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

Percentage Accurate: 79.9% → 89.2%

Time: 16.7s

Alternatives: 21

Speedup: 0.6×

• 37.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% 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: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{9 \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 a (* t (/ -4.0 c)) (fma x (/ (* 9.0 y) (* z c)) (/ b (* z c))))))
   (if (<= z -6.5e+25)
     t_1
     (if (<= z 4.6e+71)
       (/ (/ (fma x (* 9.0 y) (fma a (* -4.0 (* z t)) 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(a, (t * (-4.0 / c)), fma(x, ((9.0 * y) / (z * c)), (b / (z * c))));
	double tmp;
	if (z <= -6.5e+25) {
		tmp = t_1;
	} else if (z <= 4.6e+71) {
		tmp = (fma(x, (9.0 * y), fma(a, (-4.0 * (z * t)), 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 = fma(a, Float64(t * Float64(-4.0 / c)), fma(x, Float64(Float64(9.0 * y) / Float64(z * c)), Float64(b / Float64(z * c))))
	tmp = 0.0
	if (z <= -6.5e+25)
		tmp = t_1;
	elseif (z <= 4.6e+71)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(a, Float64(-4.0 * Float64(z * t)), 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[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(9.0 * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+25], t$95$1, If[LessEqual[z, 4.6e+71], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000005e25 or 4.6000000000000005e71 < 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 x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 83.3%

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

   if -6.50000000000000005e25 < z < 4.6000000000000005e71

   1. Initial program 96.5%

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

      1. lift-/.f64 N/A

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

      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 98.2%

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

Alternative 2: 87.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-241}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot -4, t \cdot a, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -5e-241)
     (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))
     (if (<= t_1 0.0)
       (/ (fma -4.0 (* t a) (/ b z)) c)
       (if (<= t_1 INFINITY)
         (/ (fma (* z -4.0) (* t a) (fma x (* 9.0 y) b)) (* z c))
         (* (* a -4.0) (/ t c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -5e-241) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((z * -4.0), (t * a), fma(x, (9.0 * y), b)) / (z * c);
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-241)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(z * -4.0), Float64(t * a), fma(x, Float64(9.0 * y), b)) / Float64(z * c));
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-241], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(z * -4.0), $MachinePrecision] * N[(t * a), $MachinePrecision] + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999998e-241

   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
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. metadata-eval N/A

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

      21. lower-*.f64 91.3

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

   4. Applied rewrites 91.3%

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

   if -4.9999999999999998e-241 < (/.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 23.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 36.6%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 86.8

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

   7. Applied rewrites 86.8%

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

   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 90.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. associate-*l* N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 89.2

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

   4. Applied rewrites 89.2%

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

   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. 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 14.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.2

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

   7. Applied rewrites 59.2%

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

   9. Applied rewrites 70.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-241}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot -4, t \cdot a, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))))
   (if (<= t_1 -5e-241)
     t_2
     (if (<= t_1 0.0)
       (/ (fma -4.0 (* t a) (/ b z)) c)
       (if (<= t_1 INFINITY) t_2 (* (* a -4.0) (/ t c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	double tmp;
	if (t_1 <= -5e-241) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-241)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-241], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999998e-241 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. metadata-eval N/A

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

      21. lower-*.f64 90.8

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

   4. Applied rewrites 90.8%

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

   if -4.9999999999999998e-241 < (/.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 23.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 36.6%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 86.8

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

   7. Applied rewrites 86.8%

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

   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. 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 14.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.2

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

   7. Applied rewrites 59.2%

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

   9. Applied rewrites 70.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-241}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-284}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot y, 9, \mathsf{fma}\left(-4, z \cdot \left(t \cdot a\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -2e-284)
     (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))
     (if (<= t_1 INFINITY)
       (/ (/ (fma (* x y) 9.0 (fma -4.0 (* z (* t a)) b)) c) z)
       (* (* a -4.0) (/ t c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -2e-284) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma((x * y), 9.0, fma(-4.0, (z * (t * a)), b)) / c) / z;
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-284)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(Float64(x * y), 9.0, fma(-4.0, Float64(z * Float64(t * a)), b)) / c) / z);
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-284], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + N[(-4.0 * N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -2.00000000000000007e-284

   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
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. metadata-eval N/A

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

      21. lower-*.f64 91.3

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

   4. Applied rewrites 91.3%

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

   if -2.00000000000000007e-284 < (/.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 81.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 89.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 89.2

