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

Percentage Accurate: 79.6% → 94.1%

Time: 17.7s

Alternatives: 15

Speedup: 0.9×

• 37.2% 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: 79.6% 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: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, t \cdot \left(a \cdot 4\right) - \frac{b}{z}\right)}{0 - c}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/ (fma x (/ (* y -9.0) z) (- (* t (* a 4.0)) (/ b z))) (- 0.0 c))))
   (if (<= z -1.6e+23)
     t_1
     (if (<= z 4e-35)
       (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, ((y * -9.0) / z), ((t * (a * 4.0)) - (b / z))) / (0.0 - c);
	double tmp;
	if (z <= -1.6e+23) {
		tmp = t_1;
	} else if (z <= 4e-35) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(Float64(y * -9.0) / z), Float64(Float64(t * Float64(a * 4.0)) - Float64(b / z))) / Float64(0.0 - c))
	tmp = 0.0
	if (z <= -1.6e+23)
		tmp = t_1;
	elseif (z <= 4e-35)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision] - N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.0 - c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+23], t$95$1, If[LessEqual[z, 4e-35], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e23 or 4.00000000000000003e-35 < z

   1. Initial program 64.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 84.4%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right) \]

   8. Simplified 95.6%

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

   if -1.6e23 < z < 4.00000000000000003e-35

   1. Initial program 94.7%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(a \cdot t\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \left(9 \cdot y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      15. *-lowering-*.f64 94.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \mathsf{*.f64}\left(9, y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 94.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, t \cdot \left(a \cdot 4\right) - \frac{b}{z}\right)}{0 - c}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, t \cdot \left(a \cdot 4\right) - \frac{b}{z}\right)}{0 - c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, 4 \cdot \left(t \cdot a\right)\right)}{0 - c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-71}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.5e+116)
   (/ (fma x (/ (* y -9.0) z) (* 4.0 (* t a))) (- 0.0 c))
   (if (<= z 3.4e-71)
     (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
     (/ (fma 9.0 (/ (* x y) z) (fma -4.0 (* t a) (/ 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 <= -4.5e+116) {
		tmp = fma(x, ((y * -9.0) / z), (4.0 * (t * a))) / (0.0 - c);
	} else if (z <= 3.4e-71) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else {
		tmp = fma(9.0, ((x * y) / z), fma(-4.0, (t * a), (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 <= -4.5e+116)
		tmp = Float64(fma(x, Float64(Float64(y * -9.0) / z), Float64(4.0 * Float64(t * a))) / Float64(0.0 - c));
	elseif (z <= 3.4e-71)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	else
		tmp = Float64(fma(9.0, Float64(Float64(x * y) / z), fma(-4.0, Float64(t * a), Float64(b / z))) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -4.5e+116], N[(N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.0 - c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-71], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000016e116

   1. Initial program 52.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 82.5%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right) \]

   8. Simplified 99.8%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \color{blue}{\left(4 \cdot \left(a \cdot t\right)\right)}\right), \mathsf{neg.f64}\left(c\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \left(a \cdot t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

       2. *-lowering-*.f64 79.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \mathsf{*.f64}\left(a, t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

   11. Simplified 79.6%

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

   if -4.50000000000000016e116 < z < 3.40000000000000003e-71

   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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(a \cdot t\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \left(9 \cdot y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      15. *-lowering-*.f64 94.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \mathsf{*.f64}\left(9, y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 94.4%

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

   if 3.40000000000000003e-71 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in 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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 87.9%

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

   6. Taylor expanded in c around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right), \color{blue}{c}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(a \cdot t\right)\right), c\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \frac{x \cdot y}{z} + \left(\frac{b}{z} + -4 \cdot \left(a \cdot t\right)\right)\right), c\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \frac{x \cdot y}{z} + \left(-4 \cdot \left(a \cdot t\right) + \frac{b}{z}\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \left(\frac{x \cdot y}{z}\right), \left(-4 \cdot \left(a \cdot t\right) + \frac{b}{z}\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{/.f64}\left(\left(x \cdot y\right), z\right), \left(-4 \cdot \left(a \cdot t\right) + \frac{b}{z}\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), \left(-4 \cdot \left(a \cdot t\right) + \frac{b}{z}\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), \mathsf{fma.f64}\left(-4, \left(a \cdot t\right), \left(\frac{b}{z}\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), \mathsf{fma.f64}\left(-4, \mathsf{*.f64}\left(a, t\right), \left(\frac{b}{z}\right)\right)\right), c\right) \]

