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

Percentage Accurate: 85.3% → 93.7%

Time: 27.2s

Alternatives: 19

Speedup: 0.9×

• 49.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\\ \mathbf{if}\;t \leq -4000000:\\ \;\;\;\;\mathsf{fma}\left(-j, k \cdot 27, t\_1\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -4.0 x)
          i
          (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b)))))
   (if (<= t -4000000.0)
     (fma (- j) (* k 27.0) t_1)
     (if (<= t 6.8e+111)
       (-
        (fma
         (* 18.0 x)
         (* y (* t z))
         (fma (* -4.0 a) t (fma c b (* -4.0 (* x i)))))
        (* (* j 27.0) k))
       (fma (* -27.0 j) k t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (c * b)));
	double tmp;
	if (t <= -4000000.0) {
		tmp = fma(-j, (k * 27.0), t_1);
	} else if (t <= 6.8e+111) {
		tmp = fma((18.0 * x), (y * (t * z)), fma((-4.0 * a), t, fma(c, b, (-4.0 * (x * i))))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(c * b)))
	tmp = 0.0
	if (t <= -4000000.0)
		tmp = fma(Float64(-j), Float64(k * 27.0), t_1);
	elseif (t <= 6.8e+111)
		tmp = Float64(fma(Float64(18.0 * x), Float64(y * Float64(t * z)), fma(Float64(-4.0 * a), t, fma(c, b, Float64(-4.0 * Float64(x * i))))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4000000.0], N[((-j) * N[(k * 27.0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6.8e+111], N[(N[(N[(18.0 * x), $MachinePrecision] * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e6

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right)} \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{j \cdot \left(27 \cdot k\right)}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot \left(27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j\right), 27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-j}, 27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-j, \color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. lower-*.f64 83.0

          \[\leadsto \mathsf{fma}\left(-j, \color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   if -4e6 < t < 6.8000000000000003e111

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. associate-*l* N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 18, y \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 6.8000000000000003e111 < t

   1. Initial program 96.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 96.9

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+302}\right):\\ \;\;\;\;\left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right) \cdot 18\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+302)))
     (* (* z (* x (* t y))) 18.0)
     (fma (* -27.0 j) k (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+302)) {
		tmp = (z * (x * (t * y))) * 18.0;
	} else {
		tmp = fma((-27.0 * j), k, (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+302))
		tmp = Float64(Float64(z * Float64(x * Float64(t * y))) * 18.0);
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+302]], $MachinePrecision]], N[(N[(z * N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -inf.0 or 4.0000000000000003e302 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 70.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 66.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto \left(\left(\left(z \cdot x\right) \cdot y\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto \left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right) \cdot 18 \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 4.0000000000000003e302

   1. Initial program 99.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 4 \cdot 10^{+302}\right):\\ \;\;\;\;\left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right) \cdot 18\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (fma
    (- j)
    (* k 27.0)
    (fma (* -4.0 x) i (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b))))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = fma(-j, (k * 27.0), fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (c * b))));
	} else {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = fma(Float64(-j), Float64(k * 27.0), fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[((-j) * N[(k * 27.0), $MachinePrecision] + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 93.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right)} \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{j \cdot \left(27 \cdot k\right)}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot \left(27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j\right), 27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-j}, 27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-j, \color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. lower-*.f64 92.6

          \[\leadsto \mathsf{fma}\left(-j, \color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

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

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 73.2

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 73.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 92.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (fma
    (* -27.0 j)
    k
    (fma (* -4.0 x) i (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b))))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = fma((-27.0 * j), k, fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (c * b))));
	} else {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 93.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 92.9

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 93.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

