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

Percentage Accurate: 79.6% → 86.5%

Time: 13.5s

Alternatives: 19

Speedup: 0.7×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% 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: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -0.96 \lor \neg \left(a \leq 1.06 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, t, \mathsf{fma}\left(9, x \cdot \frac{y}{a \cdot z}, \frac{b}{a \cdot z}\right)\right) \cdot \frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-4 \cdot \left(z \cdot \left(a \cdot t\right)\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -0.96) (not (<= a 1.06e-46)))
   (* (fma -4.0 t (fma 9.0 (* x (/ y (* a z))) (/ b (* a z)))) (/ a c))
   (/ (+ (/ (* -4.0 (* z (* a t))) c) (+ (* 9.0 (/ (* x y) c)) (/ b c))) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -0.96) || !(a <= 1.06e-46)) {
		tmp = fma(-4.0, t, fma(9.0, (x * (y / (a * z))), (b / (a * z)))) * (a / c);
	} else {
		tmp = (((-4.0 * (z * (a * t))) / c) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -0.96) || !(a <= 1.06e-46))
		tmp = Float64(fma(-4.0, t, fma(9.0, Float64(x * Float64(y / Float64(a * z))), Float64(b / Float64(a * z)))) * Float64(a / c));
	else
		tmp = Float64(Float64(Float64(Float64(-4.0 * Float64(z * Float64(a * t))) / c) + Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c))) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -0.96], N[Not[LessEqual[a, 1.06e-46]], $MachinePrecision]], N[(N[(-4.0 * t + N[(9.0 * N[(x * N[(y / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(-4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.95999999999999996 or 1.06e-46 < a

   1. Initial program 73.9%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in a around inf 81.1%

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

   6. Taylor expanded in c around 0 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-/l* 86.9%

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

      3. fma-define 86.9%

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

      4. fma-define 86.9%

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

      5. associate-/l* 90.7%

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

      6. *-commutative 90.7%

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

      7. *-commutative 90.7%

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

   8. Simplified 90.7%

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

   if -0.95999999999999996 < a < 1.06e-46

   1. Initial program 72.4%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. associate-*r* 88.8%

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

   7. Applied egg-rr 88.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.96 \lor \neg \left(a \leq 1.06 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, t, \mathsf{fma}\left(9, x \cdot \frac{y}{a \cdot z}, \frac{b}{a \cdot z}\right)\right) \cdot \frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-4 \cdot \left(z \cdot \left(a \cdot t\right)\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-158}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(-4 \cdot z\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{-209}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+285}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{y} - \frac{\frac{x \cdot -9}{z}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -4e-158)
     (/ (+ b (fma x (* 9.0 y) (* t (* a (* -4.0 z))))) (* z c))
     (if (<= t_1 1e-209)
       (/ (+ (+ (* 9.0 (/ (* x y) c)) (/ b c)) (* -4.0 (/ (* a (* t z)) c))) z)
       (if (<= t_1 1e+285)
         t_1
         (*
          y
          (-
           (/ (fma -4.0 (* a (/ t c)) (/ b (* z c))) y)
           (/ (/ (* x -9.0) z) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -4e-158) {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (-4.0 * z))))) / (z * c);
	} else if (t_1 <= 1e-209) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else if (t_1 <= 1e+285) {
		tmp = t_1;
	} else {
		tmp = y * ((fma(-4.0, (a * (t / c)), (b / (z * c))) / y) - (((x * -9.0) / z) / c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-158)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(-4.0 * z))))) / Float64(z * c));
	elseif (t_1 <= 1e-209)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) + Float64(-4.0 * Float64(Float64(a * Float64(t * z)) / c))) / z);
	elseif (t_1 <= 1e+285)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(fma(-4.0, Float64(a * Float64(t / c)), Float64(b / Float64(z * c))) / y) - Float64(Float64(Float64(x * -9.0) / z) / c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-158], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(-4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-209], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+285], t$95$1, N[(y * N[(N[(N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(N[(x * -9.0), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.00000000000000026e-158

   1. Initial program 87.0%

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

   3. Simplified 89.9%

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

   if -4.00000000000000026e-158 < (/.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)) < 1e-209

   1. Initial program 47.7%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in z around 0 99.8%

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

   if 1e-209 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 9.9999999999999998e284

   1. Initial program 99.5%

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

   if 9.9999999999999998e284 < (/.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 51.1%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in y around -inf 72.2%

