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

Percentage Accurate: 79.2% → 86.1%

Time: 15.7s

Alternatives: 23

Speedup: 0.8×

• 37.6% 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: 79.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, 4, \frac{\mathsf{fma}\left(\frac{y}{c} \cdot 9, \frac{x}{z}, \frac{b}{c \cdot z}\right)}{-a}\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -9e+82)
   (*
    (fma (/ t c) 4.0 (/ (fma (* (/ y c) 9.0) (/ x z) (/ b (* c z))) (- a)))
    (- a))
   (if (<= z 4.1e+179)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
     (/ (* (fma (/ y z) 9.0 (* (/ (* a t) x) -4.0)) x) 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 <= -9e+82) {
		tmp = fma((t / c), 4.0, (fma(((y / c) * 9.0), (x / z), (b / (c * z))) / -a)) * -a;
	} else if (z <= 4.1e+179) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = (fma((y / z), 9.0, (((a * t) / x) * -4.0)) * x) / 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 <= -9e+82)
		tmp = Float64(fma(Float64(t / c), 4.0, Float64(fma(Float64(Float64(y / c) * 9.0), Float64(x / z), Float64(b / Float64(c * z))) / Float64(-a))) * Float64(-a));
	elseif (z <= 4.1e+179)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = Float64(Float64(fma(Float64(y / z), 9.0, Float64(Float64(Float64(a * t) / x) * -4.0)) * x) / 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[LessEqual[z, -9e+82], N[(N[(N[(t / c), $MachinePrecision] * 4.0 + N[(N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * N[(x / z), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-a)), $MachinePrecision]), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[z, 4.1e+179], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999993e82

   1. Initial program 53.3%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. distribute-neg-frac2 N/A

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

      11. mul-1-neg N/A

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

      12. lower-/.f64 N/A

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

   5. Applied rewrites 85.5%

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

   if -8.9999999999999993e82 < z < 4.10000000000000011e179

   1. Initial program 91.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 92.0%

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

   if 4.10000000000000011e179 < z

   1. Initial program 33.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 93.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, 4, \frac{\mathsf{fma}\left(\frac{y}{c} \cdot 9, \frac{x}{z}, \frac{b}{c \cdot z}\right)}{-a}\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{c}{\mathsf{fma}\left(-4 \cdot a, t \cdot z, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)} \cdot z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c} \cdot \frac{y}{z}, 9, \frac{a \cdot t}{c} \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* 9.0 x) y) (* (* (* 4.0 z) t) a)) b) (* c z))))
   (if (<= t_1 -1e-300)
     t_1
     (if (<= t_1 0.0)
       (/ 1.0 (* (/ c (fma (* -4.0 a) (* t z) (fma (* y 9.0) x b))) z))
       (if (<= t_1 INFINITY)
         (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) (* c z))
         (fma (* (/ x c) (/ y z)) 9.0 (* (/ (* a t) 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 t_1 = ((((9.0 * x) * y) - (((4.0 * z) * t) * a)) + b) / (c * z);
	double tmp;
	if (t_1 <= -1e-300) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / ((c / fma((-4.0 * a), (t * z), fma((y * 9.0), x, b))) * z);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = fma(((x / c) * (y / z)), 9.0, (((a * t) / 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)
	t_1 = Float64(Float64(Float64(Float64(Float64(9.0 * x) * y) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-300)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(1.0 / Float64(Float64(c / fma(Float64(-4.0 * a), Float64(t * z), fma(Float64(y * 9.0), x, b))) * z));
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = fma(Float64(Float64(x / c) * Float64(y / z)), 9.0, Float64(Float64(Float64(a * t) / c) * -4.0));
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-300], t$95$1, If[LessEqual[t$95$1, 0.0], N[(1.0 / N[(N[(c / N[(N[(-4.0 * a), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000003e-300

   1. Initial program 91.3%

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

   if -1.00000000000000003e-300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 35.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 83.3%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. frac-times N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

