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

Percentage Accurate: 79.3% → 84.0%

Time: 14.3s

Alternatives: 20

Speedup: 0.9×

• 37.5% 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: 79.3% 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: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z 3.6e+29)
   (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
   (fma (* (/ y (* c z)) 9.0) x (fma (* (/ a c) -4.0) t (/ b (* c z))))))

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 <= 3.6e+29) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = fma(((y / (c * z)) * 9.0), x, fma(((a / c) * -4.0), t, (b / (c * z))));
	}
	return tmp;
}

Julia

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 <= 3.6e+29)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = fma(Float64(Float64(y / Float64(c * z)) * 9.0), x, fma(Float64(Float64(a / c) * -4.0), t, Float64(b / Float64(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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 3.6e+29], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x + N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.59999999999999976e29

   1. Initial program 85.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 92.1%

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

   if 3.59999999999999976e29 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

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

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 88.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - \left(9 \cdot x\right) \cdot y\right)}{c \cdot z}\\ t_2 := \frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-208}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

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 (- (* (* (* 4.0 z) t) a) (* (* 9.0 x) y))) (* c z)))
        (t_2 (/ (fma (* 9.0 x) y (fma (* (* -4.0 z) a) t b)) (* c z))))
   (if (<= t_1 -1e-273)
     t_2
     (if (<= t_1 2e-208)
       (/ (/ (fma (* (* t z) a) -4.0 b) c) z)
       (if (<= t_1 INFINITY) t_2 (/ (* a -4.0) (/ c t)))))))

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 - ((((4.0 * z) * t) * a) - ((9.0 * x) * y))) / (c * z);
	double t_2 = fma((9.0 * x), y, fma(((-4.0 * z) * a), t, b)) / (c * z);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 2e-208) {
		tmp = (fma(((t * z) * a), -4.0, b) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (a * -4.0) / (c / t);
	}
	return tmp;
}

Julia

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(Float64(Float64(4.0 * z) * t) * a) - Float64(Float64(9.0 * x) * y))) / Float64(c * z))
	t_2 = Float64(fma(Float64(9.0 * x), y, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-273)
		tmp = t_2;
	elseif (t_1 <= 2e-208)
		tmp = Float64(Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / c) / z);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * -4.0) / Float64(c / t));
	end
	return tmp
end

Wolfram

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[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-273], t$95$2, If[LessEqual[t$95$1, 2e-208], N[(N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(a * -4.0), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1e-273 or 2.0000000000000002e-208 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      11. associate-+l- N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 92.1%

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

   if -1e-273 < (/.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)) < 2.0000000000000002e-208

   1. Initial program 50.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 84.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 89.0

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

   7. Applied rewrites 89.0%

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

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

   1. Initial program 0.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 67.4%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.8

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

   7. Applied rewrites 55.8%

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

   9. Applied rewrites 55.6%

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

   11. Applied rewrites 55.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - \left(9 \cdot x\right) \cdot y\right)}{c \cdot z} \leq -1 \cdot 10^{-273}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - \left(9 \cdot x\right) \cdot y\right)}{c \cdot z} \leq 2 \cdot 10^{-208}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - \left(9 \cdot x\right) \cdot y\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{-1}{-z} \cdot \frac{b}{c}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -1e+103)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 -5e+43)
       (* (/ -1.0 (- z)) (/ b c))
       (if (<= t_1 1000000.0) (/ (* a -4.0) (/ c t)) (/ t_1 (* c z)))))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= -5e+43) {
		tmp = (-1.0 / -z) * (b / c);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_1 / (c * z);
	}
	return tmp;
}

Fortran

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 = (9.0d0 * x) * y
    if (t_1 <= (-1d+103)) then
        tmp = (x / z) * ((y / c) * 9.0d0)
    else if (t_1 <= (-5d+43)) then
        tmp = ((-1.0d0) / -z) * (b / c)
    else if (t_1 <= 1000000.0d0) then
        tmp = (a * (-4.0d0)) / (c / t)
    else
        tmp = t_1 / (c * z)
    end if
    code = tmp
end function

