1. Initial program 57.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. *-lowering-*.f64 34.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 34.6%

      \[\leadsto \frac{\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot -4\right)}}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(t \cdot z\right) \cdot -4\right) \cdot a}{\color{blue}{z} \cdot c} \]

      2. times-frac N/A

         \[\leadsto \frac{\left(t \cdot z\right) \cdot -4}{z} \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(t \cdot z\right) \cdot -4}{z}\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(t \cdot z\right) \cdot -4\right), z\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(z \cdot t\right) \cdot -4\right), z\right), \left(\frac{a}{c}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      9. /-lowering-/.f64 46.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 46.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z} \cdot \frac{a}{c}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}} \]

      2. frac-2neg N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)}{\color{blue}{\mathsf{neg}\left(z\right)}} \]

      3. div-inv N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)\right) \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(z\right)}}\right) \]

      4. div-inv N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)}{\color{blue}{\mathsf{neg}\left(z\right)}} \]

      5. frac-2neg N/A

         \[\leadsto \frac{a}{c} \cdot \frac{z \cdot \left(t \cdot -4\right)}{\color{blue}{z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\left(t \cdot -4\right) \cdot z}{z} \]

      7. associate-/l* N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(t \cdot -4\right) \cdot \color{blue}{\frac{z}{z}}\right) \]

      8. *-inverses N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(t \cdot -4\right) \cdot 1\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{a}{c} \cdot \left(t \cdot \color{blue}{\left(-4 \cdot 1\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \frac{a}{c} \cdot \left(t \cdot -4\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{c}\right), \color{blue}{\left(t \cdot -4\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, c\right), \left(\color{blue}{t} \cdot -4\right)\right) \]

      13. *-lowering-*.f64 65.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, c\right), \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right) \]

   9. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(t \cdot -4\right)} \]

   if -3.0999999999999998e132 < z < 130

   1. Initial program 94.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 84.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 84.2%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 130 < z

   1. Initial program 70.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. *-lowering-*.f64 44.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 44.6%

      \[\leadsto \frac{\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot -4\right)}}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(t \cdot z\right) \cdot -4\right) \cdot a}{\color{blue}{z} \cdot c} \]

      2. times-frac N/A

         \[\leadsto \frac{\left(t \cdot z\right) \cdot -4}{z} \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(t \cdot z\right) \cdot -4}{z}\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(t \cdot z\right) \cdot -4\right), z\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(z \cdot t\right) \cdot -4\right), z\right), \left(\frac{a}{c}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      9. /-lowering-/.f64 59.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 59.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z} \cdot \frac{a}{c}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}} \]

      2. clear-num N/A

         \[\leadsto \frac{a}{c} \cdot \frac{1}{\color{blue}{\frac{z}{z \cdot \left(t \cdot -4\right)}}} \]

      3. frac-times N/A

         \[\leadsto \frac{a \cdot 1}{\color{blue}{c \cdot \frac{z}{z \cdot \left(t \cdot -4\right)}}} \]

      4. *-rgt-identity N/A

         \[\leadsto \frac{a}{\color{blue}{c} \cdot \frac{z}{z \cdot \left(t \cdot -4\right)}} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(c \cdot \frac{z}{z \cdot \left(t \cdot -4\right)}\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(c \cdot \frac{1}{\color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\frac{\left(t \cdot -4\right) \cdot z}{z}}\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot \color{blue}{\frac{z}{z}}}\right)\right) \]

      10. *-inverses N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot 1}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot \color{blue}{\left(-4 \cdot 1\right)}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot -4}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \color{blue}{\left(t \cdot -4\right)}\right)\right) \]

      14. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right)\right) \]

   9. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t \cdot -4}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq 130:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+69}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \]

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.
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 -2.65e+69)
    (* (* t -4.0) (/ a c_m))
    (if (<= z 14.5) (/ b (* z c_m)) (/ a (/ c_m (* t -4.0)))))))