   6. Applied rewrites 96.8%

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

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

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-sub0 N/A

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

      12. associate-+l- N/A

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

      13. neg-sub0 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

   4. Applied rewrites 93.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 7.6

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

   5. Applied rewrites 7.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 72.3%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 80.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq -1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{1}{\frac{c}{\mathsf{fma}\left(-4 \cdot a, t \cdot z, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)} \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c} \cdot \frac{y}{z}, 9, \frac{a \cdot t}{c} \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* 9.0 x) y) (* (* (* 4.0 z) t) a)) b) (* c z))))
   (if (<= t_1 -1e-300)
     t_1
     (if (<= t_1 0.0)
       (/ (/ (fma -4.0 (* (* t z) a) (* (* y x) 9.0)) z) c)
       (if (<= t_1 INFINITY)
         (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) (* c z))
         (/ (* (* -4.0 t) a) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((9.0 * x) * y) - (((4.0 * z) * t) * a)) + b) / (c * z);
	double tmp;
	if (t_1 <= -1e-300) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (fma(-4.0, ((t * z) * a), ((y * x) * 9.0)) / z) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(9.0 * x) * y) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-300)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(-4.0, Float64(Float64(t * z) * a), Float64(Float64(y * x) * 9.0)) / z) / c);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-300], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000003e-300

   1. Initial program 91.3%

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

   if -1.00000000000000003e-300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 35.1%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 87.9

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

   5. Applied rewrites 87.9%

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

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

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-sub0 N/A

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

      12. associate-+l- N/A

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

      13. neg-sub0 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

   4. Applied rewrites 93.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 7.6

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

   5. Applied rewrites 7.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 72.3%

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

   10. Applied rewrites 72.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq -1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* 9.0 x) y) (* (* (* 4.0 z) t) a)) b) (* c z))))
   (if (<= t_1 -1e-300)
     t_1
     (if (<= t_1 0.0)
       (/ (fma (/ (* y x) z) 9.0 (* (* a t) -4.0)) c)
       (if (<= t_1 INFINITY)
         (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) (* c z))
         (/ (* (* -4.0 t) a) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((9.0 * x) * y) - (((4.0 * z) * t) * a)) + b) / (c * z);
	double tmp;
	if (t_1 <= -1e-300) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = fma(((y * x) / z), 9.0, ((a * t) * -4.0)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(9.0 * x) * y) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-300)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(Float64(Float64(y * x) / z), 9.0, Float64(Float64(a * t) * -4.0)) / c);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-300], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0 + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000003e-300

   1. Initial program 91.3%

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

   if -1.00000000000000003e-300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 35.1%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in a 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 87.7%

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

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

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-sub0 N/A

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

      12. associate-+l- N/A

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

      13. neg-sub0 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

   4. Applied rewrites 93.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 7.6

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

   5. Applied rewrites 7.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 72.3%

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

   10. Applied rewrites 72.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq -1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ t_2 := \frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* 9.0 x) y) (* (* (* 4.0 z) t) a)) b) (* c z)))
        (t_2 (/ (fma (* y x) 9.0 (fma (* (* -4.0 z) a) t b)) (* c z))))
   (if (<= t_1 -1e-300)
     t_2
     (if (<= t_1 0.0)
       (/ (fma (/ (* y x) z) 9.0 (* (* a t) -4.0)) c)
       (if (<= t_1 INFINITY) t_2 (/ (* (* -4.0 t) a) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((9.0 * x) * y) - (((4.0 * z) * t) * a)) + b) / (c * z);
	double t_2 = fma((y * x), 9.0, fma(((-4.0 * z) * a), t, b)) / (c * z);
	double tmp;
	if (t_1 <= -1e-300) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = fma(((y * x) / z), 9.0, ((a * t) * -4.0)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(9.0 * x) * y) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z))
	t_2 = Float64(fma(Float64(y * x), 9.0, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-300)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(Float64(Float64(y * x) / z), 9.0, Float64(Float64(a * t) * -4.0)) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-300], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0 + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000003e-300 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 91.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-sub0 N/A

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

      12. associate-+l- N/A

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

      13. neg-sub0 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

   4. Applied rewrites 92.2%

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

   if -1.00000000000000003e-300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 35.1%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in a 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 87.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 7.6

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

   5. Applied rewrites 7.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 72.3%

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

   10. Applied rewrites 72.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq -1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-159}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-291}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 200000:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (/ (* (* y x) 9.0) (* c z))))
   (if (<= t_1 -4e+182)
     t_2
     (if (<= t_1 -5e-159)
       (/ (* (* -4.0 t) a) c)
       (if (<= t_1 2e-291)
         (/ b (* c z))
         (if (<= t_1 200000.0) (* (/ (* a t) c) -4.0) t_2))))))

