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

Percentage Accurate: 79.9% → 93.8%

Time: 14.8s

Alternatives: 14

Speedup: 0.9×

• 38.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\frac{x}{z} \cdot y, 9, \frac{b}{z}\right)\right)}{c}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* -4.0 t) a (fma (* (/ x z) y) 9.0 (/ b z))) c)))
   (if (<= z -3.9e-113)
     t_1
     (if (<= z 3e-10)
       (/ (fma (* x 9.0) y (fma (* (* -4.0 z) a) t b)) (* c z))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((-4.0 * t), a, fma(((x / z) * y), 9.0, (b / z))) / c;
	double tmp;
	if (z <= -3.9e-113) {
		tmp = t_1;
	} else if (z <= 3e-10) {
		tmp = fma((x * 9.0), y, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(-4.0 * t), a, fma(Float64(Float64(x / z) * y), 9.0, Float64(b / z))) / c)
	tmp = 0.0
	if (z <= -3.9e-113)
		tmp = t_1;
	elseif (z <= 3e-10)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] * 9.0 + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.9e-113], t$95$1, If[LessEqual[z, 3e-10], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999999e-113 or 3e-10 < z

   1. Initial program 65.6%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 64.3%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.8

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

   7. Applied rewrites 87.8%

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

   9. Applied rewrites 91.0%

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

   11. Applied rewrites 91.7%

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

   if -3.8999999999999999e-113 < z < 3e-10

   1. Initial program 96.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 95.2%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-113}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\frac{x}{z} \cdot y, 9, \frac{b}{z}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-10}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\frac{x}{z} \cdot y, 9, \frac{b}{z}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

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 -6.5e+80)
   (/ (fma (* t a) -4.0 (* (/ (* x y) z) 9.0)) c)
   (if (<= z 2.35e+103)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* x y) 9.0 b)) c) z)
     (/ (fma (* t a) -4.0 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.5e+80) {
		tmp = fma((t * a), -4.0, (((x * y) / z) * 9.0)) / c;
	} else if (z <= 2.35e+103) {
		tmp = (fma(((-4.0 * z) * a), t, fma((x * y), 9.0, b)) / c) / z;
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.5e+80)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(Float64(Float64(x * y) / z) * 9.0)) / c);
	elseif (z <= 2.35e+103)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(x * y), 9.0, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(t * a), -4.0, 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, -6.5e+80], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.35e+103], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999998e80

   1. Initial program 54.3%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 83.8

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

   7. Applied rewrites 83.8%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 76.8%

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

   if -6.4999999999999998e80 < z < 2.35000000000000016e103

   1. Initial program 92.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 93.1%

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

   if 2.35000000000000016e103 < z

   1. Initial program 51.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 51.0%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.4

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

   7. Applied rewrites 87.4%

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

   8. Taylor expanded in b around inf

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

   10. Applied rewrites 81.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{c}, \frac{y}{c \cdot z} \cdot \left(x \cdot 9\right)\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{c \cdot z} \cdot \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.6e+104)
   (fma (* -4.0 a) (/ t c) (* (/ y (* c z)) (* x 9.0)))
   (if (<= z 2.35e+103)
     (* (/ 1.0 (* c z)) (fma (* (* -4.0 z) a) t (fma (* x y) 9.0 b)))
     (/ (fma (* t a) -4.0 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.6e+104) {
		tmp = fma((-4.0 * a), (t / c), ((y / (c * z)) * (x * 9.0)));
	} else if (z <= 2.35e+103) {
		tmp = (1.0 / (c * z)) * fma(((-4.0 * z) * a), t, fma((x * y), 9.0, b));
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.6e+104)
		tmp = fma(Float64(-4.0 * a), Float64(t / c), Float64(Float64(y / Float64(c * z)) * Float64(x * 9.0)));
	elseif (z <= 2.35e+103)
		tmp = Float64(Float64(1.0 / Float64(c * z)) * fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(x * y), 9.0, b)));
	else
		tmp = Float64(fma(Float64(t * a), -4.0, 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, -1.6e+104], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision] + N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+103], N[(N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e104