Java

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= -5e+43) {
		tmp = (-1.0 / -z) * (b / c);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_1 / (c * z);
	}
	return tmp;
}

Python

[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 = (9.0 * x) * y
	tmp = 0
	if t_1 <= -1e+103:
		tmp = (x / z) * ((y / c) * 9.0)
	elif t_1 <= -5e+43:
		tmp = (-1.0 / -z) * (b / c)
	elif t_1 <= 1000000.0:
		tmp = (a * -4.0) / (c / t)
	else:
		tmp = t_1 / (c * z)
	return tmp

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -1e+103)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= -5e+43)
		tmp = Float64(Float64(-1.0 / Float64(-z)) * Float64(b / c));
	elseif (t_1 <= 1000000.0)
		tmp = Float64(Float64(a * -4.0) / Float64(c / t));
	else
		tmp = Float64(t_1 / Float64(c * z));
	end
	return tmp
end

MATLAB

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 = (9.0 * x) * y;
	tmp = 0.0;
	if (t_1 <= -1e+103)
		tmp = (x / z) * ((y / c) * 9.0);
	elseif (t_1 <= -5e+43)
		tmp = (-1.0 / -z) * (b / c);
	elseif (t_1 <= 1000000.0)
		tmp = (a * -4.0) / (c / t);
	else
		tmp = t_1 / (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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+103], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+43], N[(N[(-1.0 / (-z)), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], N[(N[(a * -4.0), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e103

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -1e103 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000004e43

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 61.1

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 70.7%

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

   if -5.0000000000000004e43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e6

   1. Initial program 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

   9. Applied rewrites 55.8%

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

   11. Applied rewrites 55.8%

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

   if 1e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 70.1

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

   5. Applied rewrites 70.1%

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

   7. Applied rewrites 67.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{-1}{-z} \cdot \frac{b}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\frac{\left(9 \cdot y\right) \cdot x}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{-1}{-z} \cdot \frac{b}{c}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -1e+103)
     (/ (* (* 9.0 y) x) (* c z))
     (if (<= t_1 -5e+43)
       (* (/ -1.0 (- z)) (/ b c))
       (if (<= t_1 1000000.0) (/ (* a -4.0) (/ c t)) (/ t_1 (* c z)))))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = ((9.0 * y) * x) / (c * z);
	} else if (t_1 <= -5e+43) {
		tmp = (-1.0 / -z) * (b / c);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_1 / (c * z);
	}
	return tmp;
}

Fortran

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 = (9.0d0 * x) * y
    if (t_1 <= (-1d+103)) then
        tmp = ((9.0d0 * y) * x) / (c * z)
    else if (t_1 <= (-5d+43)) then
        tmp = ((-1.0d0) / -z) * (b / c)
    else if (t_1 <= 1000000.0d0) then
        tmp = (a * (-4.0d0)) / (c / t)
    else
        tmp = t_1 / (c * z)
    end if
    code = tmp
end function

Java

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = ((9.0 * y) * x) / (c * z);
	} else if (t_1 <= -5e+43) {
		tmp = (-1.0 / -z) * (b / c);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_1 / (c * z);
	}
	return tmp;
}

Python

[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 = (9.0 * x) * y
	tmp = 0
	if t_1 <= -1e+103:
		tmp = ((9.0 * y) * x) / (c * z)
	elif t_1 <= -5e+43:
		tmp = (-1.0 / -z) * (b / c)
	elif t_1 <= 1000000.0:
		tmp = (a * -4.0) / (c / t)
	else:
		tmp = t_1 / (c * z)
	return tmp

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -1e+103)
		tmp = Float64(Float64(Float64(9.0 * y) * x) / Float64(c * z));
	elseif (t_1 <= -5e+43)
		tmp = Float64(Float64(-1.0 / Float64(-z)) * Float64(b / c));
	elseif (t_1 <= 1000000.0)
		tmp = Float64(Float64(a * -4.0) / Float64(c / t));
	else
		tmp = Float64(t_1 / Float64(c * z));
	end
	return tmp
end

