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

Percentage Accurate: 79.0% → 86.2%

Time: 18.6s

Alternatives: 20

Speedup: 0.9×

• 37.9% 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: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+139}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(t, a \cdot \left(z \cdot -4\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z} \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.4e+139)
   (/ (fma -4.0 (* t a) (/ b z)) c)
   (if (<= z 2.25e+37)
     (/ (/ (fma (* x 9.0) y (fma t (* a (* z -4.0)) b)) c) z)
     (* (/ (fma x (* 9.0 y) (fma (* t a) (* z -4.0) b)) z) (/ 1.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.4e+139) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else if (z <= 2.25e+37) {
		tmp = (fma((x * 9.0), y, fma(t, (a * (z * -4.0)), b)) / c) / z;
	} else {
		tmp = (fma(x, (9.0 * y), fma((t * a), (z * -4.0), b)) / z) * (1.0 / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.4e+139)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	elseif (z <= 2.25e+37)
		tmp = Float64(Float64(fma(Float64(x * 9.0), y, fma(t, Float64(a * Float64(z * -4.0)), b)) / c) / z);
	else
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(Float64(t * a), Float64(z * -4.0), b)) / z) * Float64(1.0 / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.4e+139], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.25e+37], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000002e139

   1. Initial program 52.9%

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

   3. Taylor expanded in x around 0

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

      1. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 84.9%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 82.5

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

   8. Simplified 82.5%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 89.8

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

   11. Simplified 89.8%

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

   if -3.4000000000000002e139 < z < 2.24999999999999981e37

   1. Initial program 92.9%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 91.6%

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

      1. associate-*r* N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 95.7

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

   6. Applied egg-rr 95.7%

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

   if 2.24999999999999981e37 < z

   1. Initial program 49.4%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 80.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z} \cdot \frac{1}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+139}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(t, a \cdot \left(z \cdot -4\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z} \cdot \frac{1}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ t_2 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ t_3 := \frac{\mathsf{fma}\left(-4, \left(t \cdot a\right) \cdot z, t\_1\right)}{c \cdot z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-207}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\frac{t\_1}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{c \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma x (* 9.0 y) b))
        (t_2 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z)))
        (t_3 (/ (fma -4.0 (* (* t a) z) t_1) (* c z))))
   (if (<= t_2 -4e-207)
     t_3
     (if (<= t_2 0.0)
       (/ (/ t_1 c) z)
       (if (<= t_2 INFINITY) t_3 (fma a (* t (/ -4.0 c)) (/ b (* c z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (9.0 * y), b);
	double t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	double t_3 = fma(-4.0, ((t * a) * z), t_1) / (c * z);
	double tmp;
	if (t_2 <= -4e-207) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (t_1 / c) / z;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = fma(a, (t * (-4.0 / c)), (b / (c * z)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(x, Float64(9.0 * y), b)
	t_2 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z))
	t_3 = Float64(fma(-4.0, Float64(Float64(t * a) * z), t_1) / Float64(c * z))
	tmp = 0.0
	if (t_2 <= -4e-207)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t_1 / c) / z);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), Float64(b / Float64(c * z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = 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[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-207], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(t$95$1 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $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)) < -3.9999999999999997e-207 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 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. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. *-lowering-*.f64 89.6

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

   4. Applied egg-rr 89.6%

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

   if -3.9999999999999997e-207 < (/.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 34.7%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 99.5%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 81.4%

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

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

   1. Initial program 0.0%

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

   3. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 76.0%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 76.0

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

   8. Simplified 76.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -4 \cdot 10^{-207}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot a\right) \cdot z, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot a\right) \cdot z, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{c \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{9 \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= c 3.1e-19)
   (/ (/ (fma x (* 9.0 y) (fma (* t a) (* z -4.0) b)) z) c)
   (fma a (* t (/ -4.0 c)) (fma x (/ (* 9.0 y) (* c z)) (/ b (* c z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 3.1e-19) {
		tmp = (fma(x, (9.0 * y), fma((t * a), (z * -4.0), b)) / z) / c;
	} else {
		tmp = fma(a, (t * (-4.0 / c)), fma(x, ((9.0 * y) / (c * z)), (b / (c * z))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 3.1e-19)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(Float64(t * a), Float64(z * -4.0), b)) / z) / c);
	else
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), fma(x, Float64(Float64(9.0 * y) / Float64(c * z)), Float64(b / Float64(c * z))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[c, 3.1e-19], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(9.0 * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 3.0999999999999999e-19