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

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 73.2

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 73.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 93.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\\ \mathbf{if}\;t \leq -4000000:\\ \;\;\;\;\mathsf{fma}\left(-j, k \cdot 27, t\_1\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -4.0 x)
          i
          (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b)))))
   (if (<= t -4000000.0)
     (fma (- j) (* k 27.0) t_1)
     (if (<= t 6.8e+111)
       (-
        (fma
         x
         (* (* y 18.0) (* t z))
         (fma (* -4.0 a) t (fma c b (* -4.0 (* x i)))))
        (* (* j 27.0) k))
       (fma (* -27.0 j) k t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (c * b)));
	double tmp;
	if (t <= -4000000.0) {
		tmp = fma(-j, (k * 27.0), t_1);
	} else if (t <= 6.8e+111) {
		tmp = fma(x, ((y * 18.0) * (t * z)), fma((-4.0 * a), t, fma(c, b, (-4.0 * (x * i))))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(c * b)))
	tmp = 0.0
	if (t <= -4000000.0)
		tmp = fma(Float64(-j), Float64(k * 27.0), t_1);
	elseif (t <= 6.8e+111)
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), fma(Float64(-4.0 * a), t, fma(c, b, Float64(-4.0 * Float64(x * i))))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4000000.0], N[((-j) * N[(k * 27.0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6.8e+111], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e6

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right)} \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{j \cdot \left(27 \cdot k\right)}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot \left(27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j\right), 27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-j}, 27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-j, \color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. lower-*.f64 83.0

          \[\leadsto \mathsf{fma}\left(-j, \color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-j, k \cdot 27, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   if -4e6 < t < 6.8000000000000003e111

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. associate-*l* N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. associate-*l* N/A

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(18 \cdot y\right) \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 6.8000000000000003e111 < t

   1. Initial program 96.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

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

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 96.9

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 78.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot x\right) \cdot -4\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+246}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), t\_1\right) - t\_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(y \cdot \left(z \cdot t\right), 18 \cdot x, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* i x) -4.0)) (t_2 (* (* j 27.0) k)))
   (if (<= y -7.5e+246)
     (- (fma x (* (* y 18.0) (* t z)) t_1) t_2)
     (if (<= y -3.1e+131)
       (fma
        (* -27.0 j)
        k
        (fma (* y (* z t)) (* 18.0 x) (fma (* t a) -4.0 (* b c))))
       (if (<= y 1.25e-47)
         (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))
         (- (fma y (* (* 18.0 x) (* t z)) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (i * x) * -4.0;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (y <= -7.5e+246) {
		tmp = fma(x, ((y * 18.0) * (t * z)), t_1) - t_2;
	} else if (y <= -3.1e+131) {
		tmp = fma((-27.0 * j), k, fma((y * (z * t)), (18.0 * x), fma((t * a), -4.0, (b * c))));
	} else if (y <= 1.25e-47) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	} else {
		tmp = fma(y, ((18.0 * x) * (t * z)), t_1) - t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(i * x) * -4.0)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (y <= -7.5e+246)
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), t_1) - t_2);
	elseif (y <= -3.1e+131)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(y * Float64(z * t)), Float64(18.0 * x), fma(Float64(t * a), -4.0, Float64(b * c))));
	elseif (y <= 1.25e-47)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	else
		tmp = Float64(fma(y, Float64(Float64(18.0 * x) * Float64(t * z)), t_1) - t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[y, -7.5e+246], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[y, -3.1e+131], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(18.0 * x), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-47], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(18.0 * x), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5e246

   1. Initial program 63.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. associate-*l* N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. associate-*l* N/A

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(18 \cdot y\right) \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{-4 \cdot \left(i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 87.5

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right)} \cdot -4\right) - \left(j \cdot 27\right) \cdot k \]

   7. Applied rewrites 87.5%

      \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

   if -7.5e246 < y < -3.10000000000000016e131

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 82.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   7. Applied rewrites 86.4%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(y \cdot \left(z \cdot t\right), 18 \cdot x, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\right) \]

   if -3.10000000000000016e131 < y < 1.25000000000000003e-47

   1. Initial program 90.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   if 1.25000000000000003e-47 < y

   1. Initial program 77.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. associate-*l* N/A

          \[\leadsto \left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(x \cdot 18\right) \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 95.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{-4 \cdot \left(i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 77.6

         \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right)} \cdot -4\right) - \left(j \cdot 27\right) \cdot k \]