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

   7. Simplified 74.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -4 \cdot 10^{-158}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(-4 \cdot z\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 10^{-209}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 10^{+285}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{y} - \frac{\frac{x \cdot -9}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+299}:\\ \;\;\;\;\frac{b + t \cdot \left(9 \cdot \frac{x \cdot y}{t} - 4 \cdot \left(a \cdot z\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -2e+299)
     (/ (+ b (* t (- (* 9.0 (/ (* x y) t)) (* 4.0 (* a z))))) (* z c))
     (if (<= t_1 2e+77)
       (/ (+ (+ (* 9.0 (/ (* x y) c)) (/ b c)) (* -4.0 (/ (* a (* t z)) c))) z)
       (if (<= t_1 INFINITY)
         (/ (- b (- (* (* a t) (* z 4.0)) (* x (* 9.0 y)))) (* z c))
         (* a (* -4.0 (/ t c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -2e+299) {
		tmp = (b + (t * ((9.0 * ((x * y) / t)) - (4.0 * (a * z))))) / (z * c);
	} else if (t_1 <= 2e+77) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -2e+299) {
		tmp = (b + (t * ((9.0 * ((x * y) / t)) - (4.0 * (a * z))))) / (z * c);
	} else if (t_1 <= 2e+77) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -2e+299:
		tmp = (b + (t * ((9.0 * ((x * y) / t)) - (4.0 * (a * z))))) / (z * c)
	elif t_1 <= 2e+77:
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z
	elif t_1 <= math.inf:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c)
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e+299)
		tmp = Float64(Float64(b + Float64(t * Float64(Float64(9.0 * Float64(Float64(x * y) / t)) - Float64(4.0 * Float64(a * z))))) / Float64(z * c));
	elseif (t_1 <= 2e+77)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) + Float64(-4.0 * Float64(Float64(a * Float64(t * z)) / c))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(9.0 * y)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -2e+299)
		tmp = (b + (t * ((9.0 * ((x * y) / t)) - (4.0 * (a * z))))) / (z * c);
	elseif (t_1 <= 2e+77)
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	elseif (t_1 <= Inf)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+299], N[(N[(b + N[(t * N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+77], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -2.0000000000000001e299

   1. Initial program 78.4%

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

      1. associate-+l- 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*r* 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-+l- 85.6%

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

      6. associate-*l* 85.6%

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

      7. associate-*l* 83.6%

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

      8. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in t around inf 83.7%

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

   if -2.0000000000000001e299 < (/.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)) < 1.99999999999999997e77

   1. Initial program 84.5%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around 0 94.7%

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

   if 1.99999999999999997e77 < (/.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 78.9%

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

      1. associate-+l- 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-+l- 85.5%

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

      6. associate-*l* 85.5%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   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%

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

   3. Simplified 9.4%

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

   5. Taylor expanded in x around 0 4.1%

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

      1. metadata-eval 4.1%

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

      2. cancel-sign-sub-inv 4.1%

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

      3. associate-*r* 4.1%

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

      4. *-commutative 4.1%

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

   7. Simplified 4.1%

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

   8. Taylor expanded in a around inf 80.0%

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

   9. Taylor expanded in t around inf 80.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -2 \cdot 10^{+299}:\\ \;\;\;\;\frac{b + t \cdot \left(9 \cdot \frac{x \cdot y}{t} - 4 \cdot \left(a \cdot z\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -4e-158)
     t_1
     (if (<= t_1 0.0)
       (/ (+ (/ b c) (* -4.0 (/ (* a (* t z)) c))) z)
       (if (<= t_1 INFINITY)
         (/ (- b (- (* (* a t) (* z 4.0)) (* x (* 9.0 y)))) (* z c))
         (* a (* -4.0 (/ t c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -4e-158) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b / c) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -4e-158) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b / c) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -4e-158:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((b / c) + (-4.0 * ((a * (t * z)) / c))) / z
	elif t_1 <= math.inf:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c)
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e-158)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(b / c) + Float64(-4.0 * Float64(Float64(a * Float64(t * z)) / c))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(9.0 * y)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -4e-158)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((b / c) + (-4.0 * ((a * (t * z)) / c))) / z;
	elseif (t_1 <= Inf)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-158], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(b / c), $MachinePrecision] + N[(-4.0 * N[(N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.00000000000000026e-158

   1. Initial program 87.0%

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

   if -4.00000000000000026e-158 < (/.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 40.7%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in x around 0 36.5%

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

      1. metadata-eval 36.5%

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

      2. cancel-sign-sub-inv 36.5%

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

      3. associate-*r* 36.5%

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

      4. *-commutative 36.5%

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

   7. Simplified 36.5%

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

   8. Taylor expanded in z around 0 88.2%

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

   if -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 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 88.9%

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

      4. *-commutative 88.9%

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

      5. associate-+l- 88.9%

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

      6. associate-*l* 88.8%

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

      7. associate-*l* 88.1%

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

      8. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   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%