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);
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 <= -2.65e+69) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= 14.5) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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.
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 <= (-2.65d+69)) then
        tmp = (t * (-4.0d0)) * (a / c_m)
    else if (z <= 14.5d0) then
        tmp = b / (z * c_m)
    else
        tmp = a / (c_m / (t * (-4.0d0)))
    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;
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 <= -2.65e+69) {
		tmp = (t * -4.0) * (a / c_m);
	} else if (z <= 14.5) {
		tmp = b / (z * c_m);
	} else {
		tmp = a / (c_m / (t * -4.0));
	}
	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])
[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 <= -2.65e+69:
		tmp = (t * -4.0) * (a / c_m)
	elif z <= 14.5:
		tmp = b / (z * c_m)
	else:
		tmp = a / (c_m / (t * -4.0))
	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])
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 <= -2.65e+69)
		tmp = Float64(Float64(t * -4.0) * Float64(a / c_m));
	elseif (z <= 14.5)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(a / Float64(c_m / Float64(t * -4.0)));
	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])){:}
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 <= -2.65e+69)
		tmp = (t * -4.0) * (a / c_m);
	elseif (z <= 14.5)
		tmp = b / (z * c_m);
	else
		tmp = a / (c_m / (t * -4.0));
	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.
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, -2.65e+69], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 14.5], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.65e69

   1. Initial program 60.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. *-lowering-*.f64 31.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 31.4%

      \[\leadsto \frac{\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot -4\right)}}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(t \cdot z\right) \cdot -4\right) \cdot a}{\color{blue}{z} \cdot c} \]

      2. times-frac N/A

         \[\leadsto \frac{\left(t \cdot z\right) \cdot -4}{z} \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(t \cdot z\right) \cdot -4}{z}\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(t \cdot z\right) \cdot -4\right), z\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(z \cdot t\right) \cdot -4\right), z\right), \left(\frac{a}{c}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      9. /-lowering-/.f64 41.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 41.2%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z} \cdot \frac{a}{c}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}} \]

      2. frac-2neg N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)}{\color{blue}{\mathsf{neg}\left(z\right)}} \]

      3. div-inv N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)\right) \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(z\right)}}\right) \]

      4. div-inv N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)}{\color{blue}{\mathsf{neg}\left(z\right)}} \]

      5. frac-2neg N/A

         \[\leadsto \frac{a}{c} \cdot \frac{z \cdot \left(t \cdot -4\right)}{\color{blue}{z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\left(t \cdot -4\right) \cdot z}{z} \]

      7. associate-/l* N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(t \cdot -4\right) \cdot \color{blue}{\frac{z}{z}}\right) \]

      8. *-inverses N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(t \cdot -4\right) \cdot 1\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{a}{c} \cdot \left(t \cdot \color{blue}{\left(-4 \cdot 1\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \frac{a}{c} \cdot \left(t \cdot -4\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{c}\right), \color{blue}{\left(t \cdot -4\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, c\right), \left(\color{blue}{t} \cdot -4\right)\right) \]

      13. *-lowering-*.f64 58.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, c\right), \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right) \]

   9. Applied egg-rr 58.1%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(t \cdot -4\right)} \]

   if -2.65e69 < z < 14.5

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 53.9%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 14.5 < z

   1. Initial program 70.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. *-lowering-*.f64 44.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 44.6%

      \[\leadsto \frac{\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot -4\right)}}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(t \cdot z\right) \cdot -4\right) \cdot a}{\color{blue}{z} \cdot c} \]

      2. times-frac N/A

         \[\leadsto \frac{\left(t \cdot z\right) \cdot -4}{z} \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(t \cdot z\right) \cdot -4}{z}\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(t \cdot z\right) \cdot -4\right), z\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(z \cdot t\right) \cdot -4\right), z\right), \left(\frac{a}{c}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      9. /-lowering-/.f64 59.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 59.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z} \cdot \frac{a}{c}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}} \]

      2. clear-num N/A

         \[\leadsto \frac{a}{c} \cdot \frac{1}{\color{blue}{\frac{z}{z \cdot \left(t \cdot -4\right)}}} \]

      3. frac-times N/A

         \[\leadsto \frac{a \cdot 1}{\color{blue}{c \cdot \frac{z}{z \cdot \left(t \cdot -4\right)}}} \]

      4. *-rgt-identity N/A

         \[\leadsto \frac{a}{\color{blue}{c} \cdot \frac{z}{z \cdot \left(t \cdot -4\right)}} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(c \cdot \frac{z}{z \cdot \left(t \cdot -4\right)}\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(c \cdot \frac{1}{\color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\frac{\left(t \cdot -4\right) \cdot z}{z}}\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot \color{blue}{\frac{z}{z}}}\right)\right) \]

