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

Percentage Accurate: 79.8% → 87.7%

Time: 15.9s

Alternatives: 17

Speedup: 0.8×

• 37.9% 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: 79.8% 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: 87.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 5.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \frac{z \cdot t}{c\_m}, \mathsf{fma}\left(9, x \cdot \frac{y}{c\_m}, \frac{b}{c\_m}\right)\right)}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 5.6e+53)
    (/ (/ (+ (- (* x (* 9.0 y)) (* z (* 4.0 (* t a)))) b) z) c_m)
    (/
     (fma -4.0 (* a (/ (* z t) c_m)) (fma 9.0 (* x (/ y c_m)) (/ b c_m)))
     z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 5.6e+53) {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / z) / c_m;
	} else {
		tmp = fma(-4.0, (a * ((z * t) / c_m)), fma(9.0, (x * (y / c_m)), (b / c_m))) / z;
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 5.6e+53)
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(t * a)))) + b) / z) / c_m);
	else
		tmp = Float64(fma(-4.0, Float64(a * Float64(Float64(z * t) / c_m)), fma(9.0, Float64(x * Float64(y / c_m)), Float64(b / c_m))) / z);
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 5.6e+53], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * N[(a * N[(N[(z * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 5.6e53

   1. Initial program 84.1%

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

      1. associate-/r* 85.5%

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

      2. associate-*l* 85.9%

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

      3. associate-*l* 89.4%

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

      4. associate-*l* 89.4%

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

   4. Applied egg-rr 89.4%

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

   if 5.6e53 < c

   1. Initial program 71.0%

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

      1. associate-/r* 71.6%

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

      2. associate-*l* 71.5%

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

      3. associate-*l* 73.7%

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

      4. associate-*l* 73.7%

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

   4. Applied egg-rr 73.7%

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

   5. Taylor expanded in z around 0 80.2%

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

      1. fma-define 80.2%

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

      2. associate-/l* 82.3%

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

      3. fma-define 82.3%

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

      4. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \frac{z \cdot t}{c}, \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+95} \lor \neg \left(z \leq 10^{+108}\right):\\ \;\;\;\;\frac{x \cdot \left(\left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) - 4 \cdot \frac{t \cdot a}{x}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -9.2e+95) (not (<= z 1e+108)))
    (/ (* x (- (+ (* 9.0 (/ y z)) (/ b (* x z))) (* 4.0 (/ (* t a) x)))) c_m)
    (/ (+ b (fma x (* 9.0 y) (* z (* a (* t -4.0))))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -9.2e+95) || !(z <= 1e+108)) {
		tmp = (x * (((9.0 * (y / z)) + (b / (x * z))) - (4.0 * ((t * a) / x)))) / c_m;
	} else {
		tmp = (b + fma(x, (9.0 * y), (z * (a * (t * -4.0))))) / (c_m * z);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -9.2e+95) || !(z <= 1e+108))
		tmp = Float64(Float64(x * Float64(Float64(Float64(9.0 * Float64(y / z)) + Float64(b / Float64(x * z))) - Float64(4.0 * Float64(Float64(t * a) / x)))) / c_m);
	else
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(z * Float64(a * Float64(t * -4.0))))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -9.2e+95], N[Not[LessEqual[z, 1e+108]], $MachinePrecision]], N[(N[(x * N[(N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999989e95 or 1e108 < z

   1. Initial program 55.5%

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

      1. associate-/r* 67.3%

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

      2. associate-*l* 67.3%

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

      3. associate-*l* 76.0%

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

      4. associate-*l* 76.0%

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

   4. Applied egg-rr 76.0%

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

   5. Taylor expanded in x around inf 79.7%

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

   if -9.19999999999999989e95 < z < 1e108

   1. Initial program 93.2%

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

   3. Simplified 95.3%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+95} \lor \neg \left(z \leq 10^{+108}\right):\\ \;\;\;\;\frac{x \cdot \left(\left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) - 4 \cdot \frac{t \cdot a}{x}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c\_m}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -2e-246)
      t_1
      (if (<= t_1 0.0)
        (/ (/ (- b (* 4.0 (* a (* z t)))) c_m) z)
        (if (<= t_1 INFINITY) t_1 (* a (* -4.0 (/ t c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -2e-246) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b - (4.0 * (a * (z * t)))) / c_m) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * (-4.0 * (t / c_m));
	}
	return c_s * tmp;
}

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -2e-246) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b - (4.0 * (a * (z * t)))) / c_m) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (-4.0 * (t / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_1 <= -2e-246:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((b - (4.0 * (a * (z * t)))) / c_m) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (-4.0 * (t / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -2e-246)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / c_m) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_1 <= -2e-246)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((b - (4.0 * (a * (z * t)))) / c_m) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (-4.0 * (t / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-246], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.99999999999999991e-246 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.5%

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

   if -1.99999999999999991e-246 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 39.0%

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

      1. *-commutative 39.0%

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

      2. associate-/r* 99.5%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.8%

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

      5. associate-*l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 92.2%

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

   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. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-/r* 14.2%