   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. Step-by-step derivation

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 83.9%

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

   if 3.0999999999999999e-19 < c

   1. Initial program 66.3%

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

   3. Taylor expanded in x around 0

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

      1. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 86.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{9 \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(t, a \cdot \left(z \cdot -4\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.8e+140)
   (/ (fma -4.0 (* t a) (/ b z)) c)
   (if (<= z 3.4e+37)
     (/ (/ (fma (* x 9.0) y (fma t (* a (* z -4.0)) b)) c) z)
     (/ (/ (fma x (* 9.0 y) (fma (* t a) (* z -4.0) b)) z) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.8e+140) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else if (z <= 3.4e+37) {
		tmp = (fma((x * 9.0), y, fma(t, (a * (z * -4.0)), b)) / c) / z;
	} else {
		tmp = (fma(x, (9.0 * y), fma((t * a), (z * -4.0), b)) / z) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.8e+140)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	elseif (z <= 3.4e+37)
		tmp = Float64(Float64(fma(Float64(x * 9.0), y, fma(t, Float64(a * Float64(z * -4.0)), b)) / c) / z);
	else
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(Float64(t * a), Float64(z * -4.0), b)) / z) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.8e+140], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.4e+37], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999983e140

   1. Initial program 52.9%

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

   3. Taylor expanded in x around 0

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

      1. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 84.9%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 82.5

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

   8. Simplified 82.5%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 89.8

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

   11. Simplified 89.8%

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

   if -2.79999999999999983e140 < z < 3.40000000000000006e37

   1. Initial program 92.9%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 91.6%

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

      1. associate-*r* N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 95.7

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

   6. Applied egg-rr 95.7%

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

   if 3.40000000000000006e37 < z

   1. Initial program 49.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 80.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(t, a \cdot \left(z \cdot -4\right), b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 0.05:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.4e+55)
   (/ (fma -4.0 (* t a) (/ b z)) c)
   (if (<= z 0.05)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))
     (/ (/ (fma x (* 9.0 y) (fma (* t a) (* z -4.0) b)) z) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.4e+55) {
		tmp = fma(-4.0, (t * a), (b / z)) / c;
	} else if (z <= 0.05) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (fma(x, (9.0 * y), fma((t * a), (z * -4.0), b)) / z) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.4e+55)
		tmp = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c);
	elseif (z <= 0.05)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(Float64(t * a), Float64(z * -4.0), b)) / z) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.4e+55], N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 0.05], 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[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e55

   1. Initial program 59.3%

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

   3. Taylor expanded in x around 0

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

      1. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 88.1%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 83.3

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

   8. Simplified 83.3%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 86.6

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

   11. Simplified 86.6%

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

   if -2.3999999999999999e55 < z < 0.050000000000000003

   1. Initial program 96.3%

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

   if 0.050000000000000003 < z

   1. Initial program 54.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 82.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 0.05:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+68}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* t a) (/ b z)) c)))
   (if (<= z -6.2e+62)
     t_1
     (if (<= z 1.25e+68)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* 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(-4.0, (t * a), (b / z)) / c;
	double tmp;
	if (z <= -6.2e+62) {
		tmp = t_1;
	} else if (z <= 1.25e+68) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -6.2e+62)
		tmp = t_1;
	elseif (z <= 1.25e+68)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -6.2e+62], t$95$1, If[LessEqual[z, 1.25e+68], 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[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000029e62 or 1.2500000000000001e68 < z

   1. Initial program 54.4%

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

   3. Taylor expanded in 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 81.7%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 75.4

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

   8. Simplified 75.4%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 82.5

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

   11. Simplified 82.5%

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

   if -6.20000000000000029e62 < z < 1.2500000000000001e68

   1. Initial program 94.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+68}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+119}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{\mathsf{fma}\left(z, c, 0\right)}\\ \end{array} \end{array} \]