      10. /-lowering-/.f64 91.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), \mathsf{fma.f64}\left(-4, \mathsf{*.f64}\left(a, t\right), \mathsf{/.f64}\left(b, z\right)\right)\right), c\right) \]

   8. Simplified 91.6%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, 4 \cdot \left(t \cdot a\right)\right)}{0 - c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-71}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \mathsf{fma}\left(-4, t \cdot a, \frac{b}{z}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{if}\;x \cdot 9 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 9 \leq 2 \cdot 10^{-97}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (fma x (/ y (* z 0.1111111111111111)) (* -4.0 (* t a))) c)))
   (if (<= (* x 9.0) -2e+16)
     t_1
     (if (<= (* x 9.0) 2e-97) (fma a (* t (/ -4.0 c)) (/ b (* z c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (y / (z * 0.1111111111111111)), (-4.0 * (t * a))) / c;
	double tmp;
	if ((x * 9.0) <= -2e+16) {
		tmp = t_1;
	} else if ((x * 9.0) <= 2e-97) {
		tmp = fma(a, (t * (-4.0 / c)), (b / (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(y / Float64(z * 0.1111111111111111)), Float64(-4.0 * Float64(t * a))) / c)
	tmp = 0.0
	if (Float64(x * 9.0) <= -2e+16)
		tmp = t_1;
	elseif (Float64(x * 9.0) <= 2e-97)
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), Float64(b / Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(y / N[(z * 0.1111111111111111), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[N[(x * 9.0), $MachinePrecision], -2e+16], t$95$1, If[LessEqual[N[(x * 9.0), $MachinePrecision], 2e-97], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 9 binary64)) < -2e16 or 2.00000000000000007e-97 < (*.f64 x #s(literal 9 binary64))

   1. Initial program 74.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 78.5%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right) \]

   8. Simplified 83.6%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \color{blue}{\left(4 \cdot \left(a \cdot t\right)\right)}\right), \mathsf{neg.f64}\left(c\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \left(a \cdot t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

       2. *-lowering-*.f64 75.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \mathsf{*.f64}\left(a, t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

   11. Simplified 75.0%

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

       1. distribute-frac-neg2 N/A

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

       2. distribute-frac-neg N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x \cdot \frac{y \cdot -9}{z} + 4 \cdot \left(a \cdot t\right)\right)\right)\right), \color{blue}{c}\right) \]

   13. Applied egg-rr 75.0%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, \left(a \cdot t\right) \cdot -4\right)}{c}} \]

   if -2e16 < (*.f64 x #s(literal 9 binary64)) < 2.00000000000000007e-97

   1. Initial program 84.4%

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 89.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \color{blue}{\left(\frac{b}{c \cdot z}\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \mathsf{/.f64}\left(b, \left(c \cdot z\right)\right)\right) \]

      2. *-lowering-*.f64 87.2%

         \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right)\right) \]

   8. Simplified 87.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 9 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{elif}\;x \cdot 9 \leq 2 \cdot 10^{-97}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, 4 \cdot \left(t \cdot a\right)\right)}{0 - c}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma x (/ (* y -9.0) z) (* 4.0 (* t a))) (- 0.0 c))))
   (if (<= z -2.1e+121)
     t_1
     (if (<= z 1.15e+111)
       (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, ((y * -9.0) / z), (4.0 * (t * a))) / (0.0 - c);
	double tmp;
	if (z <= -2.1e+121) {
		tmp = t_1;
	} else if (z <= 1.15e+111) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(Float64(y * -9.0) / z), Float64(4.0 * Float64(t * a))) / Float64(0.0 - c))
	tmp = 0.0
	if (z <= -2.1e+121)
		tmp = t_1;
	elseif (z <= 1.15e+111)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.0 - c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+121], t$95$1, If[LessEqual[z, 1.15e+111], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000002e121 or 1.15000000000000001e111 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 85.0%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right) \]