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 89.2

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*r* N/A

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

      20. *-commutative N/A

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

      21. lift-*.f64 N/A

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

      22. lower-*.f64 87.5

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 87.5

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

   6. Applied rewrites 87.5%

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

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

   1. Initial program 0.0%

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

      1. 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 14.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.2

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

   7. Applied rewrites 59.2%

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

   9. Applied rewrites 70.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -2 \cdot 10^{-284}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot y, 9, \mathsf{fma}\left(-4, z \cdot \left(t \cdot a\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c)) <= Inf)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(a, Float64(-4.0 * Float64(z * t)), b)) / c) / z);
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / 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[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 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)) < +inf.0

   1. Initial program 86.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 88.7%

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

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

   1. Initial program 0.0%

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

      1. 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 14.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.2

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

   7. Applied rewrites 59.2%

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

   9. Applied rewrites 70.1%

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

4. Final simplification 86.8%

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

Alternative 6: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+275}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* y (* x 9.0))))
   (if (<= t_1 -4e+275)
     (* 9.0 (* x (/ y (* z c))))
     (if (<= t_1 -4e+87)
       (/ (/ (fma 9.0 (* x y) b) c) z)
       (if (<= t_1 1e-61)
         (/ (fma -4.0 (* t a) (/ b z)) c)
         (/ (/ (fma x (* 9.0 y) b) c) z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e+275) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t_1 <= -4e+87) {
		tmp = (fma(9.0, (x * y), b) / c) / z;
	} else if (t_1 <= 1e-61) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else {
		tmp = (fma(x, (9.0 * y), b) / c) / z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -4e+275)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t_1 <= -4e+87)
		tmp = Float64(Float64(fma(9.0, Float64(x * y), b) / c) / z);
	elseif (t_1 <= 1e-61)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	else
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), b) / c) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+275], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e+87], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e-61], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999984e275

   1. Initial program 61.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 61.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 76.6

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

   7. Applied rewrites 76.6%

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

   if -3.99999999999999984e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999998e87

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 88.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 88.8

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 88.8

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*r* N/A

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

      20. *-commutative N/A

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

      21. lift-*.f64 N/A

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

      22. lower-*.f64 88.8

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 88.8

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

   6. Applied rewrites 88.8%

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

   7. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 81.5

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

   9. Applied rewrites 81.5%

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

   if -3.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-61

   1. Initial program 75.6%

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

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 67.2%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 82.1

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

   7. Applied rewrites 82.1%

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

   if 1e-61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 84.1%

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

   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. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 74.3

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

   7. Applied rewrites 74.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+275}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+275}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (/ (fma x (* 9.0 y) b) c) z)) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -4e+275)
     (* 9.0 (* x (/ y (* z c))))
     (if (<= t_2 -4e+87)
       t_1
       (if (<= t_2 1e-61) (/ (fma -4.0 (* t a) (/ b z)) 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 = (fma(x, (9.0 * y), b) / c) / z;
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -4e+275) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t_2 <= -4e+87) {
		tmp = t_1;
	} else if (t_2 <= 1e-61) {
		tmp = fma(-4.0, (t * a), (b / z)) / 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(fma(x, Float64(9.0 * y), b) / c) / z)
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -4e+275)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t_2 <= -4e+87)
		tmp = t_1;
	elseif (t_2 <= 1e-61)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	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[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+275], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e+87], t$95$1, If[LessEqual[t$95$2, 1e-61], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999984e275

   1. Initial program 61.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 61.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 76.6

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

   7. Applied rewrites 76.6%

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

   if -3.99999999999999984e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999998e87 or 1e-61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 85.3%

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

   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. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 76.1

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

   7. Applied rewrites 76.1%

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

   if -3.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-61

   1. Initial program 75.6%

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

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 67.2%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 82.1