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+119)
     (/ (* 9.0 (* x y)) (* c z))
     (if (<= t_1 2e+110)
       (/ (* t -4.0) (/ c a))
       (* (* x 9.0) (/ y (fma z c 0.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -4e+119) {
		tmp = (9.0 * (x * y)) / (c * z);
	} else if (t_1 <= 2e+110) {
		tmp = (t * -4.0) / (c / a);
	} else {
		tmp = (x * 9.0) * (y / fma(z, c, 0.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -4e+119)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(c * z));
	elseif (t_1 <= 2e+110)
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	else
		tmp = Float64(Float64(x * 9.0) * Float64(y / fma(z, c, 0.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+119], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+110], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c + 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999978e119

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 79.1

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

   5. Simplified 79.1%

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

   if -3.99999999999999978e119 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e110

   1. Initial program 75.2%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 80.4%

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

   5. Taylor expanded in t 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. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 50.3

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

   7. Simplified 50.3%

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 50.2

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

   9. Applied egg-rr 50.2%

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

   if 2e110 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.4%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 75.3%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 71.2

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

   7. Simplified 71.2%

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

      1. associate-/l/ N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. +-lft-identity N/A

         \[\leadsto \left(x \cdot 9\right) \cdot \frac{y}{\color{blue}{0 + z \cdot c}} \]

      9. +-commutative N/A

         \[\leadsto \left(x \cdot 9\right) \cdot \frac{y}{\color{blue}{z \cdot c + 0}} \]

      10. accelerator-lowering-fma.f64 71.8

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

   9. Applied egg-rr 71.8%

      \[\leadsto \color{blue}{\left(x \cdot 9\right) \cdot \frac{y}{\mathsf{fma}\left(z, c, 0\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+119}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{\mathsf{fma}\left(z, c, 0\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* t a) (/ b z)) c)))
   (if (<= z -3.9e+86)
     t_1
     (if (<= z 5.2e+67)
       (/ (fma (* a (* z -4.0)) t (fma x (* 9.0 y) b)) (* c z))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (t * a), (b / z)) / c;
	double tmp;
	if (z <= -3.9e+86) {
		tmp = t_1;
	} else if (z <= 5.2e+67) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (9.0 * y), b)) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -3.9e+86)
		tmp = t_1;
	elseif (z <= 5.2e+67)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(9.0 * y), b)) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.9e+86], t$95$1, If[LessEqual[z, 5.2e+67], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000002e86 or 5.2000000000000001e67 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in x around 0

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

      1. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 81.0%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 74.4

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

   8. Simplified 74.4%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 81.8

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

   11. Simplified 81.8%

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

   if -3.9000000000000002e86 < z < 5.2000000000000001e67

   1. Initial program 94.2%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

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

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

      11. *-lowering-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 96.1

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

   4. Applied egg-rr 96.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* t a) (/ b z)) c)))
   (if (<= z -3.4e+87)
     t_1
     (if (<= z 5e+63)
       (/ (fma (* x 9.0) y (fma (* t a) (* z -4.0) b)) (* c z))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (t * a), (b / z)) / c;
	double tmp;
	if (z <= -3.4e+87) {
		tmp = t_1;
	} else if (z <= 5e+63) {
		tmp = fma((x * 9.0), y, fma((t * a), (z * -4.0), b)) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -3.4e+87)
		tmp = t_1;
	elseif (z <= 5e+63)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(Float64(t * a), Float64(z * -4.0), b)) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.4e+87], t$95$1, If[LessEqual[z, 5e+63], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000002e87 or 5.00000000000000011e63 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in x around 0

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

      1. 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 81.0%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 74.4

