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

Percentage Accurate: 79.1% → 93.4%

Time: 11.1s

Alternatives: 18

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: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+21} \lor \neg \left(z \leq 1.4 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(y \cdot 9, \frac{x}{z}, \frac{b}{z}\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.7e+21) (not (<= z 1.4e-94)))
   (/ (fma (* -4.0 t) a (fma (* y 9.0) (/ x z) (/ b z))) c)
   (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.7e+21) || !(z <= 1.4e-94)) {
		tmp = fma((-4.0 * t), a, fma((y * 9.0), (x / z), (b / z))) / c;
	} else {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.7e+21) || !(z <= 1.4e-94))
		tmp = Float64(fma(Float64(-4.0 * t), a, fma(Float64(y * 9.0), Float64(x / z), Float64(b / z))) / c);
	else
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.7e+21], N[Not[LessEqual[z, 1.4e-94]], $MachinePrecision]], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(y * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e21 or 1.3999999999999999e-94 < z

   1. Initial program 64.8%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 86.2%

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

   7. Applied rewrites 90.5%

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

   if -1.7e21 < z < 1.3999999999999999e-94

   1. Initial program 98.0%

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

      1. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 96.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+21} \lor \neg \left(z \leq 1.4 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(y \cdot 9, \frac{x}{z}, \frac{b}{z}\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+267}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+267)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_1 -1e-93)
       (/ (/ (fma (* y x) 9.0 b) c) z)
       (if (<= t_1 1e-26)
         (fma (* -4.0 t) (/ a c) (/ b (* z c)))
         (if (<= t_1 5e+215)
           (/ (fma (* -4.0 a) t (* (/ (* y x) z) 9.0)) c)
           (* (* (/ y c) 9.0) (/ x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+267) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_1 <= -1e-93) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else if (t_1 <= 1e-26) {
		tmp = fma((-4.0 * t), (a / c), (b / (z * c)));
	} else if (t_1 <= 5e+215) {
		tmp = fma((-4.0 * a), t, (((y * x) / z) * 9.0)) / c;
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+267)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_1 <= -1e-93)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	elseif (t_1 <= 1e-26)
		tmp = fma(Float64(-4.0 * t), Float64(a / c), Float64(b / Float64(z * c)));
	elseif (t_1 <= 5e+215)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+267], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-93], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e-26], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+215], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e267

   1. Initial program 67.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.1

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

   8. Applied rewrites 78.1%

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

   if -1.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.999999999999999e-94

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   7. 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. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.1

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

   8. Applied rewrites 79.1%

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

   if -9.999999999999999e-94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-26

   1. Initial program 79.6%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 88.0%

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

   7. Applied rewrites 85.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 84.6%

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

   if 1e-26 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000001e215

   1. Initial program 81.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 89.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.9%

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

   if 5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 52.3%

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

   3. Taylor expanded in x around inf

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

      1. 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 87.6

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

   5. Applied rewrites 87.6%

      \[\leadsto \color{blue}{\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+267}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot \left(-4 \cdot a\right), t, \left(9 \cdot x\right) \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+267)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_1 -1e-93)
       (/ (/ (fma (* y x) 9.0 b) c) z)
       (if (<= t_1 1e-26)
         (fma (* -4.0 t) (/ a c) (/ b (* z c)))
         (if (<= t_1 5e+215)
           (/ (fma (* z (* -4.0 a)) t (* (* 9.0 x) y)) (* z c))
           (* (* (/ y c) 9.0) (/ x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+267) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_1 <= -1e-93) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else if (t_1 <= 1e-26) {
		tmp = fma((-4.0 * t), (a / c), (b / (z * c)));
	} else if (t_1 <= 5e+215) {
		tmp = fma((z * (-4.0 * a)), t, ((9.0 * x) * y)) / (z * c);
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+267)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_1 <= -1e-93)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	elseif (t_1 <= 1e-26)
		tmp = fma(Float64(-4.0 * t), Float64(a / c), Float64(b / Float64(z * c)));
	elseif (t_1 <= 5e+215)
		tmp = Float64(fma(Float64(z * Float64(-4.0 * a)), t, Float64(Float64(9.0 * x) * y)) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+267], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-93], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e-26], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+215], N[(N[(N[(z * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e267