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

   7. Applied rewrites 82.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+275}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{9}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -4e+87)
     (* 9.0 (* x (/ y (* z c))))
     (if (<= t_1 5e-196)
       (* t (/ (* a -4.0) c))
       (if (<= t_1 2e-12) (/ b (* z c)) (* y (* x (/ 9.0 (* z c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e+87) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t_1 <= 5e-196) {
		tmp = t * ((a * -4.0) / c);
	} else if (t_1 <= 2e-12) {
		tmp = b / (z * c);
	} else {
		tmp = y * (x * (9.0 / (z * c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-4d+87)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (t_1 <= 5d-196) then
        tmp = t * ((a * (-4.0d0)) / c)
    else if (t_1 <= 2d-12) then
        tmp = b / (z * c)
    else
        tmp = y * (x * (9.0d0 / (z * c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e+87) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t_1 <= 5e-196) {
		tmp = t * ((a * -4.0) / c);
	} else if (t_1 <= 2e-12) {
		tmp = b / (z * c);
	} else {
		tmp = y * (x * (9.0 / (z * c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -4e+87:
		tmp = 9.0 * (x * (y / (z * c)))
	elif t_1 <= 5e-196:
		tmp = t * ((a * -4.0) / c)
	elif t_1 <= 2e-12:
		tmp = b / (z * c)
	else:
		tmp = y * (x * (9.0 / (z * c)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -4e+87)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t_1 <= 5e-196)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	elseif (t_1 <= 2e-12)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(y * Float64(x * Float64(9.0 / Float64(z * c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -4e+87)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (t_1 <= 5e-196)
		tmp = t * ((a * -4.0) / c);
	elseif (t_1 <= 2e-12)
		tmp = b / (z * c);
	else
		tmp = y * (x * (9.0 / (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+87], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-196], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-12], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * N[(9.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999998e87

   1. Initial program 73.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 75.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 67.9

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

   7. Applied rewrites 67.9%

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

   if -3.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000005e-196

   1. Initial program 75.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 82.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.9

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

   7. Applied rewrites 56.9%

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

   9. Applied rewrites 61.1%

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

   if 5.0000000000000005e-196 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999996e-12

   1. Initial program 82.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      3. lower-*.f64 61.4

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

   5. Applied rewrites 61.4%

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

   if 1.99999999999999996e-12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. 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 82.8%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 25.6

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

   7. Applied rewrites 25.6%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 55.1

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

   10. Applied rewrites 55.1%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{9}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+59}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* y (* x 9.0))) (t_2 (* 9.0 (* x (/ y (* z c))))))
   (if (<= t_1 -4e+87)
     t_2
     (if (<= t_1 5e-196)
       (* t (/ (* a -4.0) c))
       (if (<= t_1 2e+59) (/ 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 = y * (x * 9.0);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -4e+87) {
		tmp = t_2;
	} else if (t_1 <= 5e-196) {
		tmp = t * ((a * -4.0) / c);
	} else if (t_1 <= 2e+59) {
		tmp = b / (z * c);
	} 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 = y * (x * 9.0d0)
    t_2 = 9.0d0 * (x * (y / (z * c)))
    if (t_1 <= (-4d+87)) then
        tmp = t_2
    else if (t_1 <= 5d-196) then
        tmp = t * ((a * (-4.0d0)) / c)
    else if (t_1 <= 2d+59) then
        tmp = b / (z * c)
    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 = y * (x * 9.0);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -4e+87) {
		tmp = t_2;
	} else if (t_1 <= 5e-196) {
		tmp = t * ((a * -4.0) / c);
	} else if (t_1 <= 2e+59) {
		tmp = b / (z * c);
	} 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 = y * (x * 9.0)
	t_2 = 9.0 * (x * (y / (z * c)))
	tmp = 0
	if t_1 <= -4e+87:
		tmp = t_2
	elif t_1 <= 5e-196:
		tmp = t * ((a * -4.0) / c)
	elif t_1 <= 2e+59:
		tmp = 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(y * Float64(x * 9.0))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (t_1 <= -4e+87)
		tmp = t_2;
	elseif (t_1 <= 5e-196)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	elseif (t_1 <= 2e+59)
		tmp = Float64(b / Float64(z * c));
	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 = y * (x * 9.0);
	t_2 = 9.0 * (x * (y / (z * c)));
	tmp = 0.0;
	if (t_1 <= -4e+87)
		tmp = t_2;
	elseif (t_1 <= 5e-196)
		tmp = t * ((a * -4.0) / c);
	elseif (t_1 <= 2e+59)
		tmp = b / (z * c);
	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[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+87], t$95$2, If[LessEqual[t$95$1, 5e-196], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+59], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.9999999999999998e87 or 1.99999999999999994e59 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 66.2

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

   7. Applied rewrites 66.2%

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

   if -3.9999999999999998e87 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000005e-196

   1. Initial program 75.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 82.1%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.9

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

   7. Applied rewrites 56.9%

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

   9. Applied rewrites 61.1%

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

   if 5.0000000000000005e-196 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999994e59