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

   8. Simplified 74.4%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 81.8

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

   11. Simplified 81.8%

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

   if -3.4000000000000002e87 < z < 5.00000000000000011e63

   1. Initial program 94.2%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

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

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 90.5

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

   4. Applied egg-rr 90.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+87}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(t \cdot a, z \cdot -4, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+230}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-126}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.9e+230)
   (/ (* t -4.0) (/ c a))
   (if (<= z -7e-126)
     (/ (fma (* (* t a) -4.0) z b) (* c z))
     (if (<= z 2.2e+104)
       (/ (/ (fma x (* 9.0 y) b) c) z)
       (* a (/ t (* c -0.25)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.9e+230) {
		tmp = (t * -4.0) / (c / a);
	} else if (z <= -7e-126) {
		tmp = fma(((t * a) * -4.0), z, b) / (c * z);
	} else if (z <= 2.2e+104) {
		tmp = (fma(x, (9.0 * y), b) / c) / z;
	} else {
		tmp = a * (t / (c * -0.25));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.9e+230)
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	elseif (z <= -7e-126)
		tmp = Float64(fma(Float64(Float64(t * a) * -4.0), z, b) / Float64(c * z));
	elseif (z <= 2.2e+104)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), b) / c) / z);
	else
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.9e+230], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-126], N[(N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+104], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8999999999999999e230

   1. Initial program 35.5%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 41.2%

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

   5. Taylor expanded in t 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. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 76.7

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

   7. Simplified 76.7%

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 76.8

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

   9. Applied egg-rr 76.8%

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

   if -2.8999999999999999e230 < z < -7e-126

   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 x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 73.8

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

   5. Simplified 73.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 78.1

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

   7. Applied egg-rr 78.1%

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

   if -7e-126 < z < 2.2e104

   1. Initial program 92.3%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 91.6%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 82.7%

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

   if 2.2e104 < z

   1. Initial program 44.2%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 61.0

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

   7. Simplified 61.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 58.7

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+230}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-126}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+230}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-120}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.1e+230)
   (/ (* t -4.0) (/ c a))
   (if (<= z -1.08e-120)
     (/ (fma (* (* t a) -4.0) z b) (* c z))
     (if (<= z 1.3e+111)
       (/ (fma (* x 9.0) y b) (* c z))
       (* a (/ t (* c -0.25)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.1e+230) {
		tmp = (t * -4.0) / (c / a);
	} else if (z <= -1.08e-120) {
		tmp = fma(((t * a) * -4.0), z, b) / (c * z);
	} else if (z <= 1.3e+111) {
		tmp = fma((x * 9.0), y, b) / (c * z);
	} else {
		tmp = a * (t / (c * -0.25));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.1e+230)
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	elseif (z <= -1.08e-120)
		tmp = Float64(fma(Float64(Float64(t * a) * -4.0), z, b) / Float64(c * z));
	elseif (z <= 1.3e+111)
		tmp = Float64(fma(Float64(x * 9.0), y, b) / Float64(c * z));
	else
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.1e+230], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-120], N[(N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+111], N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.09999999999999981e230

   1. Initial program 35.5%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 41.2%

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

   5. Taylor expanded in t 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. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 76.7

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

   7. Simplified 76.7%

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 76.8

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

   9. Applied egg-rr 76.8%

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

   if -3.09999999999999981e230 < z < -1.0800000000000001e-120

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 73.4

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

   5. Simplified 73.4%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 77.7

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

   7. Applied egg-rr 77.7%

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

   if -1.0800000000000001e-120 < z < 1.2999999999999999e111

   1. Initial program 92.4%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

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

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 88.8

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

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 81.4%

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

   if 1.2999999999999999e111 < z

   1. Initial program 44.2%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 61.0

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

   7. Simplified 61.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 58.7

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+230}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-120}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(t \cdot z\right), b\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+113}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ t (* c -0.25)))))
   (if (<= z -2.9e+87)
     t_1
     (if (<= z -8.4e-119)
       (/ (fma a (* -4.0 (* t z)) b) (* c z))
       (if (<= z 2.7e+113) (/ (fma (* x 9.0) y b) (* c z)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (t / (c * -0.25));
	double tmp;
	if (z <= -2.9e+87) {
		tmp = t_1;
	} else if (z <= -8.4e-119) {
		tmp = fma(a, (-4.0 * (t * z)), b) / (c * z);
	} else if (z <= 2.7e+113) {
		tmp = fma((x * 9.0), y, b) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(t / Float64(c * -0.25)))
	tmp = 0.0
	if (z <= -2.9e+87)
		tmp = t_1;
	elseif (z <= -8.4e-119)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(t * z)), b) / Float64(c * z));
	elseif (z <= 2.7e+113)
		tmp = Float64(fma(Float64(x * 9.0), y, b) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+87], t$95$1, If[LessEqual[z, -8.4e-119], N[(N[(a * N[(-4.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+113], N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e87 or 2.70000000000000011e113 < z