MATLAB

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 = (9.0 * x) * y;
	tmp = 0.0;
	if (t_1 <= -1e+103)
		tmp = ((9.0 * y) * x) / (c * z);
	elseif (t_1 <= -5e+43)
		tmp = (-1.0 / -z) * (b / c);
	elseif (t_1 <= 1000000.0)
		tmp = (a * -4.0) / (c / t);
	else
		tmp = t_1 / (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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+103], N[(N[(N[(9.0 * y), $MachinePrecision] * x), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+43], N[(N[(-1.0 / (-z)), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], N[(N[(a * -4.0), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e103

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 76.3

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

   5. Applied rewrites 76.3%

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

   7. Applied rewrites 72.7%

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

   if -1e103 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000004e43

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 61.1

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 70.7%

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

   if -5.0000000000000004e43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e6

   1. Initial program 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

   9. Applied rewrites 55.8%

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

   11. Applied rewrites 55.8%

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

   if 1e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 70.1

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

   5. Applied rewrites 70.1%

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

   7. Applied rewrites 67.3%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\frac{\left(9 \cdot y\right) \cdot x}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{-1}{-z} \cdot \frac{b}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{t\_1}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{-1}{-z} \cdot \frac{b}{c}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (/ t_1 (* c z))))
   (if (<= t_1 -1e+103)
     t_2
     (if (<= t_1 -5e+43)
       (* (/ -1.0 (- z)) (/ b c))
       (if (<= t_1 1000000.0) (/ (* a -4.0) (/ c t)) t_2)))))

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 = (9.0 * x) * y;
	double t_2 = t_1 / (c * z);
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = t_2;
	} else if (t_1 <= -5e+43) {
		tmp = (-1.0 / -z) * (b / c);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = t_1 / (c * z)
    if (t_1 <= (-1d+103)) then
        tmp = t_2
    else if (t_1 <= (-5d+43)) then
        tmp = ((-1.0d0) / -z) * (b / c)
    else if (t_1 <= 1000000.0d0) then
        tmp = (a * (-4.0d0)) / (c / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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 = (9.0 * x) * y;
	double t_2 = t_1 / (c * z);
	double tmp;
	if (t_1 <= -1e+103) {
		tmp = t_2;
	} else if (t_1 <= -5e+43) {
		tmp = (-1.0 / -z) * (b / c);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 = (9.0 * x) * y
	t_2 = t_1 / (c * z)
	tmp = 0
	if t_1 <= -1e+103:
		tmp = t_2
	elif t_1 <= -5e+43:
		tmp = (-1.0 / -z) * (b / c)
	elif t_1 <= 1000000.0:
		tmp = (a * -4.0) / (c / t)
	else:
		tmp = t_2
	return tmp

Julia

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(9.0 * x) * y)
	t_2 = Float64(t_1 / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e+103)
		tmp = t_2;
	elseif (t_1 <= -5e+43)
		tmp = Float64(Float64(-1.0 / Float64(-z)) * Float64(b / c));
	elseif (t_1 <= 1000000.0)
		tmp = Float64(Float64(a * -4.0) / Float64(c / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = t_1 / (c * z);
	tmp = 0.0;
	if (t_1 <= -1e+103)
		tmp = t_2;
	elseif (t_1 <= -5e+43)
		tmp = (-1.0 / -z) * (b / c);
	elseif (t_1 <= 1000000.0)
		tmp = (a * -4.0) / (c / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+103], t$95$2, If[LessEqual[t$95$1, -5e+43], N[(N[(-1.0 / (-z)), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], N[(N[(a * -4.0), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e103 or 1e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 72.9