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

      3. associate-*l* 14.2%

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

      4. associate-*l* 19.9%

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

      5. associate-*l* 19.9%

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

   4. Applied egg-rr 19.9%

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

      1. div-inv 19.9%

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

      2. associate-*r* 19.9%

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

   6. Applied egg-rr 19.9%

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

   7. Taylor expanded in z around inf 48.5%

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

      1. associate-*r/ 48.5%

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

      2. *-commutative 48.5%

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

      3. associate-*r* 48.5%

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

      4. associate-*l/ 65.3%

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

      5. associate-*r/ 65.3%

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

   9. Simplified 65.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -2 \cdot 10^{-246}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b\\ t_2 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{t\_1}{z}}{c\_m}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1 \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (+ (- (* x (* 9.0 y)) (* z (* 4.0 (* t a)))) b))
        (t_2 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_2 5e+25)
      (/ (/ t_1 z) c_m)
      (if (<= t_2 INFINITY)
        (* t_1 (/ 1.0 (* c_m z)))
        (* a (* -4.0 (/ t c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b;
	double t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_2 <= 5e+25) {
		tmp = (t_1 / z) / c_m;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1 * (1.0 / (c_m * z));
	} else {
		tmp = a * (-4.0 * (t / c_m));
	}
	return c_s * tmp;
}

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b;
	double t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_2 <= 5e+25) {
		tmp = (t_1 / z) / c_m;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 * (1.0 / (c_m * z));
	} else {
		tmp = a * (-4.0 * (t / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b
	t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_2 <= 5e+25:
		tmp = (t_1 / z) / c_m
	elif t_2 <= math.inf:
		tmp = t_1 * (1.0 / (c_m * z))
	else:
		tmp = a * (-4.0 * (t / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(t * a)))) + b)
	t_2 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_2 <= 5e+25)
		tmp = Float64(Float64(t_1 / z) / c_m);
	elseif (t_2 <= Inf)
		tmp = Float64(t_1 * Float64(1.0 / Float64(c_m * z)));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b;
	t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_2 <= 5e+25)
		tmp = (t_1 / z) / c_m;
	elseif (t_2 <= Inf)
		tmp = t_1 * (1.0 / (c_m * z));
	else
		tmp = a * (-4.0 * (t / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, 5e+25], N[(N[(t$95$1 / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(t$95$1 * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 5.00000000000000024e25

   1. Initial program 86.5%

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

      1. associate-/r* 89.3%

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

      2. associate-*l* 89.9%

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

      3. associate-*l* 92.9%

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

      4. associate-*l* 92.9%

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

   4. Applied egg-rr 92.9%

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

   if 5.00000000000000024e25 < (/.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 89.7%

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

      1. clear-num 89.7%

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

      2. associate-/r/ 88.8%

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

      3. associate-*l* 88.9%

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

      4. associate-*l* 92.2%

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

      5. associate-*l* 92.2%

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

   4. Applied egg-rr 92.2%

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

   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. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-/r* 14.2%

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

      3. associate-*l* 14.2%

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

      4. associate-*l* 19.9%

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

      5. associate-*l* 19.9%

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

   4. Applied egg-rr 19.9%

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

      1. div-inv 19.9%

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

      2. associate-*r* 19.9%

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

   6. Applied egg-rr 19.9%

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

   7. Taylor expanded in z around inf 48.5%

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

      1. associate-*r/ 48.5%

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

      2. *-commutative 48.5%

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

      3. associate-*r* 48.5%

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

      4. associate-*l/ 65.3%

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

      5. associate-*r/ 65.3%

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

   9. Simplified 65.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\left(\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b\right) \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m} + \frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+211}:\\ \;\;\;\;\frac{b + t\_1}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4 \cdot \frac{t \cdot a}{c\_m \cdot y} + 9 \cdot \frac{x}{c\_m \cdot z}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_1 -0.04)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (if (<= t_1 5e+80)
        (+ (* -4.0 (/ (* t a) c_m)) (/ b (* c_m z)))
        (if (<= t_1 5e+211)
          (/ (+ b t_1) (* c_m z))
          (*
           y
           (+ (* -4.0 (/ (* t a) (* c_m y))) (* 9.0 (/ x (* c_m z)))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 5e+80) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else if (t_1 <= 5e+211) {
		tmp = (b + t_1) / (c_m * z);
	} else {
		tmp = y * ((-4.0 * ((t * a) / (c_m * y))) + (9.0 * (x / (c_m * z))));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-0.04d0)) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else if (t_1 <= 5d+80) then
        tmp = ((-4.0d0) * ((t * a) / c_m)) + (b / (c_m * z))
    else if (t_1 <= 5d+211) then
        tmp = (b + t_1) / (c_m * z)
    else
        tmp = y * (((-4.0d0) * ((t * a) / (c_m * y))) + (9.0d0 * (x / (c_m * z))))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 5e+80) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else if (t_1 <= 5e+211) {
		tmp = (b + t_1) / (c_m * z);
	} else {
		tmp = y * ((-4.0 * ((t * a) / (c_m * y))) + (9.0 * (x / (c_m * z))));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -0.04:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	elif t_1 <= 5e+80:
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z))
	elif t_1 <= 5e+211:
		tmp = (b + t_1) / (c_m * z)
	else:
		tmp = y * ((-4.0 * ((t * a) / (c_m * y))) + (9.0 * (x / (c_m * z))))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -0.04)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	elseif (t_1 <= 5e+80)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) / c_m)) + Float64(b / Float64(c_m * z)));
	elseif (t_1 <= 5e+211)
		tmp = Float64(Float64(b + t_1) / Float64(c_m * z));
	else
		tmp = Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / Float64(c_m * y))) + Float64(9.0 * Float64(x / Float64(c_m * z)))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -0.04)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	elseif (t_1 <= 5e+80)
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	elseif (t_1 <= 5e+211)
		tmp = (b + t_1) / (c_m * z);
	else
		tmp = y * ((-4.0 * ((t * a) / (c_m * y))) + (9.0 * (x / (c_m * z))));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -0.04], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+80], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+211], N[(N[(b + t$95$1), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / N[(c$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -0.0400000000000000008