   1. Initial program 51.2%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 73.5%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 65.1

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

   7. Simplified 65.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 65.2

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 65.2%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]

   if -2.8999999999999998e87 < z < -8.4e-119

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 84.3

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

   5. Simplified 84.3%

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

   if -8.4e-119 < z < 2.70000000000000011e113

   1. Initial program 92.4%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

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

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 88.8

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

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 81.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(t \cdot z\right), b\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+113}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -4.0 (* t a) (/ b z)) c)))
   (if (<= z -2.7e-118)
     t_1
     (if (<= z 2.7e+74) (/ (/ (fma x (* 9.0 y) b) c) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (t * a), (b / z)) / c;
	double tmp;
	if (z <= -2.7e-118) {
		tmp = t_1;
	} else if (z <= 2.7e+74) {
		tmp = (fma(x, (9.0 * y), b) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(t * a), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.7e-118)
		tmp = t_1;
	elseif (z <= 2.7e+74)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), b) / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.7e-118], t$95$1, If[LessEqual[z, 2.7e+74], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999994e-118 or 2.6999999999999998e74 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in 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. accelerator-lowering-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. *-lowering-*.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. /-lowering-/.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. Simplified 82.9%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 76.5

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

   8. Simplified 76.5%

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

   9. Taylor expanded in c around 0

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

       1. /-lowering-/.f64 N/A

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

       2. accelerator-lowering-fma.f64 N/A

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

       3. *-lowering-*.f64 N/A

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

       4. /-lowering-/.f64 83.0

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

   11. Simplified 83.0%

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

   if -2.69999999999999994e-118 < z < 2.6999999999999998e74

   1. Initial program 92.8%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 91.2%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 83.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ t (* c -0.25)))))
   (if (<= z -1.35e+25)
     t_1
     (if (<= z -8e-203)
       (/ (/ b c) z)
       (if (<= z 2.9e+68) (* x (* 9.0 (/ y (* c z)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (t / (c * -0.25));
	double tmp;
	if (z <= -1.35e+25) {
		tmp = t_1;
	} else if (z <= -8e-203) {
		tmp = (b / c) / z;
	} else if (z <= 2.9e+68) {
		tmp = x * (9.0 * (y / (c * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t / (c * (-0.25d0)))
    if (z <= (-1.35d+25)) then
        tmp = t_1
    else if (z <= (-8d-203)) then
        tmp = (b / c) / z
    else if (z <= 2.9d+68) then
        tmp = x * (9.0d0 * (y / (c * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (t / (c * -0.25));
	double tmp;
	if (z <= -1.35e+25) {
		tmp = t_1;
	} else if (z <= -8e-203) {
		tmp = (b / c) / z;
	} else if (z <= 2.9e+68) {
		tmp = x * (9.0 * (y / (c * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * (t / (c * -0.25))
	tmp = 0
	if z <= -1.35e+25:
		tmp = t_1
	elif z <= -8e-203:
		tmp = (b / c) / z
	elif z <= 2.9e+68:
		tmp = x * (9.0 * (y / (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(a * Float64(t / Float64(c * -0.25)))
	tmp = 0.0
	if (z <= -1.35e+25)
		tmp = t_1;
	elseif (z <= -8e-203)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 2.9e+68)
		tmp = Float64(x * Float64(9.0 * Float64(y / Float64(c * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (t / (c * -0.25));
	tmp = 0.0;
	if (z <= -1.35e+25)
		tmp = t_1;
	elseif (z <= -8e-203)
		tmp = (b / c) / z;
	elseif (z <= 2.9e+68)
		tmp = x * (9.0 * (y / (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[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+25], t$95$1, If[LessEqual[z, -8e-203], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.9e+68], N[(x * N[(9.0 * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e25 or 2.90000000000000011e68 < z