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

   3. Simplified 9.4%

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

   5. Taylor expanded in x around 0 4.1%

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

      1. metadata-eval 4.1%

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

      2. cancel-sign-sub-inv 4.1%

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

      3. associate-*r* 4.1%

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

      4. *-commutative 4.1%

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

   7. Simplified 4.1%

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

   8. Taylor expanded in a around inf 80.0%

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

   9. Taylor expanded in t around inf 80.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -4 \cdot 10^{-158}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot c\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{t\_1} + \frac{b}{t\_1}\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+87}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* z c))))
   (if (<= z -6.8e+16)
     (* a (+ (* -4.0 (/ t c)) (+ (* 9.0 (/ (* x y) t_1)) (/ b t_1))))
     (if (<= z 1.55e+87)
       (/ (+ (+ (* 9.0 (/ (* x y) c)) (/ b c)) (* -4.0 (/ (* a (* t z)) c))) z)
       (/ (+ (* -4.0 (* a t)) (/ b z)) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (z * c);
	double tmp;
	if (z <= -6.8e+16) {
		tmp = a * ((-4.0 * (t / c)) + ((9.0 * ((x * y) / t_1)) + (b / t_1)));
	} else if (z <= 1.55e+87) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * c)
    if (z <= (-6.8d+16)) then
        tmp = a * (((-4.0d0) * (t / c)) + ((9.0d0 * ((x * y) / t_1)) + (b / t_1)))
    else if (z <= 1.55d+87) then
        tmp = (((9.0d0 * ((x * y) / c)) + (b / c)) + ((-4.0d0) * ((a * (t * z)) / c))) / z
    else
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (z * c);
	double tmp;
	if (z <= -6.8e+16) {
		tmp = a * ((-4.0 * (t / c)) + ((9.0 * ((x * y) / t_1)) + (b / t_1)));
	} else if (z <= 1.55e+87) {
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * (z * c)
	tmp = 0
	if z <= -6.8e+16:
		tmp = a * ((-4.0 * (t / c)) + ((9.0 * ((x * y) / t_1)) + (b / t_1)))
	elif z <= 1.55e+87:
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z
	else:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(z * c))
	tmp = 0.0
	if (z <= -6.8e+16)
		tmp = Float64(a * Float64(Float64(-4.0 * Float64(t / c)) + Float64(Float64(9.0 * Float64(Float64(x * y) / t_1)) + Float64(b / t_1))));
	elseif (z <= 1.55e+87)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) + Float64(-4.0 * Float64(Float64(a * Float64(t * z)) / c))) / z);
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (z * c);
	tmp = 0.0;
	if (z <= -6.8e+16)
		tmp = a * ((-4.0 * (t / c)) + ((9.0 * ((x * y) / t_1)) + (b / t_1)));
	elseif (z <= 1.55e+87)
		tmp = (((9.0 * ((x * y) / c)) + (b / c)) + (-4.0 * ((a * (t * z)) / c))) / z;
	else
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+16], N[(a * N[(N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+87], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e16

   1. Initial program 52.5%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in a around inf 74.5%

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

   if -6.8e16 < z < 1.55e87

   1. Initial program 91.1%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around 0 92.5%

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

   if 1.55e87 < z

   1. Initial program 49.0%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in x around 0 45.1%

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

      1. metadata-eval 45.1%

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

      2. cancel-sign-sub-inv 45.1%

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

      3. associate-*r* 45.1%

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

      4. *-commutative 45.1%

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

   7. Simplified 45.1%

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

   8. Taylor expanded in a around inf 79.4%

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

   9. Taylor expanded in c around 0 83.8%

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

   10. Taylor expanded in a around 0 85.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(z \cdot c\right)} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+87}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+161}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.5e+22)
   (* a (+ (* -4.0 (/ t c)) (/ b (* a (* z c)))))
   (if (<= z 6.6e+161)
     (/ (- b (- (* (* a t) (* z 4.0)) (* x (* 9.0 y)))) (* z c))
     (/ (* a (+ (* -4.0 t) (/ b (* a z)))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.5e+22) {
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	} else if (z <= 6.6e+161) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + (b / (a * z)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-7.5d+22)) then
        tmp = a * (((-4.0d0) * (t / c)) + (b / (a * (z * c))))
    else if (z <= 6.6d+161) then
        tmp = (b - (((a * t) * (z * 4.0d0)) - (x * (9.0d0 * y)))) / (z * c)
    else
        tmp = (a * (((-4.0d0) * t) + (b / (a * z)))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.5e+22) {
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	} else if (z <= 6.6e+161) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + (b / (a * z)))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7.5e+22:
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))))
	elif z <= 6.6e+161:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c)
	else:
		tmp = (a * ((-4.0 * t) + (b / (a * z)))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.5e+22)
		tmp = Float64(a * Float64(Float64(-4.0 * Float64(t / c)) + Float64(b / Float64(a * Float64(z * c)))));
	elseif (z <= 6.6e+161)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(9.0 * y)))) / Float64(z * c));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(a * z)))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7.5e+22)
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	elseif (z <= 6.6e+161)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (z * c);
	else
		tmp = (a * ((-4.0 * t) + (b / (a * z)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.5e+22], N[(a * N[(N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(a * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+161], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000002e22