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 = (9.0 * x) * y;
	double t_2 = ((y * x) * 9.0) / (c * z);
	double tmp;
	if (t_1 <= -4e+182) {
		tmp = t_2;
	} else if (t_1 <= -5e-159) {
		tmp = ((-4.0 * t) * a) / c;
	} else if (t_1 <= 2e-291) {
		tmp = b / (c * z);
	} else if (t_1 <= 200000.0) {
		tmp = ((a * t) / c) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = ((y * x) * 9.0d0) / (c * z)
    if (t_1 <= (-4d+182)) then
        tmp = t_2
    else if (t_1 <= (-5d-159)) then
        tmp = (((-4.0d0) * t) * a) / c
    else if (t_1 <= 2d-291) then
        tmp = b / (c * z)
    else if (t_1 <= 200000.0d0) then
        tmp = ((a * t) / c) * (-4.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double t_2 = ((y * x) * 9.0) / (c * z);
	double tmp;
	if (t_1 <= -4e+182) {
		tmp = t_2;
	} else if (t_1 <= -5e-159) {
		tmp = ((-4.0 * t) * a) / c;
	} else if (t_1 <= 2e-291) {
		tmp = b / (c * z);
	} else if (t_1 <= 200000.0) {
		tmp = ((a * t) / c) * -4.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 * x) * y
	t_2 = ((y * x) * 9.0) / (c * z)
	tmp = 0
	if t_1 <= -4e+182:
		tmp = t_2
	elif t_1 <= -5e-159:
		tmp = ((-4.0 * t) * a) / c
	elif t_1 <= 2e-291:
		tmp = b / (c * z)
	elif t_1 <= 200000.0:
		tmp = ((a * t) / c) * -4.0
	else:
		tmp = t_2
	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(9.0 * x) * y)
	t_2 = Float64(Float64(Float64(y * x) * 9.0) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -4e+182)
		tmp = t_2;
	elseif (t_1 <= -5e-159)
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	elseif (t_1 <= 2e-291)
		tmp = Float64(b / Float64(c * z));
	elseif (t_1 <= 200000.0)
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = ((y * x) * 9.0) / (c * z);
	tmp = 0.0;
	if (t_1 <= -4e+182)
		tmp = t_2;
	elseif (t_1 <= -5e-159)
		tmp = ((-4.0 * t) * a) / c;
	elseif (t_1 <= 2e-291)
		tmp = b / (c * z);
	elseif (t_1 <= 200000.0)
		tmp = ((a * t) / c) * -4.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+182], t$95$2, If[LessEqual[t$95$1, -5e-159], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e-291], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200000.0], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000003e182 or 2e5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 62.2

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

   5. Applied rewrites 62.2%

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

   if -4.0000000000000003e182 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000032e-159

   1. Initial program 81.8%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 54.9%

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

   10. Applied rewrites 54.9%

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

   if -5.00000000000000032e-159 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999992e-291

   1. Initial program 85.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 59.7

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

   5. Applied rewrites 59.7%

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

   if 1.99999999999999992e-291 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e5

   1. Initial program 81.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 57.4

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

   5. Applied rewrites 57.4%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -4 \cdot 10^{+182}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-159}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 2 \cdot 10^{-291}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 200000:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, \frac{9}{c}, \frac{\mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)}{y}\right) \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8.2e+67)
   (* (fma (/ x z) (/ 9.0 c) (/ (fma (* (/ a c) -4.0) t (/ b (* c z))) y)) y)
   (if (<= z 4.1e+179)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
     (/ (* (fma (/ y z) 9.0 (* (/ (* a t) x) -4.0)) x) 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 <= -8.2e+67) {
		tmp = fma((x / z), (9.0 / c), (fma(((a / c) * -4.0), t, (b / (c * z))) / y)) * y;
	} else if (z <= 4.1e+179) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = (fma((y / z), 9.0, (((a * t) / x) * -4.0)) * x) / 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 <= -8.2e+67)
		tmp = Float64(fma(Float64(x / z), Float64(9.0 / c), Float64(fma(Float64(Float64(a / c) * -4.0), t, Float64(b / Float64(c * z))) / y)) * y);
	elseif (z <= 4.1e+179)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = Float64(Float64(fma(Float64(y / z), 9.0, Float64(Float64(Float64(a * t) / x) * -4.0)) * x) / 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[LessEqual[z, -8.2e+67], N[(N[(N[(x / z), $MachinePrecision] * N[(9.0 / c), $MachinePrecision] + N[(N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 4.1e+179], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999959e67