   1. Initial program 58.0%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 77.3%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 63.5

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

   7. Simplified 63.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 62.9

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 62.9%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]

   if -1.35e25 < z < -8.0000000000000003e-203

   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. Taylor expanded in b around inf

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

   5. Simplified 67.6%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 70.4

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

   7. Applied egg-rr 70.4%

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

   if -8.0000000000000003e-203 < z < 2.90000000000000011e68

   1. Initial program 92.6%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 90.7%

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

      1. associate-*r* N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 97.0

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 53.8

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

   9. Simplified 53.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ t (* c -0.25)))))
   (if (<= z -1.08e-7)
     t_1
     (if (<= z 1.6e+102) (/ (fma (* x 9.0) y b) (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (t / (c * -0.25));
	double tmp;
	if (z <= -1.08e-7) {
		tmp = t_1;
	} else if (z <= 1.6e+102) {
		tmp = fma((x * 9.0), y, b) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(t / Float64(c * -0.25)))
	tmp = 0.0
	if (z <= -1.08e-7)
		tmp = t_1;
	elseif (z <= 1.6e+102)
		tmp = Float64(fma(Float64(x * 9.0), y, b) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-7], t$95$1, If[LessEqual[z, 1.6e+102], N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08000000000000001e-7 or 1.6e102 < z

   1. Initial program 57.4%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 76.5%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 64.0

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

   7. Simplified 64.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 64.1

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 64.1%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]

   if -1.08000000000000001e-7 < z < 1.6e102

   1. Initial program 93.2%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

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

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 90.0

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 81.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ t (* c -0.25)))))
   (if (<= z -1.08e-7)
     t_1
     (if (<= z 2.9e+109) (/ (fma 9.0 (* x y) b) (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (t / (c * -0.25));
	double tmp;
	if (z <= -1.08e-7) {
		tmp = t_1;
	} else if (z <= 2.9e+109) {
		tmp = fma(9.0, (x * y), b) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(t / Float64(c * -0.25)))
	tmp = 0.0
	if (z <= -1.08e-7)
		tmp = t_1;
	elseif (z <= 2.9e+109)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-7], t$95$1, If[LessEqual[z, 2.9e+109], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08000000000000001e-7 or 2.9e109 < z

   1. Initial program 57.4%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 76.5%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 64.0

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

   7. Simplified 64.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 64.1

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 64.1%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]

   if -1.08000000000000001e-7 < z < 2.9e109

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 81.3

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

   5. Simplified 81.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1000000:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+56}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \end{array} \]

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 -1000000.0)
   (* a (/ t (* c -0.25)))
   (if (<= t 2.45e+56) (/ (/ b c) z) (* t (/ (* a -4.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1000000.0) {
		tmp = a * (t / (c * -0.25));
	} else if (t <= 2.45e+56) {
		tmp = (b / c) / z;
	} else {
		tmp = t * ((a * -4.0) / 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 <= (-1000000.0d0)) then
        tmp = a * (t / (c * (-0.25d0)))
    else if (t <= 2.45d+56) then
        tmp = (b / c) / z
    else
        tmp = t * ((a * (-4.0d0)) / 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 <= -1000000.0) {
		tmp = a * (t / (c * -0.25));
	} else if (t <= 2.45e+56) {
		tmp = (b / c) / z;
	} else {
		tmp = t * ((a * -4.0) / 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 <= -1000000.0:
		tmp = a * (t / (c * -0.25))
	elif t <= 2.45e+56:
		tmp = (b / c) / z
	else:
		tmp = t * ((a * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1000000.0)
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	elseif (t <= 2.45e+56)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) / 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 <= -1000000.0)
		tmp = a * (t / (c * -0.25));
	elseif (t <= 2.45e+56)
		tmp = (b / c) / z;
	else
		tmp = t * ((a * -4.0) / 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, -1000000.0], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e+56], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e6

   1. Initial program 70.3%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 65.6

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

   7. Simplified 65.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 65.9

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]

   if -1e6 < t < 2.4500000000000001e56

   1. Initial program 83.7%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 38.0%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 40.8