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

   5. Applied rewrites 72.9%

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

   7. Applied rewrites 69.7%

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

   if -1e103 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000004e43

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 61.1

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 70.7%

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

   if -5.0000000000000004e43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e6

   1. Initial program 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

   9. Applied rewrites 55.8%

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

   11. Applied rewrites 55.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{-1}{-z} \cdot \frac{b}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{t\_1}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (/ t_1 (* c z))))
   (if (<= t_1 -5e+93)
     t_2
     (if (<= t_1 -5e+43)
       (/ b (* c z))
       (if (<= t_1 1000000.0) (/ (* a -4.0) (/ c t)) t_2)))))

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 = (9.0 * x) * y;
	double t_2 = t_1 / (c * z);
	double tmp;
	if (t_1 <= -5e+93) {
		tmp = t_2;
	} else if (t_1 <= -5e+43) {
		tmp = b / (c * z);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = t_1 / (c * z)
    if (t_1 <= (-5d+93)) then
        tmp = t_2
    else if (t_1 <= (-5d+43)) then
        tmp = b / (c * z)
    else if (t_1 <= 1000000.0d0) then
        tmp = (a * (-4.0d0)) / (c / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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 = (9.0 * x) * y;
	double t_2 = t_1 / (c * z);
	double tmp;
	if (t_1 <= -5e+93) {
		tmp = t_2;
	} else if (t_1 <= -5e+43) {
		tmp = b / (c * z);
	} else if (t_1 <= 1000000.0) {
		tmp = (a * -4.0) / (c / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 = (9.0 * x) * y
	t_2 = t_1 / (c * z)
	tmp = 0
	if t_1 <= -5e+93:
		tmp = t_2
	elif t_1 <= -5e+43:
		tmp = b / (c * z)
	elif t_1 <= 1000000.0:
		tmp = (a * -4.0) / (c / t)
	else:
		tmp = t_2
	return tmp

Julia

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(9.0 * x) * y)
	t_2 = Float64(t_1 / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -5e+93)
		tmp = t_2;
	elseif (t_1 <= -5e+43)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 1000000.0)
		tmp = Float64(Float64(a * -4.0) / Float64(c / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = t_1 / (c * z);
	tmp = 0.0;
	if (t_1 <= -5e+93)
		tmp = t_2;
	elseif (t_1 <= -5e+43)
		tmp = b / (c * z);
	elseif (t_1 <= 1000000.0)
		tmp = (a * -4.0) / (c / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+93], t$95$2, If[LessEqual[t$95$1, -5e+43], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], N[(N[(a * -4.0), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000001e93 or 1e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 71.7

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

   5. Applied rewrites 71.7%

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

   7. Applied rewrites 69.4%

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

   if -5.0000000000000001e93 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000004e43

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

   if -5.0000000000000004e43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e6

   1. Initial program 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

   9. Applied rewrites 55.8%

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

   11. Applied rewrites 55.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+93}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 1000000:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{t\_1}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (/ t_1 (* c z))))
   (if (<= t_1 -5e+93)
     t_2
     (if (<= t_1 -5e+43)
       (/ b (* c z))
       (if (<= t_1 1000000.0) (* (* (/ t c) a) -4.0) t_2)))))

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 = (9.0 * x) * y;
	double t_2 = t_1 / (c * z);
	double tmp;
	if (t_1 <= -5e+93) {
		tmp = t_2;
	} else if (t_1 <= -5e+43) {
		tmp = b / (c * z);
	} else if (t_1 <= 1000000.0) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = t_1 / (c * z)
    if (t_1 <= (-5d+93)) then
        tmp = t_2
    else if (t_1 <= (-5d+43)) then
        tmp = b / (c * z)
    else if (t_1 <= 1000000.0d0) then
        tmp = ((t / c) * a) * (-4.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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 = (9.0 * x) * y;
	double t_2 = t_1 / (c * z);
	double tmp;
	if (t_1 <= -5e+93) {
		tmp = t_2;
	} else if (t_1 <= -5e+43) {
		tmp = b / (c * z);
	} else if (t_1 <= 1000000.0) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 = (9.0 * x) * y
	t_2 = t_1 / (c * z)
	tmp = 0
	if t_1 <= -5e+93:
		tmp = t_2
	elif t_1 <= -5e+43:
		tmp = b / (c * z)
	elif t_1 <= 1000000.0:
		tmp = ((t / c) * a) * -4.0
	else:
		tmp = t_2
	return tmp