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 71.8%

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

   if -0.0400000000000000008 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999961e80

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r* 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. *-commutative 84.5%

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

      6. associate-*l* 81.1%

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

      7. associate-*r* 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*l* 81.1%

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

      10. *-commutative 81.1%

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

      11. associate-*l* 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 88.6%

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

   if 4.99999999999999961e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999995e211

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 93.5%

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

      1. *-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r* 93.8%

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

      4. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   if 4.9999999999999995e211 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.1%

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

   3. Taylor expanded in b around 0 76.1%

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

   4. Taylor expanded in y around inf 88.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + \frac{b}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+211}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4 \cdot \frac{t \cdot a}{c \cdot y} + 9 \cdot \frac{x}{c \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{+57}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m} + \frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{+261}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m} + 9 \cdot \frac{x \cdot y}{a \cdot \left(c\_m \cdot z\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_1 -0.04)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (if (<= t_1 1e+57)
        (+ (* -4.0 (/ (* t a) c_m)) (/ b (* c_m z)))
        (if (<= t_1 1e+261)
          (* a (+ (* -4.0 (/ t c_m)) (* 9.0 (/ (* x y) (* a (* c_m z))))))
          (* 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);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 1e+57) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else if (t_1 <= 1e+261) {
		tmp = a * ((-4.0 * (t / c_m)) + (9.0 * ((x * y) / (a * (c_m * z)))));
	} else {
		tmp = 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.
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 * (x * 9.0d0)
    if (t_1 <= (-0.04d0)) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else if (t_1 <= 1d+57) then
        tmp = ((-4.0d0) * ((t * a) / c_m)) + (b / (c_m * z))
    else if (t_1 <= 1d+261) then
        tmp = a * (((-4.0d0) * (t / c_m)) + (9.0d0 * ((x * y) / (a * (c_m * z)))))
    else
        tmp = 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;
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 * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 1e+57) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else if (t_1 <= 1e+261) {
		tmp = a * ((-4.0 * (t / c_m)) + (9.0 * ((x * y) / (a * (c_m * z)))));
	} else {
		tmp = 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])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -0.04:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	elif t_1 <= 1e+57:
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z))
	elif t_1 <= 1e+261:
		tmp = a * ((-4.0 * (t / c_m)) + (9.0 * ((x * y) / (a * (c_m * z)))))
	else:
		tmp = 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])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -0.04)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	elseif (t_1 <= 1e+57)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) / c_m)) + Float64(b / Float64(c_m * z)));
	elseif (t_1 <= 1e+261)
		tmp = Float64(a * Float64(Float64(-4.0 * Float64(t / c_m)) + Float64(9.0 * Float64(Float64(x * y) / Float64(a * Float64(c_m * z))))));
	else
		tmp = Float64(y * Float64(9.0 * Float64(Float64(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])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -0.04)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	elseif (t_1 <= 1e+57)
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	elseif (t_1 <= 1e+261)
		tmp = a * ((-4.0 * (t / c_m)) + (9.0 * ((x * y) / (a * (c_m * z)))));
	else
		tmp = 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.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -0.04], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+57], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+261], N[(a * N[(N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(a * N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(9.0 * N[(N[(x / z), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -0.0400000000000000008

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 71.8%

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

   if -0.0400000000000000008 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000005e57

   1. Initial program 82.7%

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

   3. Taylor expanded in x around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r* 85.0%

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

      3. *-commutative 85.0%

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

      4. *-commutative 85.0%

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

      5. *-commutative 85.0%

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

      6. associate-*l* 81.5%

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

      7. associate-*r* 81.5%

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

      8. *-commutative 81.5%

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

      9. associate-*l* 81.5%

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

      10. *-commutative 81.5%

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

      11. associate-*l* 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in t around 0 89.2%

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

   if 1.00000000000000005e57 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999993e260

   1. Initial program 93.0%

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

   3. Taylor expanded in b around 0 74.1%

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

   4. Taylor expanded in a around inf 77.3%

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

   if 9.9999999999999993e260 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.9%