   1. Initial program 52.6%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 52.6%

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

   5. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. associate-/l* N/A

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

      13. associate-*r* N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 72.6

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

   7. Applied rewrites 72.6%

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

   if -1.6e104 < z < 2.35000000000000016e103

   1. Initial program 91.3%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

   4. Applied rewrites 90.6%

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

   if 2.35000000000000016e103 < z

   1. Initial program 51.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 51.0%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.4

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

   7. Applied rewrites 87.4%

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

   8. Taylor expanded in b around inf

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

   10. Applied rewrites 81.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{c}, \frac{y}{c \cdot z} \cdot \left(x \cdot 9\right)\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{c \cdot z} \cdot \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(x \cdot y, 9, b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{c}, \frac{y}{c \cdot z} \cdot \left(x \cdot 9\right)\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.6e+104)
   (fma (* -4.0 a) (/ t c) (* (/ y (* c z)) (* x 9.0)))
   (if (<= z 2.35e+103)
     (/ (fma (* x 9.0) y (fma (* (* -4.0 z) a) t b)) (* c z))
     (/ (fma (* t a) -4.0 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.6e+104) {
		tmp = fma((-4.0 * a), (t / c), ((y / (c * z)) * (x * 9.0)));
	} else if (z <= 2.35e+103) {
		tmp = fma((x * 9.0), y, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.6e+104)
		tmp = fma(Float64(-4.0 * a), Float64(t / c), Float64(Float64(y / Float64(c * z)) * Float64(x * 9.0)));
	elseif (z <= 2.35e+103)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = Float64(fma(Float64(t * a), -4.0, 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, -1.6e+104], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision] + N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+103], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e104

   1. Initial program 52.6%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 52.6%

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

   5. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. associate-/l* N/A

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

      13. associate-*r* N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 72.6

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

   7. Applied rewrites 72.6%

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

   if -1.6e104 < z < 2.35000000000000016e103

   1. Initial program 91.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 90.2%

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

   if 2.35000000000000016e103 < z

   1. Initial program 51.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 51.0%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.4

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

   7. Applied rewrites 87.4%

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

   8. Taylor expanded in b around inf

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

   10. Applied rewrites 81.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{c}, \frac{y}{c \cdot z} \cdot \left(x \cdot 9\right)\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

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 -3.4e+76)
   (/ (fma (* t a) -4.0 (* (/ (* x y) z) 9.0)) c)
   (if (<= z 2.35e+103)
     (/ (fma (* x 9.0) y (fma (* (* -4.0 z) a) t b)) (* c z))
     (/ (fma (* t a) -4.0 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.4e+76) {
		tmp = fma((t * a), -4.0, (((x * y) / z) * 9.0)) / c;
	} else if (z <= 2.35e+103) {
		tmp = fma((x * 9.0), y, fma(((-4.0 * z) * a), t, b)) / (c * z);
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.4e+76)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(Float64(Float64(x * y) / z) * 9.0)) / c);
	elseif (z <= 2.35e+103)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(c * z));
	else
		tmp = Float64(fma(Float64(t * a), -4.0, 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, -3.4e+76], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.35e+103], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999997e76

   1. Initial program 55.2%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 53.4%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 84.0

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

   7. Applied rewrites 84.0%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 77.2%

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

   if -3.3999999999999997e76 < z < 2.35000000000000016e103

   1. Initial program 92.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 90.9%

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

   if 2.35000000000000016e103 < z

   1. Initial program 51.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 51.0%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.4

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

   7. Applied rewrites 87.4%

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

   8. Taylor expanded in b around inf

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

   10. Applied rewrites 81.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4500000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

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 -4500000000.0)
   (/ (fma (* t a) -4.0 (* (/ (* x y) z) 9.0)) c)
   (if (<= z 6.2e+24)
     (/ (fma (* x y) 9.0 b) (* c z))
     (/ (fma (* t a) -4.0 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4500000000.0) {
		tmp = fma((t * a), -4.0, (((x * y) / z) * 9.0)) / c;
	} else if (z <= 6.2e+24) {
		tmp = fma((x * y), 9.0, b) / (c * z);
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4500000000.0)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(Float64(Float64(x * y) / z) * 9.0)) / c);
	elseif (z <= 6.2e+24)
		tmp = Float64(fma(Float64(x * y), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(fma(Float64(t * a), -4.0, 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, -4500000000.0], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6.2e+24], N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5e9

   1. Initial program 61.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 60.1%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 88.0