   1. Initial program 67.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.1

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

   8. Applied rewrites 78.1%

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

   if -1.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.999999999999999e-94

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   7. 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. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.1

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

   8. Applied rewrites 79.1%

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

   if -9.999999999999999e-94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-26

   1. Initial program 79.6%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 88.0%

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

   7. Applied rewrites 85.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 84.6%

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

   if 1e-26 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000001e215

   1. Initial program 81.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-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. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 44.5

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in b around 0

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

      1. fp-cancel-sub-sign-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. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 67.4

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

   8. Applied rewrites 67.4%

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

   10. Applied rewrites 70.1%

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

   if 5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 52.3%

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

   3. Taylor expanded in x around inf

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

      1. 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 87.6

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

   5. Applied rewrites 87.6%

      \[\leadsto \color{blue}{\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+267}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ (fma (* y x) 9.0 b) c) z)) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -2e+267)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_2 -1e-103)
       t_1
       (if (<= t_2 1e-26)
         (/ (fma (* (* a t) -4.0) z b) (* z c))
         (if (<= t_2 1e+206) t_1 (* (* (/ y c) 9.0) (/ x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fma((y * x), 9.0, b) / c) / z;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -2e+267) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_2 <= -1e-103) {
		tmp = t_1;
	} else if (t_2 <= 1e-26) {
		tmp = fma(((a * t) * -4.0), z, b) / (z * c);
	} else if (t_2 <= 1e+206) {
		tmp = t_1;
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -2e+267)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_2 <= -1e-103)
		tmp = t_1;
	elseif (t_2 <= 1e-26)
		tmp = Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / Float64(z * c));
	elseif (t_2 <= 1e+206)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+267], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-103], t$95$1, If[LessEqual[t$95$2, 1e-26], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+206], t$95$1, N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e267

   1. Initial program 67.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.1

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

   8. Applied rewrites 78.1%

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

   if -1.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999958e-104 or 1e-26 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e206

   1. Initial program 85.0%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   7. 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. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 74.1

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

   8. Applied rewrites 74.1%

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

   if -9.99999999999999958e-104 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-26

   1. Initial program 80.3%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-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. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

   7. Applied rewrites 78.8%

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

   if 1e206 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 50.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   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 84.7

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

   5. Applied rewrites 84.7%

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

Alternative 5: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+256}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-29}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* y x) 9.0 b) (* z c))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -1e+256)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_2 -1e-103)
       t_1
       (if (<= t_2 2e-29)
         (/ (fma (* (* a t) -4.0) z b) (* z c))
         (if (<= t_2 1e+206) t_1 (* (* (/ y c) 9.0) (/ x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((y * x), 9.0, b) / (z * c);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -1e+256) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_2 <= -1e-103) {
		tmp = t_1;
	} else if (t_2 <= 2e-29) {
		tmp = fma(((a * t) * -4.0), z, b) / (z * c);
	} else if (t_2 <= 1e+206) {
		tmp = t_1;
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -1e+256)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_2 <= -1e-103)
		tmp = t_1;
	elseif (t_2 <= 2e-29)
		tmp = Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / Float64(z * c));
	elseif (t_2 <= 1e+206)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+256], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-103], t$95$1, If[LessEqual[t$95$2, 2e-29], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+206], t$95$1, N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e256

   1. Initial program 70.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.7

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

   8. Applied rewrites 78.7%

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

   if -1e256 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999958e-104 or 1.99999999999999989e-29 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e206

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if -9.99999999999999958e-104 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999989e-29

   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 x 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. fp-cancel-sub-sign-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. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 79.2

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 79.3%

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

   if 1e206 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 50.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   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 84.7