   1. Initial program 82.5%

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

   3. 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. *-commutative N/A

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

      3. lower-*.f64 55.5

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

   5. Applied rewrites 55.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+59}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+151}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -5e+151)
     (* 9.0 (* x (/ y (* z c))))
     (if (<= t_1 1e-61)
       (/ (fma -4.0 (* t a) (/ b z)) c)
       (/ (fma (* x 9.0) y b) (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -5e+151) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t_1 <= 1e-61) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else {
		tmp = fma((x * 9.0), y, b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+151)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t_1 <= 1e-61)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	else
		tmp = Float64(fma(Float64(x * 9.0), y, b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+151], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-61], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000002e151

   1. Initial program 69.2%

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

      1. lift-/.f64 N/A

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

      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 69.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 74.6

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

   7. Applied rewrites 74.6%

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

   if -5.0000000000000002e151 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e-61

   1. Initial program 76.5%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 80.0

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

   7. Applied rewrites 80.0%

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

   if 1e-61 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.6%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 62.4

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

   5. Applied rewrites 62.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 74.0

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

   8. Applied rewrites 74.0%

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

   10. Applied rewrites 74.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+151}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), y \cdot \left(x \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (fma -4.0 (* t a) (/ b z)) c)))
   (if (<= z -6.2e+17)
     t_1
     (if (<= z 4.35e-184)
       (/ (/ (fma 9.0 (* x y) b) c) z)
       (if (<= z 4.3e+107)
         (/ (fma a (* -4.0 (* z t)) (* y (* x 9.0))) (* z 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 = fma(-4.0, (t * a), (b / z)) / c;
	double tmp;
	if (z <= -6.2e+17) {
		tmp = t_1;
	} else if (z <= 4.35e-184) {
		tmp = (fma(9.0, (x * y), b) / c) / z;
	} else if (z <= 4.3e+107) {
		tmp = fma(a, (-4.0 * (z * t)), (y * (x * 9.0))) / (z * 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(fma(-4.0, Float64(t * a), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -6.2e+17)
		tmp = t_1;
	elseif (z <= 4.35e-184)
		tmp = Float64(Float64(fma(9.0, Float64(x * y), b) / c) / z);
	elseif (z <= 4.3e+107)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), Float64(y * Float64(x * 9.0))) / Float64(z * c));
	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[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -6.2e+17], t$95$1, If[LessEqual[z, 4.35e-184], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.3e+107], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e17 or 4.3e107 < 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. 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

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 57.3%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 75.1

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

   7. Applied rewrites 75.1%

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

   if -6.2e17 < z < 4.34999999999999995e-184

   1. Initial program 97.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 99.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 99.8

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 99.8

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*r* N/A

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

      20. *-commutative N/A

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

      21. lift-*.f64 N/A

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

      22. lower-*.f64 97.4

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 97.4

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

   6. Applied rewrites 97.4%

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

   7. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 88.2

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

   9. Applied rewrites 88.2%

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

   if 4.34999999999999995e-184 < z < 4.3e107

   1. Initial program 89.2%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 73.6

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

   5. Applied rewrites 73.6%

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

   7. Applied rewrites 73.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), y \cdot \left(x \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (fma -4.0 (* t a) (/ b z)) c)))
   (if (<= z -6.2e+17)
     t_1
     (if (<= z 4.35e-184)
       (/ (/ (fma 9.0 (* x y) b) c) z)
       (if (<= z 4.3e+107)
         (/ (fma a (* -4.0 (* z t)) (* 9.0 (* x y))) (* z 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 = fma(-4.0, (t * a), (b / z)) / c;
	double tmp;
	if (z <= -6.2e+17) {
		tmp = t_1;
	} else if (z <= 4.35e-184) {
		tmp = (fma(9.0, (x * y), b) / c) / z;
	} else if (z <= 4.3e+107) {
		tmp = fma(a, (-4.0 * (z * t)), (9.0 * (x * y))) / (z * 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(fma(-4.0, Float64(t * a), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -6.2e+17)
		tmp = t_1;
	elseif (z <= 4.35e-184)
		tmp = Float64(Float64(fma(9.0, Float64(x * y), b) / c) / z);
	elseif (z <= 4.3e+107)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), Float64(9.0 * Float64(x * y))) / Float64(z * c));
	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[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -6.2e+17], t$95$1, If[LessEqual[z, 4.35e-184], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.3e+107], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e17 or 4.3e107 < 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. 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