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

   7. Applied rewrites 88.0%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 75.2%

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

   if -4.5e9 < z < 6.20000000000000022e24

   1. Initial program 93.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if 6.20000000000000022e24 < z

   1. Initial program 61.0%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 61.0%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 89.9

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in b around inf

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

   10. Applied rewrites 79.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4500000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y}{c \cdot z}\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.3e+59)
   (* (/ (* t a) c) -4.0)
   (if (<= z -4.6e-275)
     (/ (/ b c) z)
     (if (<= z 1.2e-170)
       (/ (* (* x 9.0) y) (* c z))
       (if (<= z 0.0075) (/ b (* c z)) (/ (* (* -4.0 t) a) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= -4.6e-275) {
		tmp = (b / c) / z;
	} else if (z <= 1.2e-170) {
		tmp = ((x * 9.0) * y) / (c * z);
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.3d+59)) then
        tmp = ((t * a) / c) * (-4.0d0)
    else if (z <= (-4.6d-275)) then
        tmp = (b / c) / z
    else if (z <= 1.2d-170) then
        tmp = ((x * 9.0d0) * y) / (c * z)
    else if (z <= 0.0075d0) then
        tmp = b / (c * z)
    else
        tmp = (((-4.0d0) * t) * a) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= -4.6e-275) {
		tmp = (b / c) / z;
	} else if (z <= 1.2e-170) {
		tmp = ((x * 9.0) * y) / (c * z);
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.3e+59:
		tmp = ((t * a) / c) * -4.0
	elif z <= -4.6e-275:
		tmp = (b / c) / z
	elif z <= 1.2e-170:
		tmp = ((x * 9.0) * y) / (c * z)
	elif z <= 0.0075:
		tmp = b / (c * z)
	else:
		tmp = ((-4.0 * t) * a) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.3e+59)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	elseif (z <= -4.6e-275)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 1.2e-170)
		tmp = Float64(Float64(Float64(x * 9.0) * y) / Float64(c * z));
	elseif (z <= 0.0075)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.3e+59)
		tmp = ((t * a) / c) * -4.0;
	elseif (z <= -4.6e-275)
		tmp = (b / c) / z;
	elseif (z <= 1.2e-170)
		tmp = ((x * 9.0) * y) / (c * z);
	elseif (z <= 0.0075)
		tmp = b / (c * z);
	else
		tmp = ((-4.0 * t) * a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.3e+59], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, -4.6e-275], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.2e-170], N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0075], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2999999999999999e59

   1. Initial program 57.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.0

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

   5. Applied rewrites 64.0%

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

   if -3.2999999999999999e59 < z < -4.59999999999999979e-275

   1. Initial program 88.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 96.9%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 55.4

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

   7. Applied rewrites 55.4%

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

   if -4.59999999999999979e-275 < z < 1.2e-170

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   7. Applied rewrites 64.3%

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

   if 1.2e-170 < z < 0.0074999999999999997

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

   if 0.0074999999999999997 < z

   1. Initial program 62.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.8

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

   7. Applied rewrites 87.8%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 54.9%

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

   12. Applied rewrites 54.9%

       \[\leadsto \frac{\left(-4 \cdot t\right) \cdot a}{c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y}{c \cdot z}\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-170}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.3e+59)
   (* (/ (* t a) c) -4.0)
   (if (<= z -4.6e-275)
     (/ (/ b c) z)
     (if (<= z 1.2e-170)
       (* (* (/ y (* c z)) 9.0) x)
       (if (<= z 0.0075) (/ b (* c z)) (/ (* (* -4.0 t) a) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= -4.6e-275) {
		tmp = (b / c) / z;
	} else if (z <= 1.2e-170) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.3d+59)) then
        tmp = ((t * a) / c) * (-4.0d0)
    else if (z <= (-4.6d-275)) then
        tmp = (b / c) / z
    else if (z <= 1.2d-170) then
        tmp = ((y / (c * z)) * 9.0d0) * x
    else if (z <= 0.0075d0) then
        tmp = b / (c * z)
    else
        tmp = (((-4.0d0) * t) * a) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= -4.6e-275) {
		tmp = (b / c) / z;
	} else if (z <= 1.2e-170) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.3e+59:
		tmp = ((t * a) / c) * -4.0
	elif z <= -4.6e-275:
		tmp = (b / c) / z
	elif z <= 1.2e-170:
		tmp = ((y / (c * z)) * 9.0) * x
	elif z <= 0.0075:
		tmp = b / (c * z)
	else:
		tmp = ((-4.0 * t) * a) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.3e+59)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	elseif (z <= -4.6e-275)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 1.2e-170)
		tmp = Float64(Float64(Float64(y / Float64(c * z)) * 9.0) * x);
	elseif (z <= 0.0075)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.3e+59)
		tmp = ((t * a) / c) * -4.0;
	elseif (z <= -4.6e-275)
		tmp = (b / c) / z;
	elseif (z <= 1.2e-170)
		tmp = ((y / (c * z)) * 9.0) * x;
	elseif (z <= 0.0075)
		tmp = b / (c * z);
	else
		tmp = ((-4.0 * t) * a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.3e+59], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, -4.6e-275], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.2e-170], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 0.0075], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2999999999999999e59