   8. Simplified 97.7%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \color{blue}{\left(4 \cdot \left(a \cdot t\right)\right)}\right), \mathsf{neg.f64}\left(c\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \left(a \cdot t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

       2. *-lowering-*.f64 81.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \mathsf{*.f64}\left(a, t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

   11. Simplified 81.7%

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

   if -2.1000000000000002e121 < z < 1.15000000000000001e111

   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. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(a \cdot t\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \left(9 \cdot y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      15. *-lowering-*.f64 93.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \mathsf{*.f64}\left(9, y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 93.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, 4 \cdot \left(t \cdot a\right)\right)}{0 - c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, 4 \cdot \left(t \cdot a\right)\right)}{0 - c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, b\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+204}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* a (* z -4.0)) t b) (* z c)))
        (t_2 (/ (* -4.0 (* t a)) c)))
   (if (<= z -3.5e+204)
     t_2
     (if (<= z -3.5e-133)
       t_1
       (if (<= z 1.85e-50)
         (/ (fma 9.0 (* x y) b) (* z c))
         (if (<= z 1.42e+112) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((a * (z * -4.0)), t, b) / (z * c);
	double t_2 = (-4.0 * (t * a)) / c;
	double tmp;
	if (z <= -3.5e+204) {
		tmp = t_2;
	} else if (z <= -3.5e-133) {
		tmp = t_1;
	} else if (z <= 1.85e-50) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else if (z <= 1.42e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(a * Float64(z * -4.0)), t, b) / Float64(z * c))
	t_2 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	tmp = 0.0
	if (z <= -3.5e+204)
		tmp = t_2;
	elseif (z <= -3.5e-133)
		tmp = t_1;
	elseif (z <= 1.85e-50)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	elseif (z <= 1.42e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.5e+204], t$95$2, If[LessEqual[z, -3.5e-133], t$95$1, If[LessEqual[z, 1.85e-50], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999989e204 or 1.4200000000000001e112 < z

   1. Initial program 50.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 68.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 68.9%

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

   if -3.49999999999999989e204 < z < -3.50000000000000003e-133 or 1.85e-50 < z < 1.4200000000000001e112

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4 + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      10. *-lowering-*.f64 67.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 67.6%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot \left(z \cdot -4\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot \left(z \cdot -4\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot \left(z \cdot -4\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot \left(z \cdot -4\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(z \cdot -4\right)\right) \cdot t + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\left(a \cdot \left(z \cdot -4\right)\right), t, b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(a, \left(z \cdot -4\right)\right), t, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      8. *-lowering-*.f64 67.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, -4\right)\right), t, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   7. Applied egg-rr 67.0%

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

   if -3.50000000000000003e-133 < z < 1.85e-50

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \left(x \cdot y\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-lowering-*.f64 86.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{*.f64}\left(x, y\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 86.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+204}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma a (* -4.0 (* z t)) b) (* z c)))
        (t_2 (/ (* -4.0 (* t a)) c)))
   (if (<= z -5.5e+206)
     t_2
     (if (<= z -1.6e-132)
       t_1
       (if (<= z 1.3e-52)
         (/ (fma 9.0 (* x y) b) (* z c))
         (if (<= z 3.35e+155) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(a, (-4.0 * (z * t)), b) / (z * c);
	double t_2 = (-4.0 * (t * a)) / c;
	double tmp;
	if (z <= -5.5e+206) {
		tmp = t_2;
	} else if (z <= -1.6e-132) {
		tmp = t_1;
	} else if (z <= 1.3e-52) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else if (z <= 3.35e+155) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c))
	t_2 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	tmp = 0.0
	if (z <= -5.5e+206)
		tmp = t_2;
	elseif (z <= -1.6e-132)
		tmp = t_1;
	elseif (z <= 1.3e-52)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	elseif (z <= 3.35e+155)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -5.5e+206], t$95$2, If[LessEqual[z, -1.6e-132], t$95$1, If[LessEqual[z, 1.3e-52], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e+155], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000021e206 or 3.35e155 < z