      10. *-inverses N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{\left(t \cdot -4\right) \cdot 1}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot \color{blue}{\left(-4 \cdot 1\right)}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(a, \left(\frac{c}{t \cdot -4}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \color{blue}{\left(t \cdot -4\right)}\right)\right) \]

      14. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right)\right) \]

   9. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t \cdot -4}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+69}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(t \cdot -4\right) \cdot \frac{a}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (* (* t -4.0) (/ a c_m))))
   (* c_s (if (<= z -1.55e+79) t_1 (if (<= z 7.8e-86) (/ b (* z c_m)) t_1)))))

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);
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 = (t * -4.0) * (a / c_m);
	double tmp;
	if (z <= -1.55e+79) {
		tmp = t_1;
	} else if (z <= 7.8e-86) {
		tmp = b / (z * c_m);
	} else {
		tmp = t_1;
	}
	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.
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) :: tmp
    t_1 = (t * (-4.0d0)) * (a / c_m)
    if (z <= (-1.55d+79)) then
        tmp = t_1
    else if (z <= 7.8d-86) then
        tmp = b / (z * c_m)
    else
        tmp = t_1
    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;
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 = (t * -4.0) * (a / c_m);
	double tmp;
	if (z <= -1.55e+79) {
		tmp = t_1;
	} else if (z <= 7.8e-86) {
		tmp = b / (z * c_m);
	} else {
		tmp = t_1;
	}
	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])
[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 = (t * -4.0) * (a / c_m)
	tmp = 0
	if z <= -1.55e+79:
		tmp = t_1
	elif z <= 7.8e-86:
		tmp = b / (z * c_m)
	else:
		tmp = t_1
	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])
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(t * -4.0) * Float64(a / c_m))
	tmp = 0.0
	if (z <= -1.55e+79)
		tmp = t_1;
	elseif (z <= 7.8e-86)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = t_1;
	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])){:}
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 = (t * -4.0) * (a / c_m);
	tmp = 0.0;
	if (z <= -1.55e+79)
		tmp = t_1;
	elseif (z <= 7.8e-86)
		tmp = b / (z * c_m);
	else
		tmp = t_1;
	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.
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[(t * -4.0), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.55e+79], t$95$1, If[LessEqual[z, 7.8e-86], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5499999999999999e79 or 7.8000000000000003e-86 < z

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 36.3%

      \[\leadsto \frac{\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot -4\right)}}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(t \cdot z\right) \cdot -4\right) \cdot a}{\color{blue}{z} \cdot c} \]

      2. times-frac N/A

         \[\leadsto \frac{\left(t \cdot z\right) \cdot -4}{z} \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(t \cdot z\right) \cdot -4}{z}\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(t \cdot z\right) \cdot -4\right), z\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(z \cdot t\right) \cdot -4\right), z\right), \left(\frac{a}{c}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      9. /-lowering-/.f64 47.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 47.5%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z} \cdot \frac{a}{c}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z}} \]

      2. frac-2neg N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)}{\color{blue}{\mathsf{neg}\left(z\right)}} \]

      3. div-inv N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)\right) \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(z\right)}}\right) \]

      4. div-inv N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\mathsf{neg}\left(z \cdot \left(t \cdot -4\right)\right)}{\color{blue}{\mathsf{neg}\left(z\right)}} \]

      5. frac-2neg N/A

         \[\leadsto \frac{a}{c} \cdot \frac{z \cdot \left(t \cdot -4\right)}{\color{blue}{z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{a}{c} \cdot \frac{\left(t \cdot -4\right) \cdot z}{z} \]

      7. associate-/l* N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(t \cdot -4\right) \cdot \color{blue}{\frac{z}{z}}\right) \]

      8. *-inverses N/A

         \[\leadsto \frac{a}{c} \cdot \left(\left(t \cdot -4\right) \cdot 1\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{a}{c} \cdot \left(t \cdot \color{blue}{\left(-4 \cdot 1\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \frac{a}{c} \cdot \left(t \cdot -4\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{c}\right), \color{blue}{\left(t \cdot -4\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, c\right), \left(\color{blue}{t} \cdot -4\right)\right) \]

      13. *-lowering-*.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, c\right), \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right) \]

   9. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(t \cdot -4\right)} \]

   if -1.5499999999999999e79 < z < 7.8000000000000003e-86

   1. Initial program 96.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+79}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-4}{\frac{c\_m}{a}}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (* t (/ -4.0 (/ c_m a)))))
   (* c_s (if (<= z -1.08e+70) t_1 (if (<= z 7.5e-86) (/ b (* z c_m)) t_1)))))