   1. Initial program 57.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.0

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

   5. Applied rewrites 64.0%

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

   if -3.2999999999999999e59 < z < -4.59999999999999979e-275

   1. Initial program 88.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 96.9%

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

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 55.4

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

   7. Applied rewrites 55.4%

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

   if -4.59999999999999979e-275 < z < 1.2e-170

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

   if 1.2e-170 < z < 0.0074999999999999997

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

   if 0.0074999999999999997 < z

   1. Initial program 62.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 87.8

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

   7. Applied rewrites 87.8%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 54.9%

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

   12. Applied rewrites 54.9%

       \[\leadsto \frac{\left(-4 \cdot t\right) \cdot a}{c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-170}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* t a) -4.0 (/ b z)) c)))
   (if (<= z -8.2e-71)
     t_1
     (if (<= z 6.2e+24) (/ (fma (* x y) 9.0 b) (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t * a), -4.0, (b / z)) / c;
	double tmp;
	if (z <= -8.2e-71) {
		tmp = t_1;
	} else if (z <= 6.2e+24) {
		tmp = fma((x * y), 9.0, b) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -8.2e-71)
		tmp = t_1;
	elseif (z <= 6.2e+24)
		tmp = Float64(fma(Float64(x * y), 9.0, b) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -8.2e-71], t$95$1, If[LessEqual[z, 6.2e+24], N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999987e-71 or 6.20000000000000022e24 < z

   1. Initial program 64.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 64.1%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 89.8

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

   7. Applied rewrites 89.8%

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

   8. Taylor expanded in b around inf

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

   10. Applied rewrites 74.6%

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

   if -8.19999999999999987e-71 < z < 6.20000000000000022e24

   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. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 84.4

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

   5. Applied rewrites 84.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+156}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.8e+80)
   (* (/ (* t a) c) -4.0)
   (if (<= z 9e+156) (/ (fma (* x y) 9.0 b) (* c z)) (/ (* (* -4.0 t) a) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.8e+80) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= 9e+156) {
		tmp = fma((x * y), 9.0, b) / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.8e+80)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	elseif (z <= 9e+156)
		tmp = Float64(fma(Float64(x * y), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.8e+80], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 9e+156], N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999997e80

   1. Initial program 54.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 65.4

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

   5. Applied rewrites 65.4%

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

   if -1.79999999999999997e80 < z < 9.00000000000000061e156

   1. Initial program 89.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if 9.00000000000000061e156 < z

   1. Initial program 50.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 50.4%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 81.9

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 70.8%

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

   12. Applied rewrites 70.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+156}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{1}{c \cdot z} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.2e+75)
   (* (/ (* t a) c) -4.0)
   (if (<= z 0.0075) (* (/ 1.0 (* c z)) b) (/ (* (* -4.0 t) a) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.2e+75) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= 0.0075) {
		tmp = (1.0 / (c * z)) * b;
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-4.2d+75)) then
        tmp = ((t * a) / c) * (-4.0d0)
    else if (z <= 0.0075d0) then
        tmp = (1.0d0 / (c * z)) * b
    else
        tmp = (((-4.0d0) * t) * a) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.2e+75) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= 0.0075) {
		tmp = (1.0 / (c * z)) * b;
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -4.2e+75:
		tmp = ((t * a) / c) * -4.0
	elif z <= 0.0075:
		tmp = (1.0 / (c * z)) * b
	else:
		tmp = ((-4.0 * t) * a) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4.2e+75)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	elseif (z <= 0.0075)
		tmp = Float64(Float64(1.0 / Float64(c * z)) * b);
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -4.2e+75)
		tmp = ((t * a) / c) * -4.0;
	elseif (z <= 0.0075)
		tmp = (1.0 / (c * z)) * b;
	else
		tmp = ((-4.0 * t) * a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -4.2e+75], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 0.0075], N[(N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999997e75