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 57.3%

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

   5. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 75.1

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

   7. Applied rewrites 75.1%

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

   if -6.2e17 < z < 4.34999999999999995e-184

   1. Initial program 97.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 99.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 99.8

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 99.8

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*r* N/A

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

      20. *-commutative N/A

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

      21. lift-*.f64 N/A

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

      22. lower-*.f64 97.4

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 97.4

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

   6. Applied rewrites 97.4%

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

   7. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 88.2

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

   9. Applied rewrites 88.2%

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

   if 4.34999999999999995e-184 < z < 4.3e107

   1. Initial program 89.2%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 73.6

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

   5. Applied rewrites 73.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* a -4.0) c))))
   (if (<= t -8.8e+160)
     t_1
     (if (<= t 6e-103) (/ (fma (* x 9.0) y b) (* z 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 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -8.8e+160) {
		tmp = t_1;
	} else if (t <= 6e-103) {
		tmp = fma((x * 9.0), y, b) / (z * 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(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (t <= -8.8e+160)
		tmp = t_1;
	elseif (t <= 6e-103)
		tmp = Float64(fma(Float64(x * 9.0), y, b) / Float64(z * c));
	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[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+160], t$95$1, If[LessEqual[t, 6e-103], N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.79999999999999968e160 or 6e-103 < t

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.3%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 51.9

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

   7. Applied rewrites 51.9%

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

   9. Applied rewrites 57.1%

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

   if -8.79999999999999968e160 < t < 6e-103

   1. Initial program 82.3%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 67.9

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

   8. Applied rewrites 67.9%

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

   10. Applied rewrites 68.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* a -4.0) c))))
   (if (<= t -8.8e+160)
     t_1
     (if (<= t 6e-103) (/ (fma x (* 9.0 y) b) (* z 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 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -8.8e+160) {
		tmp = t_1;
	} else if (t <= 6e-103) {
		tmp = fma(x, (9.0 * y), b) / (z * 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(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (t <= -8.8e+160)
		tmp = t_1;
	elseif (t <= 6e-103)
		tmp = Float64(fma(x, Float64(9.0 * y), b) / Float64(z * c));
	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[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+160], t$95$1, If[LessEqual[t, 6e-103], N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.79999999999999968e160 or 6e-103 < t

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.3%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 51.9

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

   7. Applied rewrites 51.9%

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

   9. Applied rewrites 57.1%

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

   if -8.79999999999999968e160 < t < 6e-103

   1. Initial program 82.3%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 67.9

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

   8. Applied rewrites 67.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* a -4.0) c))))
   (if (<= t -8.8e+160)
     t_1
     (if (<= t 6e-103) (/ (fma 9.0 (* x y) b) (* z 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 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -8.8e+160) {
		tmp = t_1;
	} else if (t <= 6e-103) {
		tmp = fma(9.0, (x * y), b) / (z * 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(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (t <= -8.8e+160)
		tmp = t_1;
	elseif (t <= 6e-103)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	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[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+160], t$95$1, If[LessEqual[t, 6e-103], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.79999999999999968e160 or 6e-103 < t

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.3%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 51.9

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

   7. Applied rewrites 51.9%

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

   9. Applied rewrites 57.1%

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

   if -8.79999999999999968e160 < t < 6e-103

   1. Initial program 82.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 67.9

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

   5. Applied rewrites 67.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.00115:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* a -4.0) c))))
   (if (<= a -3.3e-140) t_1 (if (<= a 0.00115) (/ (/ 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 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -3.3e-140) {
		tmp = t_1;
	} else if (a <= 0.00115) {
		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 = t * ((a * (-4.0d0)) / c)
    if (a <= (-3.3d-140)) then
        tmp = t_1
    else if (a <= 0.00115d0) 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 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -3.3e-140) {
		tmp = t_1;
	} else if (a <= 0.00115) {
		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 = t * ((a * -4.0) / c)
	tmp = 0
	if a <= -3.3e-140:
		tmp = t_1
	elif a <= 0.00115:
		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(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (a <= -3.3e-140)
		tmp = t_1;
	elseif (a <= 0.00115)
		tmp = Float64(Float64(b / 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 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (a <= -3.3e-140)
		tmp = t_1;
	elseif (a <= 0.00115)
		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[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e-140], t$95$1, If[LessEqual[a, 0.00115], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.29999999999999987e-140 or 0.00115 < a