   1. Initial program 52.5%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in x around 0 38.5%

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

      1. metadata-eval 38.5%

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

      2. cancel-sign-sub-inv 38.5%

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

      3. associate-*r* 38.5%

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

      4. *-commutative 38.5%

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

   7. Simplified 38.5%

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

   8. Taylor expanded in a around inf 63.3%

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

   if -7.5000000000000002e22 < z < 6.59999999999999995e161

   1. Initial program 88.4%

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

      1. associate-+l- 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 90.1%

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

      4. *-commutative 90.1%

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

      5. associate-+l- 90.1%

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

      6. associate-*l* 90.1%

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

      7. associate-*l* 87.7%

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

      8. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   if 6.59999999999999995e161 < z

   1. Initial program 39.8%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in x around 0 36.6%

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

      1. metadata-eval 36.6%

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

      2. cancel-sign-sub-inv 36.6%

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

      3. associate-*r* 36.6%

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

      4. *-commutative 36.6%

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

   7. Simplified 36.6%

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

   8. Taylor expanded in a around inf 77.9%

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

   9. Taylor expanded in c around 0 90.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+161}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(\frac{\frac{b}{t \cdot z}}{c} - a \cdot \frac{4}{c}\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1e-63)
   (* t (- (/ (/ b (* t z)) c) (* a (/ 4.0 c))))
   (if (<= a 6.5e-47)
     (/ (+ (* 9.0 (/ (* x y) c)) (/ b c)) z)
     (* a (+ (* -4.0 (/ t c)) (/ b (* a (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1e-63) {
		tmp = t * (((b / (t * z)) / c) - (a * (4.0 / c)));
	} else if (a <= 6.5e-47) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else {
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1d-63)) then
        tmp = t * (((b / (t * z)) / c) - (a * (4.0d0 / c)))
    else if (a <= 6.5d-47) then
        tmp = ((9.0d0 * ((x * y) / c)) + (b / c)) / z
    else
        tmp = a * (((-4.0d0) * (t / c)) + (b / (a * (z * c))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1e-63) {
		tmp = t * (((b / (t * z)) / c) - (a * (4.0 / c)));
	} else if (a <= 6.5e-47) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else {
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1e-63:
		tmp = t * (((b / (t * z)) / c) - (a * (4.0 / c)))
	elif a <= 6.5e-47:
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z
	else:
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1e-63)
		tmp = Float64(t * Float64(Float64(Float64(b / Float64(t * z)) / c) - Float64(a * Float64(4.0 / c))));
	elseif (a <= 6.5e-47)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) / z);
	else
		tmp = Float64(a * Float64(Float64(-4.0 * Float64(t / c)) + Float64(b / Float64(a * Float64(z * c)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1e-63)
		tmp = t * (((b / (t * z)) / c) - (a * (4.0 / c)));
	elseif (a <= 6.5e-47)
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	else
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1e-63], N[(t * N[(N[(N[(b / N[(t * z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] - N[(a * N[(4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-47], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(a * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.00000000000000007e-63

   1. Initial program 72.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in x around 0 53.8%

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

      1. metadata-eval 53.8%

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

      2. cancel-sign-sub-inv 53.8%

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

      3. associate-*r* 53.8%

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

      4. *-commutative 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in t around -inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. *-commutative 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

      4. +-commutative 64.2%

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

      5. mul-1-neg 64.2%

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

      6. unsub-neg 64.2%

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

      7. associate-*r/ 64.2%

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

      8. *-commutative 64.2%

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

      9. associate-/l* 64.1%

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

      10. *-commutative 64.1%

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

      11. associate-/r* 62.8%

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

      12. *-commutative 62.8%

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

   10. Simplified 62.8%

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

   if -1.00000000000000007e-63 < a < 6.5000000000000004e-47

   1. Initial program 73.3%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around 0 77.2%

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

   6. Taylor expanded in a around 0 75.1%

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

   if 6.5000000000000004e-47 < a

   1. Initial program 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in x around 0 64.7%

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

      1. metadata-eval 64.7%

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

      2. cancel-sign-sub-inv 64.7%

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

      3. associate-*r* 64.7%

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

      4. *-commutative 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in a around inf 78.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(\frac{\frac{b}{t \cdot z}}{c} - a \cdot \frac{4}{c}\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-46}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -3e-72)
   (* t (/ (- (/ (/ b z) t) (* a 4.0)) c))
   (if (<= a 6e-46)
     (/ (+ (* 9.0 (/ (* x y) c)) (/ b c)) z)
     (* a (+ (* -4.0 (/ t c)) (/ b (* a (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3e-72) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (a <= 6e-46) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else {
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-3d-72)) then
        tmp = t * ((((b / z) / t) - (a * 4.0d0)) / c)
    else if (a <= 6d-46) then
        tmp = ((9.0d0 * ((x * y) / c)) + (b / c)) / z
    else
        tmp = a * (((-4.0d0) * (t / c)) + (b / (a * (z * c))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3e-72) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (a <= 6e-46) {
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	} else {
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3e-72:
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c)
	elif a <= 6e-46:
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z
	else:
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3e-72)
		tmp = Float64(t * Float64(Float64(Float64(Float64(b / z) / t) - Float64(a * 4.0)) / c));
	elseif (a <= 6e-46)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c)) / z);
	else
		tmp = Float64(a * Float64(Float64(-4.0 * Float64(t / c)) + Float64(b / Float64(a * Float64(z * c)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -3e-72)
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	elseif (a <= 6e-46)
		tmp = ((9.0 * ((x * y) / c)) + (b / c)) / z;
	else
		tmp = a * ((-4.0 * (t / c)) + (b / (a * (z * c))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -3e-72], N[(t * N[(N[(N[(N[(b / z), $MachinePrecision] / t), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-46], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(a * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3e-72