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

   3. Taylor expanded in b around 0 72.9%

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

   4. Taylor expanded in y around inf 91.7%

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

   5. Taylor expanded in a around 0 86.2%

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

      1. associate-/l/ 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+57}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + \frac{b}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+261}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + 9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+294} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (*
    c_s
    (if (or (<= t_1 -2e+294) (not (<= t_1 2e+301)))
      (* y (* 9.0 (/ (/ x z) c_m)))
      (/ (/ (+ (- (* x (* 9.0 y)) (* z (* 4.0 (* t a)))) b) z) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if ((t_1 <= -2e+294) || !(t_1 <= 2e+301)) {
		tmp = y * (9.0 * ((x / z) / c_m));
	} else {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if ((t_1 <= (-2d+294)) .or. (.not. (t_1 <= 2d+301))) then
        tmp = y * (9.0d0 * ((x / z) / c_m))
    else
        tmp = ((((x * (9.0d0 * y)) - (z * (4.0d0 * (t * a)))) + b) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if ((t_1 <= -2e+294) || !(t_1 <= 2e+301)) {
		tmp = y * (9.0 * ((x / z) / c_m));
	} else {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = y * (x * 9.0)
	tmp = 0
	if (t_1 <= -2e+294) or not (t_1 <= 2e+301):
		tmp = y * (9.0 * ((x / z) / c_m))
	else:
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if ((t_1 <= -2e+294) || !(t_1 <= 2e+301))
		tmp = Float64(y * Float64(9.0 * Float64(Float64(x / z) / c_m)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(t * a)))) + b) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if ((t_1 <= -2e+294) || ~((t_1 <= 2e+301)))
		tmp = y * (9.0 * ((x / z) / c_m));
	else
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[Or[LessEqual[t$95$1, -2e+294], N[Not[LessEqual[t$95$1, 2e+301]], $MachinePrecision]], N[(y * N[(9.0 * N[(N[(x / z), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000013e294 or 2.00000000000000011e301 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 59.7%

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

   3. Taylor expanded in b around 0 60.5%

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

   4. Taylor expanded in y around inf 84.1%

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

   5. Taylor expanded in a around 0 81.7%

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

      1. associate-/l/ 88.9%

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

   7. Simplified 88.9%

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

   if -2.00000000000000013e294 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000011e301

   1. Initial program 86.1%

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

      1. associate-/r* 87.4%

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

      2. associate-*l* 87.4%

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

      3. associate-*l* 91.4%

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

      4. associate-*l* 91.4%

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

   4. Applied egg-rr 91.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+294} \lor \neg \left(y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+35} \lor \neg \left(z \leq 3 \cdot 10^{+155}\right):\\ \;\;\;\;\frac{x \cdot \left(\left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) - 4 \cdot \frac{t \cdot a}{x}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -1e+35) (not (<= z 3e+155)))
    (/ (* x (- (+ (* 9.0 (/ y z)) (/ b (* x z))) (* 4.0 (/ (* t a) x)))) c_m)
    (/ (/ (+ (- (* x (* 9.0 y)) (* z (* 4.0 (* t a)))) b) c_m) z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1e+35) || !(z <= 3e+155)) {
		tmp = (x * (((9.0 * (y / z)) + (b / (x * z))) - (4.0 * ((t * a) / x)))) / c_m;
	} else {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((z <= (-1d+35)) .or. (.not. (z <= 3d+155))) then
        tmp = (x * (((9.0d0 * (y / z)) + (b / (x * z))) - (4.0d0 * ((t * a) / x)))) / c_m
    else
        tmp = ((((x * (9.0d0 * y)) - (z * (4.0d0 * (t * a)))) + b) / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1e+35) || !(z <= 3e+155)) {
		tmp = (x * (((9.0 * (y / z)) + (b / (x * z))) - (4.0 * ((t * a) / x)))) / c_m;
	} else {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -1e+35) or not (z <= 3e+155):
		tmp = (x * (((9.0 * (y / z)) + (b / (x * z))) - (4.0 * ((t * a) / x)))) / c_m
	else:
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -1e+35) || !(z <= 3e+155))
		tmp = Float64(Float64(x * Float64(Float64(Float64(9.0 * Float64(y / z)) + Float64(b / Float64(x * z))) - Float64(4.0 * Float64(Float64(t * a) / x)))) / c_m);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(t * a)))) + b) / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -1e+35) || ~((z <= 3e+155)))
		tmp = (x * (((9.0 * (y / z)) + (b / (x * z))) - (4.0 * ((t * a) / x)))) / c_m;
	else
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -1e+35], N[Not[LessEqual[z, 3e+155]], $MachinePrecision]], N[(N[(x * N[(N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999997e34 or 3.0000000000000001e155 < z