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

   7. Applied egg-rr 40.8%

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

   if 2.4500000000000001e56 < t

   1. Initial program 71.0%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 67.4%

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

   5. Taylor expanded in t 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. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 54.0

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

   7. Simplified 54.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1000000:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+56}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \end{array} \]

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 -3.9e+21)
   (* a (/ t (* c -0.25)))
   (if (<= t 6.4e+41) (/ b (* c z)) (* t (/ (* a -4.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.9e+21) {
		tmp = a * (t / (c * -0.25));
	} else if (t <= 6.4e+41) {
		tmp = b / (c * z);
	} else {
		tmp = t * ((a * -4.0) / 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 <= (-3.9d+21)) then
        tmp = a * (t / (c * (-0.25d0)))
    else if (t <= 6.4d+41) then
        tmp = b / (c * z)
    else
        tmp = t * ((a * (-4.0d0)) / 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 <= -3.9e+21) {
		tmp = a * (t / (c * -0.25));
	} else if (t <= 6.4e+41) {
		tmp = b / (c * z);
	} else {
		tmp = t * ((a * -4.0) / 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 <= -3.9e+21:
		tmp = a * (t / (c * -0.25))
	elif t <= 6.4e+41:
		tmp = b / (c * z)
	else:
		tmp = t * ((a * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.9e+21)
		tmp = Float64(a * Float64(t / Float64(c * -0.25)));
	elseif (t <= 6.4e+41)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) / 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 <= -3.9e+21)
		tmp = a * (t / (c * -0.25));
	elseif (t <= 6.4e+41)
		tmp = b / (c * z);
	else
		tmp = t * ((a * -4.0) / 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, -3.9e+21], N[(a * N[(t / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e+41], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9e21

   1. Initial program 69.1%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 70.3

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

   7. Simplified 70.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. div-inv N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. /-lowering-/.f64 N/A

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

      10. div-inv N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \frac{t}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot a \]

      12. metadata-eval 70.6

          \[\leadsto \frac{t}{c \cdot \color{blue}{-0.25}} \cdot a \]

   9. Applied egg-rr 70.6%

      \[\leadsto \color{blue}{\frac{t}{c \cdot -0.25} \cdot a} \]

   if -3.9e21 < t < 6.40000000000000019e41

   1. Initial program 83.8%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 39.1%

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

   if 6.40000000000000019e41 < t

   1. Initial program 71.3%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 69.2%

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

   5. Taylor expanded in t 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. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 55.2

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

   7. Simplified 55.2%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \frac{t}{c \cdot -0.25}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ (* a -4.0) c))))
   (if (<= t -9.6e-74) t_1 (if (<= t 4.6e+41) (/ 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 (t <= -9.6e-74) {
		tmp = t_1;
	} else if (t <= 4.6e+41) {
		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 (t <= (-9.6d-74)) then
        tmp = t_1
    else if (t <= 4.6d+41) 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 (t <= -9.6e-74) {
		tmp = t_1;
	} else if (t <= 4.6e+41) {
		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 t <= -9.6e-74:
		tmp = t_1
	elif t <= 4.6e+41:
		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 (t <= -9.6e-74)
		tmp = t_1;
	elseif (t <= 4.6e+41)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (t <= -9.6e-74)
		tmp = t_1;
	elseif (t <= 4.6e+41)
		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[t, -9.6e-74], t$95$1, If[LessEqual[t, 4.6e+41], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5999999999999996e-74 or 4.5999999999999997e41 < t

   1. Initial program 73.5%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.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 egg-rr 77.1%

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

   5. Taylor expanded in t 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. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 54.7

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

   7. Simplified 54.7%

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

   if -9.5999999999999996e-74 < t < 4.5999999999999997e41

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 39.1%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.5% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.6%

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

3. Taylor expanded in b around inf

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

5. Simplified 34.9%

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

6. Final simplification 34.9%

   \[\leadsto \frac{b}{c \cdot z} \]
7. Add Preprocessing

Developer Target 1: 80.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024195 
(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)))