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

   5. Applied rewrites 84.7%

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

Alternative 6: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+256}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* y x) 9.0 b) (* z c))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -1e+256)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_2 -1e-103)
       t_1
       (if (<= t_2 1e-26)
         (/ (fma -4.0 (* (* t z) a) b) (* z c))
         (if (<= t_2 1e+206) t_1 (* (* (/ y c) 9.0) (/ x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((y * x), 9.0, b) / (z * c);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -1e+256) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_2 <= -1e-103) {
		tmp = t_1;
	} else if (t_2 <= 1e-26) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else if (t_2 <= 1e+206) {
		tmp = t_1;
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -1e+256)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_2 <= -1e-103)
		tmp = t_1;
	elseif (t_2 <= 1e-26)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	elseif (t_2 <= 1e+206)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+256], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-103], t$95$1, If[LessEqual[t$95$2, 1e-26], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+206], t$95$1, N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e256

   1. Initial program 70.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.7

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

   8. Applied rewrites 78.7%

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

   if -1e256 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999958e-104 or 1e-26 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e206

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 71.9

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

   5. Applied rewrites 71.9%

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

   if -9.99999999999999958e-104 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-26

   1. Initial program 80.3%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-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. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

   if 1e206 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 50.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   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 84.7

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

   5. Applied rewrites 84.7%

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

Alternative 7: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+267}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, \frac{a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+267)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_1 -1e-93)
       (/ (/ (fma (* y x) 9.0 b) c) z)
       (if (<= t_1 5e+215)
         (fma (* -4.0 t) (/ a c) (/ b (* z c)))
         (* (* (/ y c) 9.0) (/ x z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+267) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_1 <= -1e-93) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else if (t_1 <= 5e+215) {
		tmp = fma((-4.0 * t), (a / c), (b / (z * c)));
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+267)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_1 <= -1e-93)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	elseif (t_1 <= 5e+215)
		tmp = fma(Float64(-4.0 * t), Float64(a / c), Float64(b / Float64(z * c)));
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+267], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-93], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+215], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e267

   1. Initial program 67.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.1

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

   8. Applied rewrites 78.1%

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

   if -1.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.999999999999999e-94

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   7. 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. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.1

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

   8. Applied rewrites 79.1%

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

   if -9.999999999999999e-94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000001e215

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 87.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 77.0%

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

   if 5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 52.3%

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

   3. Taylor expanded in x around inf

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

      1. 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 87.6

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

   5. Applied rewrites 87.6%

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

Alternative 8: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+267}:\\ \;\;\;\;\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+267)
     (* (* 9.0 (/ x c)) (/ y z))
     (if (<= t_1 -1e-93)
       (/ (/ (fma (* y x) 9.0 b) c) z)
       (if (<= t_1 5e+215)
         (/ (fma (* -4.0 t) a (/ b z)) c)
         (* (* (/ y c) 9.0) (/ x z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+267) {
		tmp = (9.0 * (x / c)) * (y / z);
	} else if (t_1 <= -1e-93) {
		tmp = (fma((y * x), 9.0, b) / c) / z;
	} else if (t_1 <= 5e+215) {
		tmp = fma((-4.0 * t), a, (b / z)) / c;
	} else {
		tmp = ((y / c) * 9.0) * (x / z);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+267)
		tmp = Float64(Float64(9.0 * Float64(x / c)) * Float64(y / z));
	elseif (t_1 <= -1e-93)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / z);
	elseif (t_1 <= 5e+215)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(Float64(y / c) * 9.0) * Float64(x / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+267], N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-93], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+215], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e267

   1. Initial program 67.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 78.1

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

   8. Applied rewrites 78.1%

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

   if -1.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.999999999999999e-94

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   7. 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. +-commutative N/A

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

      3. div-add-rev N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-add-rev N/A

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

      8. +-commutative N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.1

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

   8. Applied rewrites 79.1%

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

   if -9.999999999999999e-94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000001e215

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 78.9%

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

   if 5.0000000000000001e215 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 52.3%