Julia

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(9.0 * x) * y)
	t_2 = Float64(t_1 / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -5e+93)
		tmp = t_2;
	elseif (t_1 <= -5e+43)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 1000000.0)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = t_1 / (c * z);
	tmp = 0.0;
	if (t_1 <= -5e+93)
		tmp = t_2;
	elseif (t_1 <= -5e+43)
		tmp = b / (c * z);
	elseif (t_1 <= 1000000.0)
		tmp = ((t / c) * a) * -4.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+93], t$95$2, If[LessEqual[t$95$1, -5e+43], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000001e93 or 1e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 71.7

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

   5. Applied rewrites 71.7%

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

   7. Applied rewrites 69.4%

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

   if -5.0000000000000001e93 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000004e43

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

   if -5.0000000000000004e43 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e6

   1. Initial program 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

   9. Applied rewrites 55.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+93}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 1000000:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -2e+134)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 5e-36)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (/ (fma (* y x) 9.0 (* (* (* -4.0 z) a) t)) (* c z))))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -2e+134) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= 5e-36) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else {
		tmp = fma((y * x), 9.0, (((-4.0 * z) * a) * t)) / (c * z);
	}
	return tmp;
}

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -2e+134)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= 5e-36)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(fma(Float64(y * x), 9.0, Float64(Float64(Float64(-4.0 * z) * a) * t)) / Float64(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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+134], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-36], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999984e134

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if -1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000004e-36

   1. Initial program 79.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 79.6

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 82.3%

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

   if 5.00000000000000004e-36 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 87.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      11. associate-+l- N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.1

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

   7. Applied rewrites 85.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 85.2

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

   9. Applied rewrites 83.9%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \left(\left(-4 \cdot z\right) \cdot a\right) \cdot t\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -2e+134)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 5e-36)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (/ (fma -4.0 (* (* t z) a) (* (* y x) 9.0)) (* c z))))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -2e+134) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= 5e-36) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else {
		tmp = fma(-4.0, ((t * z) * a), ((y * x) * 9.0)) / (c * z);
	}
	return tmp;
}

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -2e+134)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= 5e-36)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), Float64(Float64(y * x) * 9.0)) / Float64(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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+134], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-36], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999984e134

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if -1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000004e-36

   1. Initial program 79.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 79.6

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 82.3%

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

   if 5.00000000000000004e-36 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 87.8%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 85.2

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

   5. Applied rewrites 85.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq 2000000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -2e+134)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 2000000000000.0)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (/ (/ (fma (* y x) 9.0 b) c) z)))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -2e+134) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= 2000000000000.0) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	}
	return tmp;
}

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -2e+134)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= 2000000000000.0)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+134], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2000000000000.0], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999984e134

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if -1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e12

   1. Initial program 80.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 81.9%

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

   if 2e12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 86.9%

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

   3. Taylor expanded in a around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 73.1

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

   5. Applied rewrites 73.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 2000000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -2e+134)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 2e+143)
       (/ (fma (* t a) -4.0 (/ b z)) c)
       (* (/ x c) (/ (* 9.0 y) z))))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -2e+134) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= 2e+143) {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	} else {
		tmp = (x / c) * ((9.0 * y) / z);
	}
	return tmp;
}

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -2e+134)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= 2e+143)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(x / c) * Float64(Float64(9.0 * y) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+134], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+143], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x / c), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.99999999999999984e134

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if -1.99999999999999984e134 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e143

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 75.6

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 78.3%

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

   if 2e143 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 81.4

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

   5. Applied rewrites 81.4%

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

   7. Applied rewrites 76.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)))
   (if (<= t_1 -1e+131)
     (* (/ x z) (* (/ y c) 9.0))
     (if (<= t_1 5e+74)
       (/ (fma (* (* t a) -4.0) z b) (* c z))
       (* (/ x c) (/ (* 9.0 y) z))))))