   1. Initial program 55.2%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   if -4.19999999999999997e75 < z < 0.0074999999999999997

   1. Initial program 92.5%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 51.1

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

   5. Applied rewrites 51.1%

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

   7. Applied rewrites 51.7%

      \[\leadsto \frac{1}{c \cdot z} \cdot \color{blue}{b} \]

   if 0.0074999999999999997 < z

   1. Initial program 62.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in c around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{t \cdot a}, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{t \cdot a}, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \color{blue}{\frac{x \cdot y}{z} \cdot 9} + \frac{b}{z}\right)}{c} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \color{blue}{\mathsf{fma}\left(\frac{x \cdot y}{z}, 9, \frac{b}{z}\right)}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\color{blue}{\frac{x \cdot y}{z}}, 9, \frac{b}{z}\right)\right)}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{\color{blue}{y \cdot x}}{z}, 9, \frac{b}{z}\right)\right)}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{\color{blue}{y \cdot x}}{z}, 9, \frac{b}{z}\right)\right)}{c} \]

      14. lower-/.f64 87.8

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \color{blue}{\frac{b}{z}}\right)\right)}{c} \]

   7. Applied rewrites 87.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \frac{b}{z}\right)\right)}{c}} \]

   8. Taylor expanded in a around inf

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 54.9%

       \[\leadsto \frac{\left(t \cdot a\right) \cdot -4}{c} \]
   11. Step-by-step derivation

   12. Applied rewrites 54.9%

       \[\leadsto \frac{\left(-4 \cdot t\right) \cdot a}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{1}{c \cdot z} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -4.2e+75)
   (* (/ (* t a) c) -4.0)
   (if (<= z 0.0075) (/ b (* c z)) (/ (* (* -4.0 t) a) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.2e+75) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-4.2d+75)) then
        tmp = ((t * a) / c) * (-4.0d0)
    else if (z <= 0.0075d0) then
        tmp = b / (c * z)
    else
        tmp = (((-4.0d0) * t) * a) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -4.2e+75) {
		tmp = ((t * a) / c) * -4.0;
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = ((-4.0 * t) * a) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -4.2e+75:
		tmp = ((t * a) / c) * -4.0
	elif z <= 0.0075:
		tmp = b / (c * z)
	else:
		tmp = ((-4.0 * t) * a) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -4.2e+75)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	elseif (z <= 0.0075)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(-4.0 * t) * a) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -4.2e+75)
		tmp = ((t * a) / c) * -4.0;
	elseif (z <= 0.0075)
		tmp = b / (c * z);
	else
		tmp = ((-4.0 * t) * a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -4.2e+75], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 0.0075], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999997e75

   1. Initial program 55.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      4. lower-*.f64 64.3

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

   5. Applied rewrites 64.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{t \cdot a}{c}} \]

   if -4.19999999999999997e75 < z < 0.0074999999999999997

   1. Initial program 92.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 51.1

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 51.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 0.0074999999999999997 < z

   1. Initial program 62.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      4. associate-+l- N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      5. div-sub N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 9\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 9\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(x \cdot 9\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      12. *-commutative N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(9 \cdot x\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(9 \cdot x\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{\color{blue}{z \cdot c}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      15. *-commutative N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{\color{blue}{c \cdot z}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{\color{blue}{c \cdot z}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{c \cdot z} - \color{blue}{\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(9 \cdot x\right)}{c \cdot z} - \frac{a \cdot \left(t \cdot \left(4 \cdot z\right)\right) - b}{c \cdot z}} \]