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

   3. Taylor expanded in x around inf

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

      1. 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 87.6

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

   5. Applied rewrites 87.6%

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

Alternative 9: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{t\_1}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a, \frac{t\_1}{t \cdot z}\right)}{c} \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (fma (* y x) 9.0 b)))
   (if (<= z -1.7e+21)
     (/ (fma (* -4.0 t) a (/ t_1 z)) c)
     (if (<= z 1.6e+32)
       (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))
       (* (/ (fma -4.0 a (/ t_1 (* t z))) c) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((y * x), 9.0, b);
	double tmp;
	if (z <= -1.7e+21) {
		tmp = fma((-4.0 * t), a, (t_1 / z)) / c;
	} else if (z <= 1.6e+32) {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	} else {
		tmp = (fma(-4.0, a, (t_1 / (t * z))) / c) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (z <= -1.7e+21)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(t_1 / z)) / c);
	elseif (z <= 1.6e+32)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	else
		tmp = Float64(Float64(fma(-4.0, a, Float64(t_1 / Float64(t * z))) / 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.
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[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[z, -1.7e+21], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.6e+32], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * a + N[(t$95$1 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e21

   1. Initial program 63.9%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 92.0%

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

   if -1.7e21 < z < 1.5999999999999999e32

   1. Initial program 95.7%

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

      1. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 94.3%

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

   if 1.5999999999999999e32 < z

   1. Initial program 50.3%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 77.8%

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

   7. Applied rewrites 76.2%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 77.9%

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

   12. Applied rewrites 81.3%

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

Alternative 10: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+21} \lor \neg \left(z \leq 1.4 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.7e+21) (not (<= z 1.4e-94)))
   (/ (fma (* -4.0 t) a (/ (fma (* y x) 9.0 b) z)) c)
   (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.7e+21) || !(z <= 1.4e-94)) {
		tmp = fma((-4.0 * t), a, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.7e+21) || !(z <= 1.4e-94))
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.7e+21], N[Not[LessEqual[z, 1.4e-94]], $MachinePrecision]], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e21 or 1.3999999999999999e-94 < z

   1. Initial program 64.8%

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

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 86.2%

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

   if -1.7e21 < z < 1.3999999999999999e-94

   1. Initial program 98.0%

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

      1. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 96.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+21} \lor \neg \left(z \leq 1.4 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+118}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -5.5e+118)
   (/ (fma (* -4.0 a) t (* (/ (* y x) z) 9.0)) c)
   (if (<= z 8.6e+91)
     (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))
     (* (fma (/ a c) -4.0 (/ b (* (* t z) c))) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.5e+118) {
		tmp = fma((-4.0 * a), t, (((y * x) / z) * 9.0)) / c;
	} else if (z <= 8.6e+91) {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	} else {
		tmp = fma((a / c), -4.0, (b / ((t * z) * c))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.5e+118)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	elseif (z <= 8.6e+91)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(b / Float64(Float64(t * z) * 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.
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, -5.5e+118], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 8.6e+91], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000003e118

   1. Initial program 53.1%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 76.6%

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

   if -5.5000000000000003e118 < z < 8.6000000000000001e91

   1. Initial program 94.0%

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

      1. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 92.3%

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

   if 8.6000000000000001e91 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 76.7%

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 74.8%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 72.8%

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

Alternative 12: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+174}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{b}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -3e+174)
   (/ (fma (* -4.0 a) t (* (/ (* y x) z) 9.0)) c)
   (if (<= z 8.6e+91)
     (/ (fma (* 9.0 x) y (fma (* -4.0 z) (* a t) b)) (* z c))
     (* (fma (/ a c) -4.0 (/ b (* (* t z) c))) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3e+174) {
		tmp = fma((-4.0 * a), t, (((y * x) / z) * 9.0)) / c;
	} else if (z <= 8.6e+91) {
		tmp = fma((9.0 * x), y, fma((-4.0 * z), (a * t), b)) / (z * c);
	} else {
		tmp = fma((a / c), -4.0, (b / ((t * z) * c))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3e+174)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	elseif (z <= 8.6e+91)
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(b / Float64(Float64(t * z) * 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.
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, -3e+174], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 8.6e+91], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e174