   1. Initial program 45.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 70.7%

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

   if -5.50000000000000021e206 < z < -1.6000000000000001e-132 or 1.2999999999999999e-52 < z < 3.35e155

   1. Initial program 82.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4 + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      10. *-lowering-*.f64 67.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 67.4%

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

   if -1.6000000000000001e-132 < z < 1.2999999999999999e-52

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \left(x \cdot y\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-lowering-*.f64 86.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{*.f64}\left(x, y\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 86.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+206}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+155}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma x (/ y (* z 0.1111111111111111)) (* -4.0 (* t a))) c)))
   (if (<= z -1.02e+120)
     t_1
     (if (<= z 6.8e+109)
       (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (y / (z * 0.1111111111111111)), (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -1.02e+120) {
		tmp = t_1;
	} else if (z <= 6.8e+109) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(y / Float64(z * 0.1111111111111111)), Float64(-4.0 * Float64(t * a))) / c)
	tmp = 0.0
	if (z <= -1.02e+120)
		tmp = t_1;
	elseif (z <= 6.8e+109)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(y / N[(z * 0.1111111111111111), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.02e+120], t$95$1, If[LessEqual[z, 6.8e+109], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01999999999999997e120 or 6.80000000000000013e109 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 85.0%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right) \]

   8. Simplified 97.7%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \color{blue}{\left(4 \cdot \left(a \cdot t\right)\right)}\right), \mathsf{neg.f64}\left(c\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \left(a \cdot t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

       2. *-lowering-*.f64 81.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -9\right), z\right), \mathsf{*.f64}\left(4, \mathsf{*.f64}\left(a, t\right)\right)\right), \mathsf{neg.f64}\left(c\right)\right) \]

   11. Simplified 81.7%

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

       1. distribute-frac-neg2 N/A

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

       2. distribute-frac-neg N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x \cdot \frac{y \cdot -9}{z} + 4 \cdot \left(a \cdot t\right)\right)\right)\right), \color{blue}{c}\right) \]

   13. Applied egg-rr 81.6%

       \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, \left(a \cdot t\right) \cdot -4\right)}{c}} \]

   if -1.01999999999999997e120 < z < 6.80000000000000013e109

   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. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right)\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(x \cdot 9\right) \cdot y\right) + b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(a \cdot t\right) + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right) \cdot t + \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(4\right)\right)\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \left(9 \cdot y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      15. *-lowering-*.f64 93.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -4\right), a\right), t, \mathsf{fma.f64}\left(x, \mathsf{*.f64}\left(9, y\right), b\right)\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 93.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+120}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{z \cdot 0.1111111111111111}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{t \cdot a}{c}, t\_1\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, t\_1\right)\\ \end{array} \end{array} \]

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 (/ b (* z c))))
   (if (<= z -1.6e-132)
     (fma -4.0 (/ (* t a) c) t_1)
     (if (<= z 1.5e-34)
       (/ (fma 9.0 (* x y) b) (* z c))
       (fma a (* t (/ -4.0 c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (z <= -1.6e-132) {
		tmp = fma(-4.0, ((t * a) / c), t_1);
	} else if (z <= 1.5e-34) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = fma(a, (t * (-4.0 / c)), 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(b / Float64(z * c))
	tmp = 0.0
	if (z <= -1.6e-132)
		tmp = fma(-4.0, Float64(Float64(t * a) / c), t_1);
	elseif (z <= 1.5e-34)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), 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[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-132], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 1.5e-34], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e-132

   1. Initial program 72.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 84.1%

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

   6. Taylor expanded in x around 0

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

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \color{blue}{\left(\frac{a \cdot t}{c}\right)}, \left(\frac{b}{c \cdot z}\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\left(a \cdot t\right), \color{blue}{c}\right), \left(\frac{b}{c \cdot z}\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), \left(\frac{b}{c \cdot z}\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), \mathsf{/.f64}\left(b, \left(c \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 67.0%