   1. Initial program 75.5%

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

      1. lift-/.f64 N/A

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

      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 79.3%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 50.7

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

   7. Applied rewrites 50.7%

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

   9. Applied rewrites 57.7%

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

   if -3.29999999999999987e-140 < a < 0.00115

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. 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 83.6%

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

   5. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]
   6. Step-by-step derivation

      1. lower-/.f64 47.8

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   7. Applied rewrites 47.8%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 0.00115:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* a -4.0) c))))
   (if (<= a -2.15e-123) t_1 (if (<= a 8.8e-57) (/ (/ b z) 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 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -2.15e-123) {
		tmp = t_1;
	} else if (a <= 8.8e-57) {
		tmp = (b / z) / 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 = t * ((a * (-4.0d0)) / c)
    if (a <= (-2.15d-123)) then
        tmp = t_1
    else if (a <= 8.8d-57) then
        tmp = (b / z) / 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 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -2.15e-123) {
		tmp = t_1;
	} else if (a <= 8.8e-57) {
		tmp = (b / z) / 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 = t * ((a * -4.0) / c)
	tmp = 0
	if a <= -2.15e-123:
		tmp = t_1
	elif a <= 8.8e-57:
		tmp = (b / z) / 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(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (a <= -2.15e-123)
		tmp = t_1;
	elseif (a <= 8.8e-57)
		tmp = Float64(Float64(b / z) / 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 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (a <= -2.15e-123)
		tmp = t_1;
	elseif (a <= 8.8e-57)
		tmp = (b / z) / 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[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e-123], t$95$1, If[LessEqual[a, 8.8e-57], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.15000000000000016e-123 or 8.79999999999999994e-57 < a

   1. Initial program 75.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. 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 79.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]

      6. lower-*.f64 49.5

         \[\leadsto \frac{t \cdot \color{blue}{\left(-4 \cdot a\right)}}{c} \]

   7. Applied rewrites 49.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(-4 \cdot a\right)}{c}} \]
   8. Step-by-step derivation

   9. Applied rewrites 56.3%

      \[\leadsto \frac{a \cdot -4}{c} \cdot \color{blue}{t} \]

   if -2.15000000000000016e-123 < a < 8.79999999999999994e-57

   1. Initial program 80.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      3. lower-*.f64 43.0

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   5. Applied rewrites 43.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 46.8%

      \[\leadsto \frac{\frac{b}{z}}{\color{blue}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* a -4.0) c))))
   (if (<= a -2.15e-123) t_1 (if (<= a 5.2e+43) (* b (/ 1.0 (* z 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 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -2.15e-123) {
		tmp = t_1;
	} else if (a <= 5.2e+43) {
		tmp = b * (1.0 / (z * 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 = t * ((a * (-4.0d0)) / c)
    if (a <= (-2.15d-123)) then
        tmp = t_1
    else if (a <= 5.2d+43) then
        tmp = b * (1.0d0 / (z * 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 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -2.15e-123) {
		tmp = t_1;
	} else if (a <= 5.2e+43) {
		tmp = b * (1.0 / (z * 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 = t * ((a * -4.0) / c)
	tmp = 0
	if a <= -2.15e-123:
		tmp = t_1
	elif a <= 5.2e+43:
		tmp = b * (1.0 / (z * 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(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (a <= -2.15e-123)
		tmp = t_1;
	elseif (a <= 5.2e+43)
		tmp = Float64(b * Float64(1.0 / Float64(z * 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 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (a <= -2.15e-123)
		tmp = t_1;
	elseif (a <= 5.2e+43)
		tmp = b * (1.0 / (z * 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[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e-123], t$95$1, If[LessEqual[a, 5.2e+43], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.15000000000000016e-123 or 5.20000000000000042e43 < a

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 78.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]

      6. lower-*.f64 52.1

         \[\leadsto \frac{t \cdot \color{blue}{\left(-4 \cdot a\right)}}{c} \]

   7. Applied rewrites 52.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(-4 \cdot a\right)}{c}} \]
   8. Step-by-step derivation

   9. Applied rewrites 59.7%

      \[\leadsto \frac{a \cdot -4}{c} \cdot \color{blue}{t} \]

   if -2.15000000000000016e-123 < a < 5.20000000000000042e43

   1. Initial program 81.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      3. lower-*.f64 43.1

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   5. Applied rewrites 43.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