   1. Initial program 44.3%

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

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 89.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 74.9%

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

   if -3e174 < z < 8.6000000000000001e91

   1. Initial program 94.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. 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. lift-*.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.1

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

   4. Applied rewrites 93.1%

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

   if 8.6000000000000001e91 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-add N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. div-add-rev N/A

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

      10. div-add N/A

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

      11. associate-*r/ N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. lower-/.f64 N/A

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

   5. Applied rewrites 76.7%

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 74.8%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 72.8%

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

Alternative 13: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-105}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \mathbf{elif}\;b \leq 780000000:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1e+65)
   (/ (/ b c) z)
   (if (<= b 6.2e-105)
     (* (* t (/ a c)) -4.0)
     (if (<= b 780000000.0) (/ (* (* x 9.0) y) (* z c)) (/ b (* c z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1e+65) {
		tmp = (b / c) / z;
	} else if (b <= 6.2e-105) {
		tmp = (t * (a / c)) * -4.0;
	} else if (b <= 780000000.0) {
		tmp = ((x * 9.0) * y) / (z * c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1d+65)) then
        tmp = (b / c) / z
    else if (b <= 6.2d-105) then
        tmp = (t * (a / c)) * (-4.0d0)
    else if (b <= 780000000.0d0) then
        tmp = ((x * 9.0d0) * y) / (z * c)
    else
        tmp = b / (c * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1e+65) {
		tmp = (b / c) / z;
	} else if (b <= 6.2e-105) {
		tmp = (t * (a / c)) * -4.0;
	} else if (b <= 780000000.0) {
		tmp = ((x * 9.0) * y) / (z * c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1e+65:
		tmp = (b / c) / z
	elif b <= 6.2e-105:
		tmp = (t * (a / c)) * -4.0
	elif b <= 780000000.0:
		tmp = ((x * 9.0) * y) / (z * c)
	else:
		tmp = b / (c * z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1e+65)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 6.2e-105)
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	elseif (b <= 780000000.0)
		tmp = Float64(Float64(Float64(x * 9.0) * y) / Float64(z * c));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1e+65)
		tmp = (b / c) / z;
	elseif (b <= 6.2e-105)
		tmp = (t * (a / c)) * -4.0;
	elseif (b <= 780000000.0)
		tmp = ((x * 9.0) * y) / (z * c);
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1e+65], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 6.2e-105], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, 780000000.0], N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.9999999999999999e64

   1. Initial program 75.9%

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

   3. Taylor expanded in b around 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 54.8

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

   5. Applied rewrites 54.8%

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

   7. Applied rewrites 62.3%

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

   if -9.9999999999999999e64 < b < 6.20000000000000029e-105

   1. Initial program 74.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 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. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      3. associate-*r/ N/A

         \[\leadsto \left(\frac{b}{c \cdot z} + \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      4. div-add N/A

         \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      6. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      9. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

      10. div-add N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. associate-*r/ N/A

          \[\leadsto \frac{\left(\frac{b}{z} + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      13. metadata-eval N/A

          \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \left(a \cdot t\right)}{c} \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}}{c} \]

      15. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   5. Applied rewrites 83.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.7%

      \[\leadsto \mathsf{fma}\left(-4 \cdot t, \color{blue}{\frac{a}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 72.4%

       \[\leadsto \mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot \color{blue}{t} \]

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   12. 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. *-commutative N/A

          \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

       4. associate-/l* N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       6. lower-/.f64 50.9

          \[\leadsto \left(t \cdot \color{blue}{\frac{a}{c}}\right) \cdot -4 \]

   13. Applied rewrites 50.9%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]

   if 6.20000000000000029e-105 < b < 7.8e8

   1. Initial program 83.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      3. associate-*r/ N/A

         \[\leadsto \left(\frac{b}{c \cdot z} + \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      4. div-add N/A

         \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      6. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      9. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