   1. Initial program 55.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 79.1%

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

   if -8.19999999999999959e67 < z < 4.10000000000000011e179

   1. Initial program 92.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 93.3%

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

   if 4.10000000000000011e179 < z

   1. Initial program 33.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 93.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, \frac{9}{c}, \frac{\mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)}{y}\right) \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8.2e+67)
   (fma (* (/ y (* c z)) 9.0) x (fma (* (/ a c) -4.0) t (/ b (* c z))))
   (if (<= z 4.1e+179)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
     (/ (* (fma (/ y z) 9.0 (* (/ (* a t) x) -4.0)) x) 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 <= -8.2e+67) {
		tmp = fma(((y / (c * z)) * 9.0), x, fma(((a / c) * -4.0), t, (b / (c * z))));
	} else if (z <= 4.1e+179) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = (fma((y / z), 9.0, (((a * t) / x) * -4.0)) * x) / 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 <= -8.2e+67)
		tmp = fma(Float64(Float64(y / Float64(c * z)) * 9.0), x, fma(Float64(Float64(a / c) * -4.0), t, Float64(b / Float64(c * z))));
	elseif (z <= 4.1e+179)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = Float64(Float64(fma(Float64(y / z), 9.0, Float64(Float64(Float64(a * t) / x) * -4.0)) * x) / 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[LessEqual[z, -8.2e+67], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x + N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+179], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999959e67

   1. Initial program 55.4%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

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

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.1%

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

   if -8.19999999999999959e67 < z < 4.10000000000000011e179

   1. Initial program 92.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 93.3%

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

   if 4.10000000000000011e179 < z

   1. Initial program 33.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 93.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+85}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x z) (* (/ y c) 9.0))))
   (if (<= t_1 -5e+196)
     t_2
     (if (<= t_1 1e+85) (/ (/ (fma (* (* -4.0 z) a) t b) c) z) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = t_2;
	} else if (t_1 <= 1e+85) {
		tmp = (fma(((-4.0 * z) * a), t, b) / c) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+196)
		tmp = t_2;
	elseif (t_1 <= 1e+85)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, b) / c) / z);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+196], t$95$2, If[LessEqual[t$95$1, 1e+85], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e196 or 1e85 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -4.9999999999999998e196 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e85

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 72.8

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 72.8

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

   7. Applied rewrites 72.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. remove-double-div N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

   9. Applied rewrites 74.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+85}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 200000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x z) (* (/ y c) 9.0))))
   (if (<= t_1 -5e+196)
     t_2
     (if (<= t_1 200000.0) (/ (/ (fma (* (* a t) -4.0) z b) z) c) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = t_2;
	} else if (t_1 <= 200000.0) {
		tmp = (fma(((a * t) * -4.0), z, b) / z) / c;
	} else {
		tmp = t_2;
	}
	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(9.0 * x) * y)
	t_2 = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+196)
		tmp = t_2;
	elseif (t_1 <= 200000.0)
		tmp = Float64(Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / z) / c);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+196], t$95$2, If[LessEqual[t$95$1, 200000.0], N[(N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e196 or 2e5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 69.3

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

   5. Applied rewrites 69.3%

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

   if -4.9999999999999998e196 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e5

   1. Initial program 83.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 77.1

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

   5. Applied rewrites 77.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 200000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c} \cdot \frac{y}{z}, 9, \frac{a \cdot t}{c} \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.9e+68)
   (fma (* (/ x c) (/ y z)) 9.0 (* (/ (* a t) c) -4.0))
   (if (<= z 4.1e+179)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
     (/ (* (fma (/ y z) 9.0 (* (/ (* a t) x) -4.0)) x) 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 <= -1.9e+68) {
		tmp = fma(((x / c) * (y / z)), 9.0, (((a * t) / c) * -4.0));
	} else if (z <= 4.1e+179) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = (fma((y / z), 9.0, (((a * t) / x) * -4.0)) * x) / 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 <= -1.9e+68)
		tmp = fma(Float64(Float64(x / c) * Float64(y / z)), 9.0, Float64(Float64(Float64(a * t) / c) * -4.0));
	elseif (z <= 4.1e+179)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = Float64(Float64(fma(Float64(y / z), 9.0, Float64(Float64(Float64(a * t) / x) * -4.0)) * x) / 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[LessEqual[z, -1.9e+68], N[(N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+179], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e68