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);
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 = t * (-4.0 / (c_m / a));
	double tmp;
	if (z <= -1.08e+70) {
		tmp = t_1;
	} else if (z <= 7.5e-86) {
		tmp = b / (z * c_m);
	} else {
		tmp = t_1;
	}
	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.
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) :: tmp
    t_1 = t * ((-4.0d0) / (c_m / a))
    if (z <= (-1.08d+70)) then
        tmp = t_1
    else if (z <= 7.5d-86) then
        tmp = b / (z * c_m)
    else
        tmp = t_1
    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;
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 = t * (-4.0 / (c_m / a));
	double tmp;
	if (z <= -1.08e+70) {
		tmp = t_1;
	} else if (z <= 7.5e-86) {
		tmp = b / (z * c_m);
	} else {
		tmp = t_1;
	}
	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])
[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 = t * (-4.0 / (c_m / a))
	tmp = 0
	if z <= -1.08e+70:
		tmp = t_1
	elif z <= 7.5e-86:
		tmp = b / (z * c_m)
	else:
		tmp = t_1
	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])
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(t * Float64(-4.0 / Float64(c_m / a)))
	tmp = 0.0
	if (z <= -1.08e+70)
		tmp = t_1;
	elseif (z <= 7.5e-86)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = t_1;
	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])){:}
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 = t * (-4.0 / (c_m / a));
	tmp = 0.0;
	if (z <= -1.08e+70)
		tmp = t_1;
	elseif (z <= 7.5e-86)
		tmp = b / (z * c_m);
	else
		tmp = t_1;
	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.
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[(t * N[(-4.0 / N[(c$95$m / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.08e+70], t$95$1, If[LessEqual[z, 7.5e-86], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0799999999999999e70 or 7.50000000000000055e-86 < z

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 36.3%

      \[\leadsto \frac{\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot -4\right)}}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(t \cdot z\right) \cdot -4\right) \cdot a}{\color{blue}{z} \cdot c} \]

      2. times-frac N/A

         \[\leadsto \frac{\left(t \cdot z\right) \cdot -4}{z} \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(t \cdot z\right) \cdot -4}{z}\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(t \cdot z\right) \cdot -4\right), z\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(z \cdot t\right) \cdot -4\right), z\right), \left(\frac{a}{c}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t \cdot -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \left(\frac{a}{c}\right)\right) \]

      9. /-lowering-/.f64 47.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -4\right)\right), z\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 47.5%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t \cdot -4\right)}{z} \cdot \frac{a}{c}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(t \cdot -4\right) \cdot z}{z} \cdot \frac{a}{c} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(t \cdot -4\right) \cdot \frac{z}{z}\right) \cdot \frac{\color{blue}{a}}{c} \]

      3. *-inverses N/A

         \[\leadsto \left(\left(t \cdot -4\right) \cdot 1\right) \cdot \frac{a}{c} \]

      4. associate-*l* N/A

         \[\leadsto \left(t \cdot \left(-4 \cdot 1\right)\right) \cdot \frac{\color{blue}{a}}{c} \]

      5. metadata-eval N/A

         \[\leadsto \left(t \cdot -4\right) \cdot \frac{a}{c} \]

      6. associate-*l* N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot \frac{a}{c}\right)}\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot \frac{1}{\color{blue}{\frac{c}{a}}}\right)\right) \]

      9. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\frac{-4}{\color{blue}{\frac{c}{a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{\left(\frac{c}{a}\right)}\right)\right) \]

      11. /-lowering-/.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \mathsf{/.f64}\left(c, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{t \cdot \frac{-4}{\frac{c}{a}}} \]

   if -1.0799999999999999e70 < z < 7.50000000000000055e-86

   1. Initial program 96.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 35.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{z \cdot c\_m} \end{array} \]

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.
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 (* 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);
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 / (z * c_m));
}

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.
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 / (z * c_m))
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;
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 / (z * c_m));
}

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])
[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 / (z * c_m))

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])
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(z * c_m)))
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])){:}
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 / (z * c_m));
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.
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[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

   3. *-lowering-*.f64 35.8%

      \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

5. Simplified 35.8%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Add Preprocessing

Developer Target 1: 81.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))