      10. div-add N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. associate-*r/ N/A

          \[\leadsto \frac{\left(\frac{b}{z} + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      13. metadata-eval N/A

          \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \left(a \cdot t\right)}{c} \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}}{c} \]

      15. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   5. Applied rewrites 93.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. times-frac N/A

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right)} \cdot \frac{y}{z} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{x}{c}}\right) \cdot \frac{y}{z} \]

      6. lower-/.f64 45.0

         \[\leadsto \left(9 \cdot \frac{x}{c}\right) \cdot \color{blue}{\frac{y}{z}} \]

   8. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{c}\right) \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.1%

       \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{\color{blue}{z \cdot c}} \]

   if 7.8e8 < b

   1. Initial program 82.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in 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 58.2

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 58.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 68.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20} \lor \neg \left(z \leq 7 \cdot 10^{+90}\right):\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -8e+20) (not (<= z 7e+90)))
   (* (* t (/ a c)) -4.0)
   (/ (fma (* y x) 9.0 b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -8e+20) || !(z <= 7e+90)) {
		tmp = (t * (a / c)) * -4.0;
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -8e+20) || !(z <= 7e+90))
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -8e+20], N[Not[LessEqual[z, 7e+90]], $MachinePrecision]], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e20 or 6.9999999999999997e90 < z

   1. Initial program 54.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      3. associate-*r/ N/A

         \[\leadsto \left(\frac{b}{c \cdot z} + \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      4. div-add N/A

         \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      6. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      9. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

      10. div-add N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. associate-*r/ N/A

          \[\leadsto \frac{\left(\frac{b}{z} + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      13. metadata-eval N/A

          \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \left(a \cdot t\right)}{c} \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}}{c} \]

      15. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   5. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 69.8%

      \[\leadsto \mathsf{fma}\left(-4 \cdot t, \color{blue}{\frac{a}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 68.9%

       \[\leadsto \mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot \color{blue}{t} \]

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   12. 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. *-commutative N/A

          \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

       4. associate-/l* N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       6. lower-/.f64 55.9

          \[\leadsto \left(t \cdot \color{blue}{\frac{a}{c}}\right) \cdot -4 \]

   13. Applied rewrites 55.9%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]

   if -8e20 < z < 6.9999999999999997e90

   1. Initial program 94.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 80.7

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 80.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20} \lor \neg \left(z \leq 7 \cdot 10^{+90}\right):\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+65} \lor \neg \left(b \leq 3.5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.02e+65) (not (<= b 3.5e+41)))
   (/ b (* c z))
   (* (* t (/ a c)) -4.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.02e+65) || !(b <= 3.5e+41)) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.02d+65)) .or. (.not. (b <= 3.5d+41))) then
        tmp = b / (c * z)
    else
        tmp = (t * (a / c)) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.02e+65) || !(b <= 3.5e+41)) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (a / c)) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.02e+65) or not (b <= 3.5e+41):
		tmp = b / (c * z)
	else:
		tmp = (t * (a / c)) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.02e+65) || !(b <= 3.5e+41))
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.02e+65) || ~((b <= 3.5e+41)))
		tmp = b / (c * z);
	else
		tmp = (t * (a / c)) * -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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.02e+65], N[Not[LessEqual[b, 3.5e+41]], $MachinePrecision]], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.02000000000000005e65 or 3.4999999999999999e41 < b

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 58.6

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -1.02000000000000005e65 < b < 3.4999999999999999e41

   1. Initial program 77.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      3. associate-*r/ N/A

         \[\leadsto \left(\frac{b}{c \cdot z} + \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      4. div-add N/A

         \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      6. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      9. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

      10. div-add N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. associate-*r/ N/A

          \[\leadsto \frac{\left(\frac{b}{z} + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      13. metadata-eval N/A

          \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \left(a \cdot t\right)}{c} \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}}{c} \]

      15. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   5. Applied rewrites 86.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 82.2%

      \[\leadsto \mathsf{fma}\left(-4 \cdot t, \color{blue}{\frac{a}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 72.7%

       \[\leadsto \mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot \color{blue}{t} \]