   5. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

      4. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{t \cdot a}, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{t \cdot a}, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \color{blue}{\frac{x \cdot y}{z} \cdot 9} + \frac{b}{z}\right)}{c} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \color{blue}{\mathsf{fma}\left(\frac{x \cdot y}{z}, 9, \frac{b}{z}\right)}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\color{blue}{\frac{x \cdot y}{z}}, 9, \frac{b}{z}\right)\right)}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{\color{blue}{y \cdot x}}{z}, 9, \frac{b}{z}\right)\right)}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{\color{blue}{y \cdot x}}{z}, 9, \frac{b}{z}\right)\right)}{c} \]

      14. lower-/.f64 87.8

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \color{blue}{\frac{b}{z}}\right)\right)}{c} \]

   7. Applied rewrites 87.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \frac{b}{z}\right)\right)}{c}} \]

   8. Taylor expanded in a around inf

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 54.9%

       \[\leadsto \frac{\left(t \cdot a\right) \cdot -4}{c} \]
   11. Step-by-step derivation

   12. Applied rewrites 54.9%

       \[\leadsto \frac{\left(-4 \cdot t\right) \cdot a}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(-4 \cdot t\right) \cdot a}{c}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0075:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* (* -4.0 t) a) c)))
   (if (<= z -4.2e+75) t_1 (if (<= z 0.0075) (/ b (* c z)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * t) * a) / c;
	double tmp;
	if (z <= -4.2e+75) {
		tmp = t_1;
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * t) * a) / c
    if (z <= (-4.2d+75)) then
        tmp = t_1
    else if (z <= 0.0075d0) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * t) * a) / c;
	double tmp;
	if (z <= -4.2e+75) {
		tmp = t_1;
	} else if (z <= 0.0075) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * t) * a) / c
	tmp = 0
	if z <= -4.2e+75:
		tmp = t_1
	elif z <= 0.0075:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * t) * a) / c)
	tmp = 0.0
	if (z <= -4.2e+75)
		tmp = t_1;
	elseif (z <= 0.0075)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * t) * a) / c;
	tmp = 0.0;
	if (z <= -4.2e+75)
		tmp = t_1;
	elseif (z <= 0.0075)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -4.2e+75], t$95$1, If[LessEqual[z, 0.0075], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999997e75 or 0.0074999999999999997 < z

   1. Initial program 58.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      4. associate-+l- N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      5. div-sub N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 9\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 9\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(x \cdot 9\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      12. *-commutative N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(9 \cdot x\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(9 \cdot x\right)}}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{\color{blue}{z \cdot c}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      15. *-commutative N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{\color{blue}{c \cdot z}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{\color{blue}{c \cdot z}} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{y \cdot \left(9 \cdot x\right)}{c \cdot z} - \color{blue}{\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

   4. Applied rewrites 57.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(9 \cdot x\right)}{c \cdot z} - \frac{a \cdot \left(t \cdot \left(4 \cdot z\right)\right) - b}{c \cdot z}} \]

   5. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

      4. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{t \cdot a}, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{t \cdot a}, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \color{blue}{\frac{x \cdot y}{z} \cdot 9} + \frac{b}{z}\right)}{c} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \color{blue}{\mathsf{fma}\left(\frac{x \cdot y}{z}, 9, \frac{b}{z}\right)}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\color{blue}{\frac{x \cdot y}{z}}, 9, \frac{b}{z}\right)\right)}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{\color{blue}{y \cdot x}}{z}, 9, \frac{b}{z}\right)\right)}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{\color{blue}{y \cdot x}}{z}, 9, \frac{b}{z}\right)\right)}{c} \]

      14. lower-/.f64 85.9

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \color{blue}{\frac{b}{z}}\right)\right)}{c} \]

   7. Applied rewrites 85.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y \cdot x}{z}, 9, \frac{b}{z}\right)\right)}{c}} \]

   8. Taylor expanded in a around inf

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 59.6%

       \[\leadsto \frac{\left(t \cdot a\right) \cdot -4}{c} \]
   11. Step-by-step derivation

   12. Applied rewrites 59.6%

       \[\leadsto \frac{\left(-4 \cdot t\right) \cdot a}{c} \]

   if -4.19999999999999997e75 < z < 0.0074999999999999997

   1. Initial program 92.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 51.1

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 51.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 35.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (c * z)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.8%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   2. lower-*.f64 36.3

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 36.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 81.0% 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 2024240 
(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)))