   7. Applied rewrites 43.0%

      \[\leadsto \frac{1}{z \cdot c} \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \end{array} \]

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 (<= t -3.5e+123)
   (* (* a -4.0) (/ t c))
   (if (<= t 5.5e-179) (/ b (* z c)) (/ (* -4.0 (* t a)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.5e+123) {
		tmp = (a * -4.0) * (t / c);
	} else if (t <= 5.5e-179) {
		tmp = b / (z * c);
	} else {
		tmp = (-4.0 * (t * a)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-3.5d+123)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (t <= 5.5d-179) then
        tmp = b / (z * c)
    else
        tmp = ((-4.0d0) * (t * a)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.5e+123) {
		tmp = (a * -4.0) * (t / c);
	} else if (t <= 5.5e-179) {
		tmp = b / (z * c);
	} else {
		tmp = (-4.0 * (t * a)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.5e+123:
		tmp = (a * -4.0) * (t / c)
	elif t <= 5.5e-179:
		tmp = b / (z * c)
	else:
		tmp = (-4.0 * (t * a)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.5e+123)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (t <= 5.5e-179)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(-4.0 * Float64(t * a)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.5e+123)
		tmp = (a * -4.0) * (t / c);
	elseif (t <= 5.5e-179)
		tmp = b / (z * c);
	else
		tmp = (-4.0 * (t * a)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.5e+123], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-179], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5e123

   1. Initial program 67.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]

      6. lower-*.f64 55.5

         \[\leadsto \frac{t \cdot \color{blue}{\left(-4 \cdot a\right)}}{c} \]

   7. Applied rewrites 55.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(-4 \cdot a\right)}{c}} \]
   8. Step-by-step derivation

   9. Applied rewrites 60.3%

      \[\leadsto \left(a \cdot -4\right) \cdot \color{blue}{\frac{t}{c}} \]

   if -3.5e123 < t < 5.5000000000000003e-179

   1. Initial program 82.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      3. lower-*.f64 41.1

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   5. Applied rewrites 41.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 5.5000000000000003e-179 < t

   1. Initial program 76.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]

      4. lower-*.f64 44.4

         \[\leadsto \frac{-4 \cdot \color{blue}{\left(a \cdot t\right)}}{c} \]

   5. Applied rewrites 44.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (* -4.0 (* t a)) c)))
   (if (<= t -3.5e+123) t_1 (if (<= t 5.5e-179) (/ b (* z 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 = (-4.0 * (t * a)) / c;
	double tmp;
	if (t <= -3.5e+123) {
		tmp = t_1;
	} else if (t <= 5.5e-179) {
		tmp = b / (z * 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 = ((-4.0d0) * (t * a)) / c
    if (t <= (-3.5d+123)) then
        tmp = t_1
    else if (t <= 5.5d-179) then
        tmp = b / (z * 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 = (-4.0 * (t * a)) / c;
	double tmp;
	if (t <= -3.5e+123) {
		tmp = t_1;
	} else if (t <= 5.5e-179) {
		tmp = b / (z * 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 = (-4.0 * (t * a)) / c
	tmp = 0
	if t <= -3.5e+123:
		tmp = t_1
	elif t <= 5.5e-179:
		tmp = b / (z * 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(-4.0 * Float64(t * a)) / c)
	tmp = 0.0
	if (t <= -3.5e+123)
		tmp = t_1;
	elseif (t <= 5.5e-179)
		tmp = Float64(b / Float64(z * 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 = (-4.0 * (t * a)) / c;
	tmp = 0.0;
	if (t <= -3.5e+123)
		tmp = t_1;
	elseif (t <= 5.5e-179)
		tmp = b / (z * 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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -3.5e+123], t$95$1, If[LessEqual[t, 5.5e-179], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e123 or 5.5000000000000003e-179 < t

   1. Initial program 73.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]

      4. lower-*.f64 47.4

         \[\leadsto \frac{-4 \cdot \color{blue}{\left(a \cdot t\right)}}{c} \]

   5. Applied rewrites 47.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

   if -3.5e123 < t < 5.5000000000000003e-179

   1. Initial program 82.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      3. lower-*.f64 41.1

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   5. Applied rewrites 41.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in 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. *-commutative N/A

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   3. lower-*.f64 31.8

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

5. Applied rewrites 31.8%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Add Preprocessing

Developer Target 1: 80.6% 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 2024233 
(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)))