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right)\right) \]

   8. Simplified 67.0%

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

   if -1.6000000000000001e-132 < z < 1.5e-34

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \left(x \cdot y\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{*.f64}\left(x, y\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 84.4%

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

   if 1.5e-34 < z

   1. Initial program 65.0%

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 87.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \color{blue}{\left(\frac{b}{c \cdot z}\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \mathsf{/.f64}\left(b, \left(c \cdot z\right)\right)\right) \]

      2. *-lowering-*.f64 76.3%

         \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right)\right) \]

   8. Simplified 76.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{t \cdot a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \frac{b}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, \frac{t \cdot a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma -4.0 (/ (* t a) c) (/ b (* z c)))))
   (if (<= z -1.6e-132)
     t_1
     (if (<= z 1.25e-49) (/ (fma 9.0 (* x y) b) (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, ((t * a) / c), (b / (z * c)));
	double tmp;
	if (z <= -1.6e-132) {
		tmp = t_1;
	} else if (z <= 1.25e-49) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(-4.0, Float64(Float64(t * a) / c), Float64(b / Float64(z * c)))
	tmp = 0.0
	if (z <= -1.6e-132)
		tmp = t_1;
	elseif (z <= 1.25e-49)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-132], t$95$1, If[LessEqual[z, 1.25e-49], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-132 or 1.25e-49 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 86.1%

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

   6. Taylor expanded in x around 0

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

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \color{blue}{\left(\frac{a \cdot t}{c}\right)}, \left(\frac{b}{c \cdot z}\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\left(a \cdot t\right), \color{blue}{c}\right), \left(\frac{b}{c \cdot z}\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), \left(\frac{b}{c \cdot z}\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), \mathsf{/.f64}\left(b, \left(c \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{fma.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right)\right) \]

   8. Simplified 71.2%

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

   if -1.6000000000000001e-132 < z < 1.25e-49

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \left(x \cdot y\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-lowering-*.f64 86.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{*.f64}\left(x, y\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 86.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{t \cdot a}{c}, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{t \cdot a}{c}, \frac{b}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{\mathsf{fma}\left(z, c, 0\right)}\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -2.1e+130)
     t_1
     (if (<= b -6.6e-87)
       (* y (* 9.0 (/ x (fma z c 0.0))))
       (if (<= b 1.9e+152) (/ (* -4.0 (* t a)) c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.1e+130) {
		tmp = t_1;
	} else if (b <= -6.6e-87) {
		tmp = y * (9.0 * (x / fma(z, c, 0.0)));
	} else if (b <= 1.9e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -2.1e+130)
		tmp = t_1;
	elseif (b <= -6.6e-87)
		tmp = Float64(y * Float64(9.0 * Float64(x / fma(z, c, 0.0))));
	elseif (b <= 1.9e+152)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) / c);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.1e+130], t$95$1, If[LessEqual[b, -6.6e-87], N[(y * N[(9.0 * N[(x / N[(z * c + 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+152], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.0999999999999999e130 or 1.9e152 < b

   1. Initial program 82.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{b}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 61.6%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 68.5%

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

   if -2.0999999999999999e130 < b < -6.6000000000000001e-87

   1. Initial program 85.3%

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 78.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), \color{blue}{\left(c \cdot z\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(y \cdot x\right)\right), \left(c \cdot z\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(9 \cdot y\right) \cdot x\right), \left(\color{blue}{c} \cdot z\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(9 \cdot y\right), x\right), \left(\color{blue}{c} \cdot z\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(9, y\right), x\right), \left(c \cdot z\right)\right) \]

      7. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(9, y\right), x\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right) \]

   8. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x}{c \cdot z}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, \left(\frac{x}{z \cdot \color{blue}{c}}\right)\right)\right) \]