   1. Initial program 62.4%

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

      1. associate-/r* 70.1%

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

      2. associate-*l* 70.1%

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

      3. associate-*l* 77.2%

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

      4. associate-*l* 77.2%

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

   4. Applied egg-rr 77.2%

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

   5. Taylor expanded in x around inf 80.8%

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

   if -9.9999999999999997e34 < z < 3.0000000000000001e155

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-/r* 91.8%

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

      3. associate-*l* 92.4%

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

      4. associate-*l* 93.9%

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

      5. associate-*l* 93.9%

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

   4. Applied egg-rr 93.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+35} \lor \neg \left(z \leq 3 \cdot 10^{+155}\right):\\ \;\;\;\;\frac{x \cdot \left(\left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) - 4 \cdot \frac{t \cdot a}{x}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m} + \frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_1 -0.04)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (if (<= t_1 5e+80)
        (+ (* -4.0 (/ (* t a) c_m)) (/ b (* c_m z)))
        (/ (* x (+ (* 9.0 (/ y z)) (/ b (* 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);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 5e+80) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else {
		tmp = (x * ((9.0 * (y / z)) + (b / (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.
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 * (x * 9.0d0)
    if (t_1 <= (-0.04d0)) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else if (t_1 <= 5d+80) then
        tmp = ((-4.0d0) * ((t * a) / c_m)) + (b / (c_m * z))
    else
        tmp = (x * ((9.0d0 * (y / z)) + (b / (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;
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 * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 5e+80) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else {
		tmp = (x * ((9.0 * (y / z)) + (b / (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])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -0.04:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	elif t_1 <= 5e+80:
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z))
	else:
		tmp = (x * ((9.0 * (y / z)) + (b / (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])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -0.04)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	elseif (t_1 <= 5e+80)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) / c_m)) + Float64(b / Float64(c_m * z)));
	else
		tmp = Float64(Float64(x * Float64(Float64(9.0 * Float64(y / z)) + Float64(b / Float64(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])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -0.04)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	elseif (t_1 <= 5e+80)
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	else
		tmp = (x * ((9.0 * (y / z)) + (b / (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.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -0.04], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+80], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -0.0400000000000000008

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 71.8%

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

   if -0.0400000000000000008 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999961e80

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r* 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. *-commutative 84.5%

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

      6. associate-*l* 81.1%

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

      7. associate-*r* 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*l* 81.1%

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

      10. *-commutative 81.1%

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

      11. associate-*l* 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 88.6%

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

   if 4.99999999999999961e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 80.9%

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

      1. associate-/r* 82.7%

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

      2. associate-*l* 82.7%

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

      3. associate-*l* 82.7%

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

      4. associate-*l* 82.7%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in x around inf 78.0%

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

   6. Taylor expanded in x around inf 77.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + \frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m} + \frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + t\_1}{z}}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_1 -0.04)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (if (<= t_1 5e+80)
        (+ (* -4.0 (/ (* t a) c_m)) (/ b (* c_m z)))
        (/ (/ (+ b t_1) z) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 5e+80) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else {
		tmp = ((b + t_1) / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-0.04d0)) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else if (t_1 <= 5d+80) then
        tmp = ((-4.0d0) * ((t * a) / c_m)) + (b / (c_m * z))
    else
        tmp = ((b + t_1) / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -0.04) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else if (t_1 <= 5e+80) {
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	} else {
		tmp = ((b + t_1) / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -0.04:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	elif t_1 <= 5e+80:
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z))
	else:
		tmp = ((b + t_1) / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -0.04)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	elseif (t_1 <= 5e+80)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) / c_m)) + Float64(b / Float64(c_m * z)));
	else
		tmp = Float64(Float64(Float64(b + t_1) / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -0.04)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	elseif (t_1 <= 5e+80)
		tmp = (-4.0 * ((t * a) / c_m)) + (b / (c_m * z));
	else
		tmp = ((b + t_1) / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -0.04], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+80], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + t$95$1), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -0.0400000000000000008

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 71.8%

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

   if -0.0400000000000000008 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999961e80

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r* 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. *-commutative 84.5%

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

      6. associate-*l* 81.1%

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

      7. associate-*r* 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*l* 81.1%

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

      10. *-commutative 81.1%

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

      11. associate-*l* 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 88.6%

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

   if 4.99999999999999961e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 80.9%

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

      1. associate-/r* 82.7%

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

      2. associate-*l* 82.7%

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

      3. associate-*l* 82.7%

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

      4. associate-*l* 82.7%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in x around inf 78.0%