   1. Initial program 71.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in x around 0 53.1%

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

      1. metadata-eval 53.1%

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

      2. cancel-sign-sub-inv 53.1%

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

      3. associate-*r* 53.1%

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

      4. *-commutative 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in t around -inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. *-commutative 63.4%

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

      3. distribute-rgt-neg-in 63.4%

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

      4. +-commutative 63.4%

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

      5. mul-1-neg 63.4%

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

      6. unsub-neg 63.4%

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

      7. associate-*r/ 63.4%

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

      8. *-commutative 63.4%

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

      9. associate-/l* 63.3%

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

      10. *-commutative 63.3%

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

      11. associate-/r* 62.0%

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

      12. *-commutative 62.0%

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

   10. Simplified 62.0%

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

       1. associate-*r/ 62.0%

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

       2. sub-div 64.8%

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

       3. associate-/r* 64.8%

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

   12. Applied egg-rr 64.8%

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

   if -3e-72 < a < 5.99999999999999975e-46

   1. Initial program 73.9%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in z around 0 77.9%

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

   6. Taylor expanded in a around 0 75.4%

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

   if 5.99999999999999975e-46 < a

   1. Initial program 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in x around 0 64.7%

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

      1. metadata-eval 64.7%

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

      2. cancel-sign-sub-inv 64.7%

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

      3. associate-*r* 64.7%

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

      4. *-commutative 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in a around inf 78.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-46}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{a \cdot \left(z \cdot c\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-37} \lor \neg \left(z \leq 2.1 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.6e-37) (not (<= z 2.1e+45)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* y (* 9.0 x))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.6e-37) || !(z <= 2.1e+45)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2.6d-37)) .or. (.not. (z <= 2.1d+45))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (y * (9.0d0 * x))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.6e-37) || !(z <= 2.1e+45)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.6e-37) or not (z <= 2.1e+45):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (y * (9.0 * x))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.6e-37) || !(z <= 2.1e+45))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.6e-37) || ~((z <= 2.1e+45)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (y * (9.0 * x))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.6e-37], N[Not[LessEqual[z, 2.1e+45]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999998e-37 or 2.09999999999999995e45 < z

   1. Initial program 54.5%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in x around 0 43.5%

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

      1. metadata-eval 43.5%

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

      2. cancel-sign-sub-inv 43.5%

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

      3. associate-*r* 43.5%

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

      4. *-commutative 43.5%

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

   7. Simplified 43.5%

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

   8. Taylor expanded in a around inf 69.2%

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

   9. Taylor expanded in c around 0 73.1%

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

   10. Taylor expanded in a around 0 76.8%

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

   if -2.5999999999999998e-37 < z < 2.09999999999999995e45

   1. Initial program 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in t around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-*r* 78.6%

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

      3. *-commutative 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-37} \lor \neg \left(z \leq 2.1 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(\frac{9}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+123}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \left(x \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.1e+47)
   (* x (* (/ 9.0 z) (/ y c)))
   (if (<= y 2.05e+123)
     (/ (+ (* -4.0 (* a t)) (/ b z)) c)
     (* (/ 9.0 z) (* x (/ y c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.1e+47) {
		tmp = x * ((9.0 / z) * (y / c));
	} else if (y <= 2.05e+123) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (9.0 / z) * (x * (y / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-3.1d+47)) then
        tmp = x * ((9.0d0 / z) * (y / c))
    else if (y <= 2.05d+123) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (9.0d0 / z) * (x * (y / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.1e+47) {
		tmp = x * ((9.0 / z) * (y / c));
	} else if (y <= 2.05e+123) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (9.0 / z) * (x * (y / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.1e+47:
		tmp = x * ((9.0 / z) * (y / c))
	elif y <= 2.05e+123:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (9.0 / z) * (x * (y / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.1e+47)
		tmp = Float64(x * Float64(Float64(9.0 / z) * Float64(y / c)));
	elseif (y <= 2.05e+123)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(9.0 / z) * Float64(x * Float64(y / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.1e+47)
		tmp = x * ((9.0 / z) * (y / c));
	elseif (y <= 2.05e+123)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (9.0 / z) * (x * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.1e+47], N[(x * N[(N[(9.0 / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+123], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(9.0 / z), $MachinePrecision] * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000001e47

   1. Initial program 61.5%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in x around inf 41.7%

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

      1. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   8. Taylor expanded in x around 0 41.7%