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 = (9.0 * x) * y;
	double tmp;
	if (t_1 <= -1e+131) {
		tmp = (x / z) * ((y / c) * 9.0);
	} else if (t_1 <= 5e+74) {
		tmp = fma(((t * a) * -4.0), z, b) / (c * z);
	} else {
		tmp = (x / c) * ((9.0 * y) / z);
	}
	return tmp;
}

Julia

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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -1e+131)
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	elseif (t_1 <= 5e+74)
		tmp = Float64(fma(Float64(Float64(t * a) * -4.0), z, b) / Float64(c * z));
	else
		tmp = Float64(Float64(x / c) * Float64(Float64(9.0 * y) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+131], N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+74], N[(N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / c), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999991e130

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 81.4

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

   5. Applied rewrites 81.4%

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

   if -9.9999999999999991e130 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999963e74

   1. Initial program 82.3%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if 4.99999999999999963e74 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 78.5

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

   5. Applied rewrites 78.5%

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

   7. Applied rewrites 70.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x c) (/ (* 9.0 y) z))))
   (if (<= t_1 -5e+93)
     t_2
     (if (<= t_1 5e+74) (/ (fma (* (* t z) a) -4.0 b) (* c z)) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / c) * ((9.0 * y) / z);
	double tmp;
	if (t_1 <= -5e+93) {
		tmp = t_2;
	} else if (t_1 <= 5e+74) {
		tmp = fma(((t * z) * a), -4.0, b) / (c * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

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(9.0 * x) * y)
	t_2 = Float64(Float64(x / c) * Float64(Float64(9.0 * y) / z))
	tmp = 0.0
	if (t_1 <= -5e+93)
		tmp = t_2;
	elseif (t_1 <= 5e+74)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(c * z));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

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[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / c), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+93], t$95$2, If[LessEqual[t$95$1, 5e+74], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000001e93 or 4.99999999999999963e74 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 75.8

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

   5. Applied rewrites 75.8%

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

   7. Applied rewrites 75.9%

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

   if -5.0000000000000001e93 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999963e74

   1. Initial program 83.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. neg-sub0 N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      11. associate-+l- N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 85.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 72.2

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

   7. Applied rewrites 72.2%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+209}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z 1.7e+209)
   (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
   (/ (fma (* t a) -4.0 (/ b z)) c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 1.7e+209) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= 1.7e+209)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 1.7e+209], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.6999999999999998e209

   1. Initial program 84.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 90.6%

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

   if 1.6999999999999998e209 < z

   1. Initial program 54.1%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 70.0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+209}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

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 (<= t -3.5e-65)
   (* (* (/ t c) a) -4.0)
   (if (<= t 2.55e-79) (/ (/ b c) z) (* (* (/ a c) t) -4.0))))

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 (t <= -3.5e-65) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 2.55e-79) {
		tmp = (b / c) / z;
	} else {
		tmp = ((a / c) * t) * -4.0;
	}
	return tmp;
}

Fortran

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 (t <= (-3.5d-65)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t <= 2.55d-79) then
        tmp = (b / c) / z
    else
        tmp = ((a / c) * t) * (-4.0d0)
    end if
    code = tmp
end function

Java

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 (t <= -3.5e-65) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 2.55e-79) {
		tmp = (b / c) / z;
	} else {
		tmp = ((a / c) * t) * -4.0;
	}
	return tmp;
}

Python

[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 t <= -3.5e-65:
		tmp = ((t / c) * a) * -4.0
	elif t <= 2.55e-79:
		tmp = (b / c) / z
	else:
		tmp = ((a / c) * t) * -4.0
	return tmp

Julia

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 (t <= -3.5e-65)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 2.55e-79)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	end
	return tmp
end