      7. +-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, \left(\frac{x}{z \cdot c + \color{blue}{0}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(x, \color{blue}{\left(z \cdot c + 0\right)}\right)\right)\right) \]

      9. accelerator-lowering-fma.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(x, \mathsf{fma.f64}\left(z, \color{blue}{c}, 0\right)\right)\right)\right) \]

   10. Applied egg-rr 51.6%

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

   if -6.6000000000000001e-87 < b < 1.9e152

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 51.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 51.7%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{\mathsf{fma}\left(z, c, 0\right)}\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot \left(c \cdot 0.1111111111111111\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -2.5e+130)
     t_1
     (if (<= b -1.75e-91)
       (* y (/ x (* z (* c 0.1111111111111111))))
       (if (<= b 5.5e+151) (/ (* -4.0 (* t a)) c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.5e+130) {
		tmp = t_1;
	} else if (b <= -1.75e-91) {
		tmp = y * (x / (z * (c * 0.1111111111111111)));
	} else if (b <= 5.5e+151) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-2.5d+130)) then
        tmp = t_1
    else if (b <= (-1.75d-91)) then
        tmp = y * (x / (z * (c * 0.1111111111111111d0)))
    else if (b <= 5.5d+151) then
        tmp = ((-4.0d0) * (t * a)) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.5e+130) {
		tmp = t_1;
	} else if (b <= -1.75e-91) {
		tmp = y * (x / (z * (c * 0.1111111111111111)));
	} else if (b <= 5.5e+151) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -2.5e+130:
		tmp = t_1
	elif b <= -1.75e-91:
		tmp = y * (x / (z * (c * 0.1111111111111111)))
	elif b <= 5.5e+151:
		tmp = (-4.0 * (t * a)) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -2.5e+130)
		tmp = t_1;
	elseif (b <= -1.75e-91)
		tmp = Float64(y * Float64(x / Float64(z * Float64(c * 0.1111111111111111))));
	elseif (b <= 5.5e+151)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -2.5e+130)
		tmp = t_1;
	elseif (b <= -1.75e-91)
		tmp = y * (x / (z * (c * 0.1111111111111111)));
	elseif (b <= 5.5e+151)
		tmp = (-4.0 * (t * a)) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.5e+130], t$95$1, If[LessEqual[b, -1.75e-91], N[(y * N[(x / N[(z * N[(c * 0.1111111111111111), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+151], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4999999999999998e130 or 5.4999999999999994e151 < b

   1. Initial program 82.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{b}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 61.6%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 68.5%

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

   if -2.4999999999999998e130 < b < -1.7499999999999999e-91

   1. Initial program 85.3%

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}, \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t}{c} \cdot \color{blue}{-4}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(\frac{t \cdot -4}{\color{blue}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \left(t \cdot \color{blue}{\frac{-4}{c}}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c}\right)}\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 + \frac{b}{c \cdot z}\right)\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) + \frac{b}{c \cdot z}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(-4, c\right)\right), \left(x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)\right) \]

   5. Simplified 78.3%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-9 \cdot \frac{x \cdot y}{z} + \left(-1 \cdot \frac{b}{z} + 4 \cdot \left(a \cdot t\right)\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right) \]

   8. Simplified 93.8%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)}\right) \]

       6. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{9 \cdot y}{\color{blue}{c \cdot z}}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y \cdot 9}{\color{blue}{c} \cdot z}\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\frac{9}{c \cdot z}}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{9}{c \cdot z}\right)}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(9, \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(9, \left(z \cdot \color{blue}{c}\right)\right)\right)\right) \]

       12. *-lowering-*.f64 48.6%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(9, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   11. Simplified 48.6%

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(\left(x \cdot \frac{9}{z \cdot c}\right), \color{blue}{y}\right) \]

       4. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x \cdot \frac{1}{\frac{z \cdot c}{9}}\right), y\right) \]

       5. un-div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{\frac{z \cdot c}{9}}\right), y\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{z \cdot c}{9}\right)\right), y\right) \]

       7. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(z \cdot \frac{c}{9}\right)\right), y\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\frac{c}{9}\right)\right)\right), y\right) \]