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

      1. associate-*r/ 41.8%

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

      2. *-commutative 41.8%

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

      3. associate-*l* 41.8%

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

      4. *-commutative 41.8%

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

      5. *-commutative 41.8%

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

      6. associate-*r/ 43.8%

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

      7. times-frac 47.9%

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

   10. Simplified 47.9%

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

   if -3.1000000000000001e47 < y < 2.04999999999999995e123

   1. Initial program 75.4%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in x around 0 61.4%

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

      1. metadata-eval 61.4%

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

      2. cancel-sign-sub-inv 61.4%

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

      3. associate-*r* 61.4%

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

      4. *-commutative 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in a around inf 67.5%

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

   9. Taylor expanded in c around 0 68.1%

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

   10. Taylor expanded in a around 0 76.1%

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

   if 2.04999999999999995e123 < y

   1. Initial program 77.5%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in x around inf 52.1%

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

      1. associate-*r/ 52.1%

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

      2. *-commutative 52.1%

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

      3. times-frac 54.3%

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

      4. associate-/l* 63.2%

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

   7. Simplified 63.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(\frac{9}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+123}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \left(x \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -90000000000000 \lor \neg \left(y \leq 3.8 \cdot 10^{+122}\right):\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -90000000000000.0) (not (<= y 3.8e+122)))
   (* 9.0 (* x (/ (/ y c) z)))
   (* a (* -4.0 (/ t c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -90000000000000.0) || !(y <= 3.8e+122)) {
		tmp = 9.0 * (x * ((y / c) / z));
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y <= (-90000000000000.0d0)) .or. (.not. (y <= 3.8d+122))) then
        tmp = 9.0d0 * (x * ((y / c) / z))
    else
        tmp = a * ((-4.0d0) * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -90000000000000.0) || !(y <= 3.8e+122)) {
		tmp = 9.0 * (x * ((y / c) / z));
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -90000000000000.0) or not (y <= 3.8e+122):
		tmp = 9.0 * (x * ((y / c) / z))
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -90000000000000.0) || !(y <= 3.8e+122))
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c) / z)));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y <= -90000000000000.0) || ~((y <= 3.8e+122)))
		tmp = 9.0 * (x * ((y / c) / z));
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -90000000000000.0], N[Not[LessEqual[y, 3.8e+122]], $MachinePrecision]], N[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e13 or 3.7999999999999998e122 < y

   1. Initial program 69.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around inf 47.1%

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

      1. *-commutative 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in x around 0 47.1%

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

      1. associate-/l* 51.0%

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

      2. associate-/r* 54.8%

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

   10. Simplified 54.8%

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

   if -9e13 < y < 3.7999999999999998e122

   1. Initial program 75.3%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around 0 61.8%

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

      1. metadata-eval 61.8%

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

      2. cancel-sign-sub-inv 61.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in a around inf 68.2%

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

   9. Taylor expanded in t around inf 48.0%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90000000000000 \lor \neg \left(y \leq 3.8 \cdot 10^{+122}\right):\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+15} \lor \neg \left(y \leq 8.6 \cdot 10^{+123}\right):\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -1.95e+15) (not (<= y 8.6e+123)))
   (* 9.0 (* x (/ y (* z c))))
   (* a (* -4.0 (/ t c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.95e+15) || !(y <= 8.6e+123)) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y <= (-1.95d+15)) .or. (.not. (y <= 8.6d+123))) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else
        tmp = a * ((-4.0d0) * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.95e+15) || !(y <= 8.6e+123)) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -1.95e+15) or not (y <= 8.6e+123):
		tmp = 9.0 * (x * (y / (z * c)))
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -1.95e+15) || !(y <= 8.6e+123))
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y <= -1.95e+15) || ~((y <= 8.6e+123)))
		tmp = 9.0 * (x * (y / (z * c)));
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -1.95e+15], N[Not[LessEqual[y, 8.6e+123]], $MachinePrecision]], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e15 or 8.59999999999999972e123 < y

   1. Initial program 69.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around inf 47.1%

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

      1. *-commutative 47.1%

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

   7. Simplified 47.1%

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

      1. associate-/l* 51.0%

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

   9. Applied egg-rr 51.0%

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

   if -1.95e15 < y < 8.59999999999999972e123

   1. Initial program 75.3%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around 0 61.8%

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

      1. metadata-eval 61.8%

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

      2. cancel-sign-sub-inv 61.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in a around inf 68.2%