   1. Initial program 55.4%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 80.6%

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

   if -1.9e68 < z < 4.10000000000000011e179

   1. Initial program 92.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 93.3%

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

   if 4.10000000000000011e179 < z

   1. Initial program 33.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 93.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c} \cdot \frac{y}{z}, 9, \frac{a \cdot t}{c} \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z}, 9, \frac{a \cdot t}{x} \cdot -4\right) \cdot x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 200000:\\ \;\;\;\;\frac{\left(\left(t \cdot z\right) \cdot a\right) \cdot -4 + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x z) (* (/ y c) 9.0))))
   (if (<= t_1 -2e+136)
     t_2
     (if (<= t_1 200000.0) (/ (+ (* (* (* t z) a) -4.0) b) (* c z)) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -2e+136) {
		tmp = t_2;
	} else if (t_1 <= 200000.0) {
		tmp = ((((t * z) * a) * -4.0) + b) / (c * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (9.0d0 * x) * y
    t_2 = (x / z) * ((y / c) * 9.0d0)
    if (t_1 <= (-2d+136)) then
        tmp = t_2
    else if (t_1 <= 200000.0d0) then
        tmp = ((((t * z) * a) * (-4.0d0)) + b) / (c * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -2e+136) {
		tmp = t_2;
	} else if (t_1 <= 200000.0) {
		tmp = ((((t * z) * a) * -4.0) + b) / (c * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 * x) * y
	t_2 = (x / z) * ((y / c) * 9.0)
	tmp = 0
	if t_1 <= -2e+136:
		tmp = t_2
	elif t_1 <= 200000.0:
		tmp = ((((t * z) * a) * -4.0) + b) / (c * z)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+136)
		tmp = t_2;
	elseif (t_1 <= 200000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(t * z) * a) * -4.0) + b) / Float64(c * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (9.0 * x) * y;
	t_2 = (x / z) * ((y / c) * 9.0);
	tmp = 0.0;
	if (t_1 <= -2e+136)
		tmp = t_2;
	elseif (t_1 <= 200000.0)
		tmp = ((((t * z) * a) * -4.0) + b) / (c * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+136], t$95$2, If[LessEqual[t$95$1, 200000.0], N[(N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000012e136 or 2e5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -2.00000000000000012e136 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e5

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 200000:\\ \;\;\;\;\frac{\left(\left(t \cdot z\right) \cdot a\right) \cdot -4 + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x z) (* (/ y c) 9.0))))
   (if (<= t_1 -5e+196)
     t_2
     (if (<= t_1 1e+85) (/ (fma (* (* -4.0 z) a) t b) (* c z)) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = t_2;
	} else if (t_1 <= 1e+85) {
		tmp = fma(((-4.0 * z) * a), t, b) / (c * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+196)
		tmp = t_2;
	elseif (t_1 <= 1e+85)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, b) / Float64(c * z));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+196], t$95$2, If[LessEqual[t$95$1, 1e+85], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e196 or 1e85 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -4.9999999999999998e196 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e85

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 72.8

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 72.8

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

   7. Applied rewrites 72.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. clear-num N/A

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

      7. lower-/.f64 73.0

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

   9. Applied rewrites 73.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a \cdot z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x z) (* (/ y c) 9.0))))
   (if (<= t_1 -5e+196)
     t_2
     (if (<= t_1 1e+85) (/ (fma (* -4.0 t) (* a z) b) (* c z)) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = t_2;
	} else if (t_1 <= 1e+85) {
		tmp = fma((-4.0 * t), (a * z), b) / (c * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+196)
		tmp = t_2;
	elseif (t_1 <= 1e+85)
		tmp = Float64(fma(Float64(-4.0 * t), Float64(a * z), b) / Float64(c * z));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+196], t$95$2, If[LessEqual[t$95$1, 1e+85], N[(N[(N[(-4.0 * t), $MachinePrecision] * N[(a * z), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e196 or 1e85 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -4.9999999999999998e196 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e85