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

      1. associate-*r* 78.1%

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

      2. *-commutative 78.1%

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

   7. Applied egg-rr 78.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -0.04:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + \frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(x \cdot 9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+120}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{9 \cdot y}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-250}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c\_m}\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -1.4e+120)
    (/ b (* c_m z))
    (if (<= b -3.5e-54)
      (* x (/ (* 9.0 y) (* c_m z)))
      (if (<= b -7.2e-250)
        (/ (* t (* a -4.0)) c_m)
        (if (<= b 6.1e+22) (* a (* -4.0 (/ t c_m))) (/ (/ b z) c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -1.4e+120) {
		tmp = b / (c_m * z);
	} else if (b <= -3.5e-54) {
		tmp = x * ((9.0 * y) / (c_m * z));
	} else if (b <= -7.2e-250) {
		tmp = (t * (a * -4.0)) / c_m;
	} else if (b <= 6.1e+22) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (b <= (-1.4d+120)) then
        tmp = b / (c_m * z)
    else if (b <= (-3.5d-54)) then
        tmp = x * ((9.0d0 * y) / (c_m * z))
    else if (b <= (-7.2d-250)) then
        tmp = (t * (a * (-4.0d0))) / c_m
    else if (b <= 6.1d+22) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = (b / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -1.4e+120) {
		tmp = b / (c_m * z);
	} else if (b <= -3.5e-54) {
		tmp = x * ((9.0 * y) / (c_m * z));
	} else if (b <= -7.2e-250) {
		tmp = (t * (a * -4.0)) / c_m;
	} else if (b <= 6.1e+22) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -1.4e+120:
		tmp = b / (c_m * z)
	elif b <= -3.5e-54:
		tmp = x * ((9.0 * y) / (c_m * z))
	elif b <= -7.2e-250:
		tmp = (t * (a * -4.0)) / c_m
	elif b <= 6.1e+22:
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = (b / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -1.4e+120)
		tmp = Float64(b / Float64(c_m * z));
	elseif (b <= -3.5e-54)
		tmp = Float64(x * Float64(Float64(9.0 * y) / Float64(c_m * z)));
	elseif (b <= -7.2e-250)
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c_m);
	elseif (b <= 6.1e+22)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(Float64(b / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -1.4e+120)
		tmp = b / (c_m * z);
	elseif (b <= -3.5e-54)
		tmp = x * ((9.0 * y) / (c_m * z));
	elseif (b <= -7.2e-250)
		tmp = (t * (a * -4.0)) / c_m;
	elseif (b <= 6.1e+22)
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = (b / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -1.4e+120], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-54], N[(x * N[(N[(9.0 * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e-250], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[b, 6.1e+22], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if b < -1.4e120

   1. Initial program 85.1%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 59.4%

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

   if -1.4e120 < b < -3.49999999999999982e-54

   1. Initial program 77.6%

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

      1. associate-/r* 81.8%

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

      2. associate-*l* 81.8%

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

      3. associate-*l* 85.4%

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

      4. associate-*l* 85.4%

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

   4. Applied egg-rr 85.4%

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

   5. Taylor expanded in x around inf 48.7%

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

      1. associate-*r/ 48.8%

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

      2. *-commutative 48.8%

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

      3. associate-*l* 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

      6. associate-/l* 52.3%

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

   7. Simplified 52.3%

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

   if -3.49999999999999982e-54 < b < -7.19999999999999964e-250

   1. Initial program 72.2%

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

   3. Taylor expanded in z around inf 69.8%

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

      1. associate-*r/ 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -7.19999999999999964e-250 < b < 6.0999999999999998e22

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-/r* 82.4%

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

      3. associate-*l* 82.4%

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

      4. associate-*l* 85.7%

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

      5. associate-*l* 85.7%

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

   4. Applied egg-rr 85.7%

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

      1. div-inv 85.6%

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

      2. associate-*r* 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in z around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. *-commutative 54.4%

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

      3. associate-*r* 54.4%

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

      4. associate-*l/ 58.8%

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

      5. associate-*r/ 58.8%

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

   9. Simplified 58.8%

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

   if 6.0999999999999998e22 < b

   1. Initial program 80.4%

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

      1. associate-/r* 80.5%

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

      2. associate-*l* 82.1%

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

      3. associate-*l* 85.3%

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

      4. associate-*l* 85.3%

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

   4. Applied egg-rr 85.3%

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

   5. Taylor expanded in b around inf 60.3%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+120}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{9 \cdot y}{c \cdot z}\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-250}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+122}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-248}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c\_m}\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -1e+122)
    (/ b (* c_m z))
    (if (<= b -2.7e-55)
      (* 9.0 (* x (/ y (* c_m z))))
      (if (<= b -2.1e-248)
        (/ (* t (* a -4.0)) c_m)
        (if (<= b 2.75e+19) (* a (* -4.0 (/ t c_m))) (/ (/ b z) c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -1e+122) {
		tmp = b / (c_m * z);
	} else if (b <= -2.7e-55) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (b <= -2.1e-248) {
		tmp = (t * (a * -4.0)) / c_m;
	} else if (b <= 2.75e+19) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (b <= (-1d+122)) then
        tmp = b / (c_m * z)
    else if (b <= (-2.7d-55)) then
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    else if (b <= (-2.1d-248)) then
        tmp = (t * (a * (-4.0d0))) / c_m
    else if (b <= 2.75d+19) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = (b / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -1e+122) {
		tmp = b / (c_m * z);
	} else if (b <= -2.7e-55) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (b <= -2.1e-248) {
		tmp = (t * (a * -4.0)) / c_m;
	} else if (b <= 2.75e+19) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -1e+122:
		tmp = b / (c_m * z)
	elif b <= -2.7e-55:
		tmp = 9.0 * (x * (y / (c_m * z)))
	elif b <= -2.1e-248:
		tmp = (t * (a * -4.0)) / c_m
	elif b <= 2.75e+19:
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = (b / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -1e+122)
		tmp = Float64(b / Float64(c_m * z));
	elseif (b <= -2.7e-55)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	elseif (b <= -2.1e-248)
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c_m);
	elseif (b <= 2.75e+19)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(Float64(b / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -1e+122)
		tmp = b / (c_m * z);
	elseif (b <= -2.7e-55)
		tmp = 9.0 * (x * (y / (c_m * z)));
	elseif (b <= -2.1e-248)
		tmp = (t * (a * -4.0)) / c_m;
	elseif (b <= 2.75e+19)
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = (b / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -1e+122], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-55], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-248], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[b, 2.75e+19], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if b < -1.00000000000000001e122