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   12. 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. *-commutative N/A

          \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

       4. associate-/l* N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       6. lower-/.f64 47.1

          \[\leadsto \left(t \cdot \color{blue}{\frac{a}{c}}\right) \cdot -4 \]

   13. Applied rewrites 47.1%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+65} \lor \neg \left(b \leq 3.5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+65} \lor \neg \left(b \leq 4.8 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.02e+65) (not (<= b 4.8e+54)))
   (/ b (* c z))
   (* -4.0 (/ (* a t) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.02e+65) || !(b <= 4.8e+54)) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.02d+65)) .or. (.not. (b <= 4.8d+54))) then
        tmp = b / (c * z)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.02e+65) || !(b <= 4.8e+54)) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.02e+65) or not (b <= 4.8e+54):
		tmp = b / (c * z)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.02e+65) || !(b <= 4.8e+54))
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.02e+65) || ~((b <= 4.8e+54)))
		tmp = b / (c * z);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.02e+65], N[Not[LessEqual[b, 4.8e+54]], $MachinePrecision]], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.02000000000000005e65 or 4.79999999999999997e54 < b

   1. Initial program 78.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 59.3

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -1.02000000000000005e65 < b < 4.79999999999999997e54

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z 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. lower-*.f64 48.1

         \[\leadsto -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

   5. Applied rewrites 48.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+65} \lor \neg \left(b \leq 4.8 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;\left(t \cdot \frac{a}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5.6e+64)
   (/ (/ b c) z)
   (if (<= b 3.5e+41) (* (* t (/ a c)) -4.0) (/ b (* c z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.6e+64) {
		tmp = (b / c) / z;
	} else if (b <= 3.5e+41) {
		tmp = (t * (a / c)) * -4.0;
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5.6d+64)) then
        tmp = (b / c) / z
    else if (b <= 3.5d+41) then
        tmp = (t * (a / c)) * (-4.0d0)
    else
        tmp = b / (c * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.6e+64) {
		tmp = (b / c) / z;
	} else if (b <= 3.5e+41) {
		tmp = (t * (a / c)) * -4.0;
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.6e+64:
		tmp = (b / c) / z
	elif b <= 3.5e+41:
		tmp = (t * (a / c)) * -4.0
	else:
		tmp = b / (c * z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.6e+64)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 3.5e+41)
		tmp = Float64(Float64(t * Float64(a / c)) * -4.0);
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5.6e+64)
		tmp = (b / c) / z;
	elseif (b <= 3.5e+41)
		tmp = (t * (a / c)) * -4.0;
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5.6e+64], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 3.5e+41], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.60000000000000047e64

   1. Initial program 74.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in 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 53.7

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 53.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -5.60000000000000047e64 < b < 3.4999999999999999e41

   1. Initial program 78.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x 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. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      3. associate-*r/ N/A

         \[\leadsto \left(\frac{b}{c \cdot z} + \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      4. div-add N/A

         \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      6. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c} + \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      9. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

      10. div-add N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. associate-*r/ N/A

          \[\leadsto \frac{\left(\frac{b}{z} + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} + -4 \cdot \left(a \cdot t\right)}{c} \]

      13. metadata-eval N/A

          \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \left(a \cdot t\right)}{c} \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}}{c} \]

      15. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   5. Applied rewrites 86.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 82.8%

      \[\leadsto \mathsf{fma}\left(-4 \cdot t, \color{blue}{\frac{a}{c}}, \frac{\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 73.2%

       \[\leadsto \mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot \color{blue}{t} \]

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   12. 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. *-commutative N/A

          \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

       4. associate-/l* N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

       6. lower-/.f64 47.4

          \[\leadsto \left(t \cdot \color{blue}{\frac{a}{c}}\right) \cdot -4 \]

   13. Applied rewrites 47.4%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]

   if 3.4999999999999999e41 < b

   1. Initial program 79.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 62.1

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 62.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 34.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (c * z)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.8%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 32.8

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 32.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 79.5% 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 2024339 
(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)))