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   7. Applied rewrites 73.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a \cdot z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 200000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* 9.0 x) y)) (t_2 (* (/ x z) (* (/ y c) 9.0))))
   (if (<= t_1 -5e+98)
     t_2
     (if (<= t_1 200000.0) (/ (fma (* (* a t) -4.0) z b) (* c z)) t_2))))

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 = (9.0 * x) * y;
	double t_2 = (x / z) * ((y / c) * 9.0);
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = t_2;
	} else if (t_1 <= 200000.0) {
		tmp = fma(((a * t) * -4.0), z, b) / (c * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 * x) * y)
	t_2 = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+98)
		tmp = t_2;
	elseif (t_1 <= 200000.0)
		tmp = Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / Float64(c * z));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+98], t$95$2, If[LessEqual[t$95$1, 200000.0], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e98 or 2e5 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 66.0

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

   5. Applied rewrites 66.0%

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

   if -4.9999999999999998e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e5

   1. Initial program 84.3%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 77.4

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

   5. Applied rewrites 77.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 200000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{c}}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+254}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (/ (* y x) z) 9.0 (* (* a t) -4.0)) c)))
   (if (<= y -6.8e-172)
     t_1
     (if (<= y 1.28e+23)
       (/ (/ (fma (* (* -4.0 z) a) t b) c) z)
       (if (<= y 7.8e+254) t_1 (* (/ x z) (* (/ y c) 9.0)))))))

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 t_1 = fma(((y * x) / z), 9.0, ((a * t) * -4.0)) / c;
	double tmp;
	if (y <= -6.8e-172) {
		tmp = t_1;
	} else if (y <= 1.28e+23) {
		tmp = (fma(((-4.0 * z) * a), t, b) / c) / z;
	} else if (y <= 7.8e+254) {
		tmp = t_1;
	} else {
		tmp = (x / z) * ((y / c) * 9.0);
	}
	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)
	t_1 = Float64(fma(Float64(Float64(y * x) / z), 9.0, Float64(Float64(a * t) * -4.0)) / c)
	tmp = 0.0
	if (y <= -6.8e-172)
		tmp = t_1;
	elseif (y <= 1.28e+23)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, b) / c) / z);
	elseif (y <= 7.8e+254)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(y / c) * 9.0));
	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] / z), $MachinePrecision] * 9.0 + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[y, -6.8e-172], t$95$1, If[LessEqual[y, 1.28e+23], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.8e+254], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999997e-172 or 1.28e23 < y < 7.8000000000000003e254

   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 b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 64.5

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

   5. Applied rewrites 64.5%

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

   6. Taylor expanded in a 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 73.8%

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

   if -6.7999999999999997e-172 < y < 1.28e23

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 72.7

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

   5. Applied rewrites 72.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 72.4

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 72.4

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

   7. Applied rewrites 72.4%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. remove-double-div N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

   9. Applied rewrites 76.6%

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

   if 7.8000000000000003e254 < y

   1. Initial program 56.2%

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

   3. Taylor expanded in y around 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 89.0

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

   5. Applied rewrites 89.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{c}}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+254}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\frac{y}{c} \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c} \cdot \frac{y}{z}, 9, \frac{a \cdot t}{c} \cdot -4\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.9e+68)
   (fma (* (/ x c) (/ y z)) 9.0 (* (/ (* a t) c) -4.0))
   (if (<= z 3.6e+179)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
     (/ (fma (/ (* y x) z) 9.0 (* (* a t) -4.0)) 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 <= -1.9e+68) {
		tmp = fma(((x / c) * (y / z)), 9.0, (((a * t) / c) * -4.0));
	} else if (z <= 3.6e+179) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = fma(((y * x) / z), 9.0, ((a * t) * -4.0)) / 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 <= -1.9e+68)
		tmp = fma(Float64(Float64(x / c) * Float64(y / z)), 9.0, Float64(Float64(Float64(a * t) / c) * -4.0));
	elseif (z <= 3.6e+179)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(Float64(y * x) / z), 9.0, Float64(Float64(a * t) * -4.0)) / 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[LessEqual[z, -1.9e+68], N[(N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] * 9.0 + N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+179], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0 + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e68