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

   9. Taylor expanded in t around inf 48.0%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+15} \lor \neg \left(y \leq 8.6 \cdot 10^{+123}\right):\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{9}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \left(x \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -9e+14)
   (* x (* (/ 9.0 z) (/ y c)))
   (if (<= y 4e+122) (* a (* -4.0 (/ t c))) (* (/ 9.0 z) (* x (/ y c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -9e+14) {
		tmp = x * ((9.0 / z) * (y / c));
	} else if (y <= 4e+122) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = (9.0 / z) * (x * (y / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-9d+14)) then
        tmp = x * ((9.0d0 / z) * (y / c))
    else if (y <= 4d+122) then
        tmp = a * ((-4.0d0) * (t / c))
    else
        tmp = (9.0d0 / z) * (x * (y / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -9e+14) {
		tmp = x * ((9.0 / z) * (y / c));
	} else if (y <= 4e+122) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = (9.0 / z) * (x * (y / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -9e+14:
		tmp = x * ((9.0 / z) * (y / c))
	elif y <= 4e+122:
		tmp = a * (-4.0 * (t / c))
	else:
		tmp = (9.0 / z) * (x * (y / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -9e+14)
		tmp = Float64(x * Float64(Float64(9.0 / z) * Float64(y / c)));
	elseif (y <= 4e+122)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	else
		tmp = Float64(Float64(9.0 / z) * Float64(x * Float64(y / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -9e+14)
		tmp = x * ((9.0 / z) * (y / c));
	elseif (y <= 4e+122)
		tmp = a * (-4.0 * (t / c));
	else
		tmp = (9.0 / z) * (x * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -9e+14], N[(x * N[(N[(9.0 / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+122], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 / z), $MachinePrecision] * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e14

   1. Initial program 63.6%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in x around inf 43.2%

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

      1. *-commutative 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in x around 0 43.2%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 43.2%

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

      4. *-commutative 43.2%

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

      5. *-commutative 43.2%

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

      6. associate-*r/ 44.9%

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

      7. times-frac 48.4%

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

   10. Simplified 48.4%

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

   if -9e14 < y < 4.00000000000000006e122

   1. Initial program 75.3%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around 0 61.8%

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

      1. metadata-eval 61.8%

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

      2. cancel-sign-sub-inv 61.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in a around inf 68.2%

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

   9. Taylor expanded in t around inf 48.0%

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

   if 4.00000000000000006e122 < y

   1. Initial program 77.5%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in x around inf 52.1%

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

      1. associate-*r/ 52.1%

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

      2. *-commutative 52.1%

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

      3. times-frac 54.3%

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

      4. associate-/l* 63.2%

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

   7. Simplified 63.2%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{9}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \left(x \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{9}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.9e+14)
   (* x (* (/ 9.0 z) (/ y c)))
   (if (<= y 3.6e+122) (* a (* -4.0 (/ t c))) (* 9.0 (* x (/ (/ y c) z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.9e+14) {
		tmp = x * ((9.0 / z) * (y / c));
	} else if (y <= 3.6e+122) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = 9.0 * (x * ((y / c) / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-3.9d+14)) then
        tmp = x * ((9.0d0 / z) * (y / c))
    else if (y <= 3.6d+122) then
        tmp = a * ((-4.0d0) * (t / c))
    else
        tmp = 9.0d0 * (x * ((y / c) / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.9e+14) {
		tmp = x * ((9.0 / z) * (y / c));
	} else if (y <= 3.6e+122) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = 9.0 * (x * ((y / c) / z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.9e+14:
		tmp = x * ((9.0 / z) * (y / c))
	elif y <= 3.6e+122:
		tmp = a * (-4.0 * (t / c))
	else:
		tmp = 9.0 * (x * ((y / c) / z))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.9e+14)
		tmp = Float64(x * Float64(Float64(9.0 / z) * Float64(y / c)));
	elseif (y <= 3.6e+122)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	else
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c) / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.9e+14)
		tmp = x * ((9.0 / z) * (y / c));
	elseif (y <= 3.6e+122)
		tmp = a * (-4.0 * (t / c));
	else
		tmp = 9.0 * (x * ((y / c) / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.9e+14], N[(x * N[(N[(9.0 / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+122], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e14

   1. Initial program 63.6%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in x around inf 43.2%

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

      1. *-commutative 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in x around 0 43.2%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 43.2%

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

      4. *-commutative 43.2%

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

      5. *-commutative 43.2%

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

      6. associate-*r/ 44.9%

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

      7. times-frac 48.4%

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

   10. Simplified 48.4%

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

   if -3.9e14 < y < 3.6000000000000003e122

   1. Initial program 75.3%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around 0 61.8%

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

      1. metadata-eval 61.8%

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

      2. cancel-sign-sub-inv 61.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in a around inf 68.2%

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

   9. Taylor expanded in t around inf 48.0%

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

   if 3.6000000000000003e122 < y

   1. Initial program 77.5%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in x around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in x around 0 52.1%