MATLAB

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 (t <= -3.5e-65)
		tmp = ((t / c) * a) * -4.0;
	elseif (t <= 2.55e-79)
		tmp = (b / c) / z;
	else
		tmp = ((a / c) * t) * -4.0;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.5e-65], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 2.55e-79], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000005e-65

   1. Initial program 75.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 89.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   7. Applied rewrites 55.5%

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

   9. Applied rewrites 61.1%

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

   if -3.50000000000000005e-65 < t < 2.55e-79

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 86.3%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 44.1

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

   7. Applied rewrites 44.1%

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

   if 2.55e-79 < t

   1. Initial program 84.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 89.9%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 45.0

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

   7. Applied rewrites 45.0%

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

   9. Applied rewrites 51.1%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

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 (<= t -3.5e-65)
   (* (* (/ t c) a) -4.0)
   (if (<= t 1.7e-217) (/ (/ b z) c) (* (* (/ a c) t) -4.0))))

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 (t <= -3.5e-65) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 1.7e-217) {
		tmp = (b / z) / c;
	} else {
		tmp = ((a / c) * t) * -4.0;
	}
	return tmp;
}

Fortran

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 (t <= (-3.5d-65)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t <= 1.7d-217) then
        tmp = (b / z) / c
    else
        tmp = ((a / c) * t) * (-4.0d0)
    end if
    code = tmp
end function

Java

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 (t <= -3.5e-65) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 1.7e-217) {
		tmp = (b / z) / c;
	} else {
		tmp = ((a / c) * t) * -4.0;
	}
	return tmp;
}

Python

[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 t <= -3.5e-65:
		tmp = ((t / c) * a) * -4.0
	elif t <= 1.7e-217:
		tmp = (b / z) / c
	else:
		tmp = ((a / c) * t) * -4.0
	return tmp

Julia

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 (t <= -3.5e-65)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 1.7e-217)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	end
	return tmp
end

MATLAB

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 (t <= -3.5e-65)
		tmp = ((t / c) * a) * -4.0;
	elseif (t <= 1.7e-217)
		tmp = (b / z) / c;
	else
		tmp = ((a / c) * t) * -4.0;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.5e-65], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 1.7e-217], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000005e-65

   1. Initial program 75.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 89.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   7. Applied rewrites 55.5%

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

   9. Applied rewrites 61.1%

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

   if -3.50000000000000005e-65 < t < 1.70000000000000008e-217

   1. Initial program 88.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 44.4

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

   5. Applied rewrites 44.4%

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

   7. Applied rewrites 42.5%

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

   if 1.70000000000000008e-217 < t

   1. Initial program 82.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 86.3%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 35.5

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

   7. Applied rewrites 35.5%

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

   9. Applied rewrites 40.2%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

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 (<= t -3.5e-65)
   (* (* (/ t c) a) -4.0)
   (if (<= t 3.15e-81) (/ b (* c z)) (* (* (/ a c) t) -4.0))))

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 (t <= -3.5e-65) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 3.15e-81) {
		tmp = b / (c * z);
	} else {
		tmp = ((a / c) * t) * -4.0;
	}
	return tmp;
}

Fortran

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 (t <= (-3.5d-65)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (t <= 3.15d-81) then
        tmp = b / (c * z)
    else
        tmp = ((a / c) * t) * (-4.0d0)
    end if
    code = tmp
end function

Java

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 (t <= -3.5e-65) {
		tmp = ((t / c) * a) * -4.0;
	} else if (t <= 3.15e-81) {
		tmp = b / (c * z);
	} else {
		tmp = ((a / c) * t) * -4.0;
	}
	return tmp;
}

Python

[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 t <= -3.5e-65:
		tmp = ((t / c) * a) * -4.0
	elif t <= 3.15e-81:
		tmp = b / (c * z)
	else:
		tmp = ((a / c) * t) * -4.0
	return tmp

Julia

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 (t <= -3.5e-65)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (t <= 3.15e-81)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	end
	return tmp
end