   1. Initial program 55.4%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 80.6%

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

   if -1.9e68 < z < 3.5999999999999998e179

   1. Initial program 92.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 93.3%

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

   if 3.5999999999999998e179 < z

   1. Initial program 33.0%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in a 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 88.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c} \cdot \frac{y}{z}, 9, \frac{a \cdot t}{c} \cdot -4\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) z) 9.0 (* (* a t) -4.0)) c)))
   (if (<= z -2.2e+70)
     t_1
     (if (<= z 3.6e+179)
       (/ (/ (fma (* (* -4.0 z) a) t (fma (* y x) 9.0 b)) c) z)
       t_1))))

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) / z), 9.0, ((a * t) * -4.0)) / c;
	double tmp;
	if (z <= -2.2e+70) {
		tmp = t_1;
	} else if (z <= 3.6e+179) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * x), 9.0, b)) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(Float64(y * x) / z), 9.0, Float64(Float64(a * t) * -4.0)) / c)
	tmp = 0.0
	if (z <= -2.2e+70)
		tmp = t_1;
	elseif (z <= 3.6e+179)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * x), 9.0, b)) / c) / z);
	else
		tmp = t_1;
	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] / z), $MachinePrecision] * 9.0 + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.2e+70], t$95$1, If[LessEqual[z, 3.6e+179], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000001e70 or 3.5999999999999998e179 < z

   1. Initial program 51.5%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 56.2

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in a 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 78.6%

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

   if -2.20000000000000001e70 < z < 3.5999999999999998e179

   1. Initial program 91.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 92.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot x, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+95}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (/ (* (* -4.0 t) a) c)))
   (if (<= z -1.06e+29)
     t_1
     (if (<= z 7e+95) (/ (fma (* 9.0 x) y b) (* c z)) t_1))))

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 = ((-4.0 * t) * a) / c;
	double tmp;
	if (z <= -1.06e+29) {
		tmp = t_1;
	} else if (z <= 7e+95) {
		tmp = fma((9.0 * x), y, b) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * t) * a) / c)
	tmp = 0.0
	if (z <= -1.06e+29)
		tmp = t_1;
	elseif (z <= 7e+95)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(c * z));
	else
		tmp = t_1;
	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[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.06e+29], t$95$1, If[LessEqual[z, 7e+95], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0600000000000001e29 or 6.99999999999999999e95 < z

   1. Initial program 58.8%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. metadata-eval N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c} \]

      6. +-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + 9 \cdot \left(x \cdot y\right)}}{z}}{c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), 9 \cdot \left(x \cdot y\right)\right)}}{z}}{c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

      15. lower-*.f64 61.4

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

   5. Applied rewrites 61.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z}}{c}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.0%

      \[\leadsto \frac{\left(t \cdot a\right) \cdot -4}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 62.1%

       \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

   if -1.0600000000000001e29 < z < 6.99999999999999999e95

   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

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in a around 0

      \[\leadsto \frac{\frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{c}}{z} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{c}}{z} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{c}}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{c}}{z} \]

      4. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{c}}{z} \]

      5. lower-*.f64 77.9

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{c}}{z} \]

   7. Applied rewrites 77.9%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{c}}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}}{z} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\color{blue}{z \cdot c}} \]

      5. lower-/.f64 78.1

         \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}} \]

   9. Applied rewrites 78.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+29}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+95}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.68 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -4.8e+151) t_1 (if (<= b 1.68e+41) (/ (* (* -4.0 t) a) c) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -4.8e+151) {
		tmp = t_1;
	} else if (b <= 1.68e+41) {
		tmp = ((-4.0 * t) * a) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-4.8d+151)) then
        tmp = t_1
    else if (b <= 1.68d+41) then
        tmp = (((-4.0d0) * t) * a) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -4.8e+151) {
		tmp = t_1;
	} else if (b <= 1.68e+41) {
		tmp = ((-4.0 * t) * a) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -4.8e+151:
		tmp = t_1
	elif b <= 1.68e+41:
		tmp = ((-4.0 * t) * a) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -4.8e+151)
		tmp = t_1;
	elseif (b <= 1.68e+41)
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -4.8e+151)
		tmp = t_1;
	elseif (b <= 1.68e+41)
		tmp = ((-4.0 * t) * a) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -4.8e+151], t$95$1, If[LessEqual[b, 1.68e+41], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.8000000000000002e151 or 1.68000000000000008e41 < b