   1. Initial program 85.1%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 59.4%

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

   if -1.00000000000000001e122 < b < -2.70000000000000004e-55

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-/r* 85.5%

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

      3. associate-*l* 85.5%

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

      4. associate-*l* 89.1%

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

      5. associate-*l* 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in x around inf 48.7%

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

      1. associate-/l* 52.2%

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

      2. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if -2.70000000000000004e-55 < b < -2.1e-248

   1. Initial program 72.2%

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

   3. Taylor expanded in z around inf 69.8%

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

      1. associate-*r/ 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -2.1e-248 < b < 2.75e19

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-/r* 82.4%

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

      3. associate-*l* 82.4%

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

      4. associate-*l* 85.7%

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

      5. associate-*l* 85.7%

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

   4. Applied egg-rr 85.7%

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

      1. div-inv 85.6%

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

      2. associate-*r* 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in z around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. *-commutative 54.4%

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

      3. associate-*r* 54.4%

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

      4. associate-*l/ 58.8%

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

      5. associate-*r/ 58.8%

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

   9. Simplified 58.8%

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

   if 2.75e19 < b

   1. Initial program 80.4%

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

      1. associate-/r* 80.5%

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

      2. associate-*l* 82.1%

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

      3. associate-*l* 85.3%

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

      4. associate-*l* 85.3%

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

   4. Applied egg-rr 85.3%

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

   5. Taylor expanded in b around inf 60.3%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+122}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-248}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 8 \cdot 10^{-119}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 8e-119)
    (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))
    (/ (/ (+ (- (* x (* 9.0 y)) (* z (* 4.0 (* t a)))) b) c_m) z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 8e-119) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (c_m <= 8d-119) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c_m * z)
    else
        tmp = ((((x * (9.0d0 * y)) - (z * (4.0d0 * (t * a)))) + b) / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 8e-119) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 8e-119:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	else:
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 8e-119)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(t * a)))) + b) / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 8e-119)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	else
		tmp = ((((x * (9.0 * y)) - (z * (4.0 * (t * a)))) + b) / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 8e-119], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 8.0000000000000001e-119

   1. Initial program 83.5%

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

   if 8.0000000000000001e-119 < c

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-/r* 81.3%

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

      3. associate-*l* 81.3%

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

      4. associate-*l* 84.7%

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

      5. associate-*l* 84.7%

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

   4. Applied egg-rr 84.7%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 8 \cdot 10^{-119}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(x \cdot \left(9 \cdot y\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right) + b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -5500000000000:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c\_m}\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -5500000000000.0)
    (/ (/ b c_m) z)
    (if (<= b -8.5e-51)
      (* y (* 9.0 (/ (/ x z) c_m)))
      (if (<= b 8e+21) (* a (* -4.0 (/ t c_m))) (/ (/ b z) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -5500000000000.0) {
		tmp = (b / c_m) / z;
	} else if (b <= -8.5e-51) {
		tmp = y * (9.0 * ((x / z) / c_m));
	} else if (b <= 8e+21) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (b <= (-5500000000000.0d0)) then
        tmp = (b / c_m) / z
    else if (b <= (-8.5d-51)) then
        tmp = y * (9.0d0 * ((x / z) / c_m))
    else if (b <= 8d+21) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = (b / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -5500000000000.0) {
		tmp = (b / c_m) / z;
	} else if (b <= -8.5e-51) {
		tmp = y * (9.0 * ((x / z) / c_m));
	} else if (b <= 8e+21) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -5500000000000.0:
		tmp = (b / c_m) / z
	elif b <= -8.5e-51:
		tmp = y * (9.0 * ((x / z) / c_m))
	elif b <= 8e+21:
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = (b / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -5500000000000.0)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (b <= -8.5e-51)
		tmp = Float64(y * Float64(9.0 * Float64(Float64(x / z) / c_m)));
	elseif (b <= 8e+21)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(Float64(b / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -5500000000000.0)
		tmp = (b / c_m) / z;
	elseif (b <= -8.5e-51)
		tmp = y * (9.0 * ((x / z) / c_m));
	elseif (b <= 8e+21)
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = (b / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -5500000000000.0], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -8.5e-51], N[(y * N[(9.0 * N[(N[(x / z), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+21], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if b < -5.5e12

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-/r* 85.8%

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

      3. associate-*l* 85.8%

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

      4. associate-*l* 89.1%

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

      5. associate-*l* 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in b around inf 54.7%