MATLAB

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 (t <= -3.5e-65)
		tmp = ((t / c) * a) * -4.0;
	elseif (t <= 3.15e-81)
		tmp = b / (c * z);
	else
		tmp = ((a / c) * t) * -4.0;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.5e-65], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 3.15e-81], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000005e-65

   1. Initial program 75.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 89.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   7. Applied rewrites 55.5%

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

   9. Applied rewrites 61.1%

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

   if -3.50000000000000005e-65 < t < 3.15000000000000011e-81

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 40.3

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

   5. Applied rewrites 40.3%

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

   if 3.15000000000000011e-81 < t

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 90.0%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 44.4

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

   7. Applied rewrites 44.4%

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

   9. Applied rewrites 50.5%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ t c) a) -4.0)))
   (if (<= t -3.5e-65) t_1 (if (<= t 3.15e-81) (/ b (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t / c) * a) * -4.0;
	double tmp;
	if (t <= -3.5e-65) {
		tmp = t_1;
	} else if (t <= 3.15e-81) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t / c) * a) * (-4.0d0)
    if (t <= (-3.5d-65)) then
        tmp = t_1
    else if (t <= 3.15d-81) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t / c) * a) * -4.0;
	double tmp;
	if (t <= -3.5e-65) {
		tmp = t_1;
	} else if (t <= 3.15e-81) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((t / c) * a) * -4.0
	tmp = 0
	if t <= -3.5e-65:
		tmp = t_1
	elif t <= 3.15e-81:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t / c) * a) * -4.0)
	tmp = 0.0
	if (t <= -3.5e-65)
		tmp = t_1;
	elseif (t <= 3.15e-81)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t / c) * a) * -4.0;
	tmp = 0.0;
	if (t <= -3.5e-65)
		tmp = t_1;
	elseif (t <= 3.15e-81)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[t, -3.5e-65], t$95$1, If[LessEqual[t, 3.15e-81], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.50000000000000005e-65 or 3.15000000000000011e-81 < t

   1. Initial program 80.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 90.0%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 49.6

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

   7. Applied rewrites 49.6%

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

   9. Applied rewrites 55.4%

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

   if -3.50000000000000005e-65 < t < 3.15000000000000011e-81

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 40.3

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

   5. Applied rewrites 40.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{c} \cdot -4\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ (* t a) c) -4.0)))
   (if (<= t -3.5e-65) t_1 (if (<= t 3.15e-81) (/ b (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * a) / c) * -4.0;
	double tmp;
	if (t <= -3.5e-65) {
		tmp = t_1;
	} else if (t <= 3.15e-81) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) / c) * (-4.0d0)
    if (t <= (-3.5d-65)) then
        tmp = t_1
    else if (t <= 3.15d-81) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * a) / c) * -4.0;
	double tmp;
	if (t <= -3.5e-65) {
		tmp = t_1;
	} else if (t <= 3.15e-81) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * a) / c) * -4.0
	tmp = 0
	if t <= -3.5e-65:
		tmp = t_1
	elif t <= 3.15e-81:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * a) / c) * -4.0)
	tmp = 0.0
	if (t <= -3.5e-65)
		tmp = t_1;
	elseif (t <= 3.15e-81)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * a) / c) * -4.0;
	tmp = 0.0;
	if (t <= -3.5e-65)
		tmp = t_1;
	elseif (t <= 3.15e-81)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[t, -3.5e-65], t$95$1, If[LessEqual[t, 3.15e-81], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.50000000000000005e-65 or 3.15000000000000011e-81 < t

   1. Initial program 80.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 49.6

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

   5. Applied rewrites 49.6%

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

   if -3.50000000000000005e-65 < t < 3.15000000000000011e-81

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 40.3

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

   5. Applied rewrites 40.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.4% accurate, 2.8× speedup

Math

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

FPCore

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);
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.
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;
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])
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])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

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.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.3%

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

3. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 31.5

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

5. Applied rewrites 31.5%

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

Developer Target 1: 79.8% 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 2024270 
(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)))