   1. Initial program 78.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 82.6%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]
   6. Step-by-step derivation

      1. lower-/.f64 62.8

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   7. Applied rewrites 62.8%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if -4.8000000000000002e151 < b < 1.68000000000000008e41

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}}{c} \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\frac{\color{blue}{9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z}}{c} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c} \]

      6. +-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + 9 \cdot \left(x \cdot y\right)}}{z}}{c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), 9 \cdot \left(x \cdot y\right)\right)}}{z}}{c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

      15. lower-*.f64 69.4

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

   5. Applied rewrites 69.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z}}{c}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 50.6%

      \[\leadsto \frac{\left(t \cdot a\right) \cdot -4}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.7%

       \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.68 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (/ (* (* -4.0 t) a) c)))
   (if (<= z -1.32e-132) t_1 (if (<= z 1.7e+90) (/ b (* c z)) t_1))))

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 = ((-4.0 * t) * a) / c;
	double tmp;
	if (z <= -1.32e-132) {
		tmp = t_1;
	} else if (z <= 1.7e+90) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * t) * a) / c
    if (z <= (-1.32d-132)) then
        tmp = t_1
    else if (z <= 1.7d+90) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * t) * a) / c;
	double tmp;
	if (z <= -1.32e-132) {
		tmp = t_1;
	} else if (z <= 1.7e+90) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * t) * a) / c
	tmp = 0
	if z <= -1.32e-132:
		tmp = t_1
	elif z <= 1.7e+90:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * t) * a) / c)
	tmp = 0.0
	if (z <= -1.32e-132)
		tmp = t_1;
	elseif (z <= 1.7e+90)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * t) * a) / c;
	tmp = 0.0;
	if (z <= -1.32e-132)
		tmp = t_1;
	elseif (z <= 1.7e+90)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.32e-132], t$95$1, If[LessEqual[z, 1.7e+90], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32000000000000004e-132 or 1.70000000000000009e90 < z

   1. Initial program 63.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}}{c} \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\frac{\color{blue}{9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z}}{c} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c} \]

      6. +-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + 9 \cdot \left(x \cdot y\right)}}{z}}{c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), 9 \cdot \left(x \cdot y\right)\right)}}{z}}{c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

      15. lower-*.f64 62.8

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z}}{c}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 59.2%

      \[\leadsto \frac{\left(t \cdot a\right) \cdot -4}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 59.2%

       \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

   if -1.32000000000000004e-132 < z < 1.70000000000000009e90

   1. Initial program 96.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 48.5

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 48.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-132}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{a \cdot t}{c} \cdot -4\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ (* a t) c) -4.0)))
   (if (<= z -1.32e-132) t_1 (if (<= z 1.7e+90) (/ b (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * t) / c) * -4.0;
	double tmp;
	if (z <= -1.32e-132) {
		tmp = t_1;
	} else if (z <= 1.7e+90) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a * t) / c) * (-4.0d0)
    if (z <= (-1.32d-132)) then
        tmp = t_1
    else if (z <= 1.7d+90) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * t) / c) * -4.0;
	double tmp;
	if (z <= -1.32e-132) {
		tmp = t_1;
	} else if (z <= 1.7e+90) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((a * t) / c) * -4.0
	tmp = 0
	if z <= -1.32e-132:
		tmp = t_1
	elif z <= 1.7e+90:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a * t) / c) * -4.0)
	tmp = 0.0
	if (z <= -1.32e-132)
		tmp = t_1;
	elseif (z <= 1.7e+90)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((a * t) / c) * -4.0;
	tmp = 0.0;
	if (z <= -1.32e-132)
		tmp = t_1;
	elseif (z <= 1.7e+90)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -1.32e-132], t$95$1, If[LessEqual[z, 1.7e+90], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32000000000000004e-132 or 1.70000000000000009e90 < z

   1. Initial program 63.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      4. lower-*.f64 59.2

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

   5. Applied rewrites 59.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{t \cdot a}{c}} \]

   if -1.32000000000000004e-132 < z < 1.70000000000000009e90

   1. Initial program 96.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 48.5

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 48.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-132}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 34.8% 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 79.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in 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 33.2

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 33.2%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.2% 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 2024243 
(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)))