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

   if -5.5e12 < b < -8.50000000000000036e-51

   1. Initial program 81.7%

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

   3. Taylor expanded in b around 0 73.8%

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

   4. Taylor expanded in y around inf 67.8%

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

   5. Taylor expanded in a around 0 51.5%

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

      1. associate-/l/ 51.5%

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

   7. Simplified 51.5%

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

   if -8.50000000000000036e-51 < b < 8e21

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-/r* 77.6%

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

      3. associate-*l* 77.6%

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

      4. associate-*l* 80.6%

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

      5. associate-*l* 80.6%

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

   4. Applied egg-rr 80.6%

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

      1. div-inv 80.5%

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

      2. associate-*r* 80.5%

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

   6. Applied egg-rr 80.5%

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

   7. Taylor expanded in z around inf 59.6%

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

      1. associate-*r/ 59.6%

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

      2. *-commutative 59.6%

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

      3. associate-*r* 59.6%

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

      4. associate-*l/ 61.8%

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

      5. associate-*r/ 61.8%

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

   9. Simplified 61.8%

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

   if 8e21 < b

   1. Initial program 80.4%

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

      1. associate-/r* 80.5%

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

      2. associate-*l* 82.1%

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

      3. associate-*l* 85.3%

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

      4. associate-*l* 85.3%

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

   4. Applied egg-rr 85.3%

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

   5. Taylor expanded in b around inf 60.3%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5500000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{\frac{x}{z}}{c}\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+103} \lor \neg \left(t \leq 9.6 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= t -6.6e+103) (not (<= t 9.6e-52)))
    (* a (* -4.0 (/ t c_m)))
    (/ (+ b (* 9.0 (* x y))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((t <= -6.6e+103) || !(t <= 9.6e-52)) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((t <= (-6.6d+103)) .or. (.not. (t <= 9.6d-52))) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((t <= -6.6e+103) || !(t <= 9.6e-52)) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (t <= -6.6e+103) or not (t <= 9.6e-52):
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((t <= -6.6e+103) || !(t <= 9.6e-52))
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((t <= -6.6e+103) || ~((t <= 9.6e-52)))
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[t, -6.6e+103], N[Not[LessEqual[t, 9.6e-52]], $MachinePrecision]], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -6.60000000000000017e103 or 9.6000000000000007e-52 < t

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-/r* 77.6%

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

      3. associate-*l* 77.7%

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

      4. associate-*l* 82.7%

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

      5. associate-*l* 82.7%

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

   4. Applied egg-rr 82.7%

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

      1. div-inv 82.6%

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

      2. associate-*r* 82.6%

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

   6. Applied egg-rr 82.6%

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

   7. Taylor expanded in z around inf 52.2%

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

      1. associate-*r/ 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-*r* 52.2%

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

      4. associate-*l/ 56.9%

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

      5. associate-*r/ 56.9%

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

   9. Simplified 56.9%

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

   if -6.60000000000000017e103 < t < 9.6000000000000007e-52

   1. Initial program 85.7%

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

   3. Taylor expanded in x around inf 70.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+103} \lor \neg \left(t \leq 9.6 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -5.5e+127)
    (/ b (* c_m z))
    (if (<= b 7.8e+23) (* a (* -4.0 (/ t c_m))) (/ (/ b z) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -5.5e+127) {
		tmp = b / (c_m * z);
	} else if (b <= 7.8e+23) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (b <= (-5.5d+127)) then
        tmp = b / (c_m * z)
    else if (b <= 7.8d+23) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = (b / z) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -5.5e+127) {
		tmp = b / (c_m * z);
	} else if (b <= 7.8e+23) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = (b / z) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -5.5e+127:
		tmp = b / (c_m * z)
	elif b <= 7.8e+23:
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = (b / z) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -5.5e+127)
		tmp = Float64(b / Float64(c_m * z));
	elseif (b <= 7.8e+23)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(Float64(b / z) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -5.5e+127)
		tmp = b / (c_m * z);
	elseif (b <= 7.8e+23)
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = (b / z) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -5.5e+127], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+23], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -5.50000000000000041e127

   1. Initial program 84.1%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in b around inf 61.1%

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

   if -5.50000000000000041e127 < b < 7.8000000000000001e23

   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. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 81.8%

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

      2. associate-/r* 79.5%

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

      3. associate-*l* 79.5%

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

      4. associate-*l* 82.5%

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

      5. associate-*l* 82.5%

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

   4. Applied egg-rr 82.5%

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

      1. div-inv 82.3%

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

      2. associate-*r* 82.3%

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

   6. Applied egg-rr 82.3%

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

   7. Taylor expanded in z around inf 54.3%

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

      1. associate-*r/ 54.3%

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

      2. *-commutative 54.3%

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

      3. associate-*r* 54.3%

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

      4. associate-*l/ 56.6%

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

      5. associate-*r/ 56.6%

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

   9. Simplified 56.6%

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

   if 7.8000000000000001e23 < b

   1. Initial program 80.4%

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

      1. associate-/r* 80.5%

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

      2. associate-*l* 82.1%

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

      3. associate-*l* 85.3%

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

      4. associate-*l* 85.3%

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

   4. Applied egg-rr 85.3%

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

   5. Taylor expanded in b around inf 60.3%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

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

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

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

Derivation

1. Initial program 81.9%

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

3. Simplified 85.6%

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

5. Taylor expanded in b around inf 34.9%

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

6. Final simplification 34.9%

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

Developer target: 80.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))