       9. div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(c \cdot \frac{1}{9}\right)\right)\right), y\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(c, \left(\frac{1}{9}\right)\right)\right)\right), y\right) \]

       11. metadata-eval 51.5%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(c, \frac{1}{9}\right)\right)\right), y\right) \]

   13. Applied egg-rr 51.5%

       \[\leadsto \color{blue}{\frac{x}{z \cdot \left(c \cdot 0.1111111111111111\right)} \cdot y} \]

   if -1.7499999999999999e-91 < b < 5.4999999999999994e151

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 51.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 51.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot \left(c \cdot 0.1111111111111111\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -1.48 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+104}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* -4.0 (* t a)) c)))
   (if (<= z -1.48e+23)
     t_1
     (if (<= z 1e+104) (/ (fma 9.0 (* x y) b) (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double tmp;
	if (z <= -1.48e+23) {
		tmp = t_1;
	} else if (z <= 1e+104) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	tmp = 0.0
	if (z <= -1.48e+23)
		tmp = t_1;
	elseif (z <= 1e+104)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.48e+23], t$95$1, If[LessEqual[z, 1e+104], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4799999999999999e23 or 1e104 < z

   1. Initial program 60.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 61.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 61.5%

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

   if -1.4799999999999999e23 < z < 1e104

   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. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right)}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \left(x \cdot y\right), b\right), \mathsf{*.f64}\left(\color{blue}{z}, c\right)\right) \]

      3. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{fma.f64}\left(9, \mathsf{*.f64}\left(x, y\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 73.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+23}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 10^{+104}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -2.4e+142) t_1 (if (<= b 1.9e+152) (/ (* -4.0 (* t a)) c) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.4e+142) {
		tmp = t_1;
	} else if (b <= 1.9e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-2.4d+142)) then
        tmp = t_1
    else if (b <= 1.9d+152) then
        tmp = ((-4.0d0) * (t * a)) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.4e+142) {
		tmp = t_1;
	} else if (b <= 1.9e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -2.4e+142:
		tmp = t_1
	elif b <= 1.9e+152:
		tmp = (-4.0 * (t * a)) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -2.4e+142)
		tmp = t_1;
	elseif (b <= 1.9e+152)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -2.4e+142)
		tmp = t_1;
	elseif (b <= 1.9e+152)
		tmp = (-4.0 * (t * a)) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.4e+142], t$95$1, If[LessEqual[b, 1.9e+152], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3999999999999999e142 or 1.9e152 < b

   1. Initial program 81.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{b}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 63.5%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 69.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 69.5%

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

   if -2.3999999999999999e142 < b < 1.9e152

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 49.0%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -6e+145) t_1 (if (<= b 7.5e+152) (/ (* -4.0 (* t a)) c) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -6e+145) {
		tmp = t_1;
	} else if (b <= 7.5e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b / (z * c)
    if (b <= (-6d+145)) then
        tmp = t_1
    else if (b <= 7.5d+152) then
        tmp = ((-4.0d0) * (t * a)) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -6e+145) {
		tmp = t_1;
	} else if (b <= 7.5e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -6e+145:
		tmp = t_1
	elif b <= 7.5e+152:
		tmp = (-4.0 * (t * a)) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -6e+145)
		tmp = t_1;
	elseif (b <= 7.5e+152)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -6e+145)
		tmp = t_1;
	elseif (b <= 7.5e+152)
		tmp = (-4.0 * (t * a)) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+145], t$95$1, If[LessEqual[b, 7.5e+152], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.0000000000000005e145 or 7.50000000000000046e152 < b

   1. Initial program 81.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{b}, \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 63.5%

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

   if -6.0000000000000005e145 < b < 7.50000000000000046e152

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), c\right) \]

      4. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), c\right) \]

   5. Simplified 49.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+145}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

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

Derivation

1. Initial program 78.2%

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

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{b}, \mathsf{*.f64}\left(z, c\right)\right) \]
4. Step-by-step derivation

5. Simplified 32.3%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
6. 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 2024193 
(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)))