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

      1. associate-/l* 59.0%

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

      2. associate-/r* 63.3%

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

   10. Simplified 63.3%

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

Alternative 15: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+147} \lor \neg \left(b \leq 3.9 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -6e+147) (not (<= b 3.9e+27)))
   (/ (/ b c) z)
   (* a (* -4.0 (/ t c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -6e+147) || !(b <= 3.9e+27)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-6d+147)) .or. (.not. (b <= 3.9d+27))) then
        tmp = (b / c) / z
    else
        tmp = a * ((-4.0d0) * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -6e+147) || !(b <= 3.9e+27)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -6e+147) or not (b <= 3.9e+27):
		tmp = (b / c) / z
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -6e+147) || !(b <= 3.9e+27))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -6e+147) || ~((b <= 3.9e+27)))
		tmp = (b / c) / z;
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -6e+147], N[Not[LessEqual[b, 3.9e+27]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.99999999999999987e147 or 3.8999999999999999e27 < b

   1. Initial program 79.5%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 56.9%

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

      1. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in b around 0 56.9%

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

      1. associate-/r* 65.5%

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

   10. Simplified 65.5%

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

   if -5.99999999999999987e147 < b < 3.8999999999999999e27

   1. Initial program 70.2%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in x around 0 41.9%

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

      1. metadata-eval 41.9%

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

      2. cancel-sign-sub-inv 41.9%

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

      3. associate-*r* 41.9%

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

      4. *-commutative 41.9%

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

   7. Simplified 41.9%

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

   8. Taylor expanded in a around inf 56.6%

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

   9. Taylor expanded in t around inf 49.6%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+147} \lor \neg \left(b \leq 3.9 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+107} \lor \neg \left(b \leq 1.6 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.1e+107) (not (<= b 1.6e+28)))
   (/ (/ b c) z)
   (* -4.0 (* t (/ a c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.1e+107) || !(b <= 1.6e+28)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.1d+107)) .or. (.not. (b <= 1.6d+28))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.1e+107) || !(b <= 1.6e+28)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.1e+107) or not (b <= 1.6e+28):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.1e+107) || !(b <= 1.6e+28))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.1e+107) || ~((b <= 1.6e+28)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.1e+107], N[Not[LessEqual[b, 1.6e+28]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e107 or 1.6e28 < b

   1. Initial program 78.1%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in b around 0 55.3%

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

      1. associate-/r* 63.1%

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

   10. Simplified 63.1%

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

   if -1.1e107 < b < 1.6e28

   1. Initial program 70.5%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in x around 0 41.5%

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

      1. metadata-eval 41.5%

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

      2. cancel-sign-sub-inv 41.5%

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

      3. associate-*r* 41.5%

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

      4. *-commutative 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in b around 0 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-/l* 50.3%

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

   10. Simplified 50.3%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+107} \lor \neg \left(b \leq 1.6 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+148}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.2e+148)
   (* (/ b c) (/ 1.0 z))
   (if (<= b 1.65e+28) (* a (* -4.0 (/ t c))) (/ (/ b c) z))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.2e+148) {
		tmp = (b / c) * (1.0 / z);
	} else if (b <= 1.65e+28) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.2d+148)) then
        tmp = (b / c) * (1.0d0 / z)
    else if (b <= 1.65d+28) then
        tmp = a * ((-4.0d0) * (t / c))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.2e+148) {
		tmp = (b / c) * (1.0 / z);
	} else if (b <= 1.65e+28) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.2e+148:
		tmp = (b / c) * (1.0 / z)
	elif b <= 1.65e+28:
		tmp = a * (-4.0 * (t / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.2e+148)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	elseif (b <= 1.65e+28)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.2e+148)
		tmp = (b / c) * (1.0 / z);
	elseif (b <= 1.65e+28)
		tmp = a * (-4.0 * (t / c));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.2e+148], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e+28], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999997e148

   1. Initial program 80.7%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in b around inf 61.9%

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

      1. *-commutative 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in b around 0 61.9%

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

      1. associate-/r* 74.3%

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

   10. Simplified 74.3%

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

       1. div-inv 74.4%

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

   12. Applied egg-rr 74.4%

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

   if -1.19999999999999997e148 < b < 1.65e28

   1. Initial program 70.2%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in x around 0 41.9%

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

      1. metadata-eval 41.9%

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

      2. cancel-sign-sub-inv 41.9%

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

      3. associate-*r* 41.9%

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

      4. *-commutative 41.9%

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

   7. Simplified 41.9%

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

   8. Taylor expanded in a around inf 56.6%

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

   9. Taylor expanded in t around inf 49.6%

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

   if 1.65e28 < b

   1. Initial program 78.8%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in b around inf 54.0%

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

      1. *-commutative 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in b around 0 54.0%

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

      1. associate-/r* 60.3%

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

   10. Simplified 60.3%

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

Alternative 18: 34.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.1%

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

3. Simplified 77.3%

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

5. Taylor expanded in b around inf 31.7%

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

   1. *-commutative 31.7%

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

7. Simplified 31.7%

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

8. Taylor expanded in b around 0 31.7%

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

   1. associate-/r* 33.4%

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

10. Simplified 33.4%

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

Alternative 19: 35.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.1%

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

3. Simplified 77.3%

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

5. Taylor expanded in b around inf 31.7%

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

   1. *-commutative 31.7%

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

7. Simplified 31.7%

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

Developer Target 1: 80.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

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