   7. Applied rewrites 77.6%

      \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 76.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+188} \lor \neg \left(y \leq 1.25 \cdot 10^{-47}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \left(i \cdot x\right) \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= y -5.4e+188) (not (<= y 1.25e-47)))
   (- (fma x (* (* y 18.0) (* t z)) (* (* i x) -4.0)) (* (* j 27.0) k))
   (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((y <= -5.4e+188) || !(y <= 1.25e-47)) {
		tmp = fma(x, ((y * 18.0) * (t * z)), ((i * x) * -4.0)) - ((j * 27.0) * k);
	} else {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((y <= -5.4e+188) || !(y <= 1.25e-47))
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), Float64(Float64(i * x) * -4.0)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[y, -5.4e+188], N[Not[LessEqual[y, 1.25e-47]], $MachinePrecision]], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e188 or 1.25000000000000003e-47 < y

   1. Initial program 74.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. associate-*l* N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. associate-*l* N/A

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(18 \cdot y\right) \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{-4 \cdot \left(i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 78.5

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right)} \cdot -4\right) - \left(j \cdot 27\right) \cdot k \]

   7. Applied rewrites 78.5%

      \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

   if -5.4e188 < y < 1.25000000000000003e-47

   1. Initial program 91.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+188} \lor \neg \left(y \leq 1.25 \cdot 10^{-47}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \left(i \cdot x\right) \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot x\right) \cdot -4\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+188}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), t\_1\right) - t\_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* i x) -4.0)) (t_2 (* (* j 27.0) k)))
   (if (<= y -5.4e+188)
     (- (fma x (* (* y 18.0) (* t z)) t_1) t_2)
     (if (<= y 1.25e-47)
       (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))
       (- (fma y (* (* 18.0 x) (* t z)) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (i * x) * -4.0;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (y <= -5.4e+188) {
		tmp = fma(x, ((y * 18.0) * (t * z)), t_1) - t_2;
	} else if (y <= 1.25e-47) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	} else {
		tmp = fma(y, ((18.0 * x) * (t * z)), t_1) - t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(i * x) * -4.0)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (y <= -5.4e+188)
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), t_1) - t_2);
	elseif (y <= 1.25e-47)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	else
		tmp = Float64(fma(y, Float64(Float64(18.0 * x) * Float64(t * z)), t_1) - t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[y, -5.4e+188], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[y, 1.25e-47], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(18.0 * x), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4e188

   1. Initial program 65.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. associate-*l* N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. associate-*l* N/A

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(18 \cdot y\right) \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{-4 \cdot \left(i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 88.6

         \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right)} \cdot -4\right) - \left(j \cdot 27\right) \cdot k \]

   7. Applied rewrites 88.6%

      \[\leadsto \mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

   if -5.4e188 < y < 1.25000000000000003e-47

   1. Initial program 91.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   if 1.25000000000000003e-47 < y

   1. Initial program 77.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. associate-*l* N/A

          \[\leadsto \left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(x \cdot 18\right) \cdot \left(z \cdot t\right), \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 95.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{-4 \cdot \left(i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 77.6

         \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right)} \cdot -4\right) - \left(j \cdot 27\right) \cdot k \]

   7. Applied rewrites 77.6%

      \[\leadsto \mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \color{blue}{\left(i \cdot x\right) \cdot -4}\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 84.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -9.6 \cdot 10^{-6} \lor \neg \left(i \leq 780000000000\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -9.6e-6) (not (<= i 780000000000.0)))
   (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -9.6e-6) || !(i <= 780000000000.0)) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -9.6e-6) || !(i <= 780000000000.0))
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -9.6e-6], N[Not[LessEqual[i, 780000000000.0]], $MachinePrecision]], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -9.5999999999999996e-6 or 7.8e11 < i

   1. Initial program 81.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 84.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   if -9.5999999999999996e-6 < i < 7.8e11

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.6 \cdot 10^{-6} \lor \neg \left(i \leq 780000000000\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+53)
     (fma (* -27.0 j) k (* b c))
     (if (<= t_1 2e+160)
       (fma c b (* (fma i x (* a t)) -4.0))
       (* -27.0 (* k j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+53) {
		tmp = fma((-27.0 * j), k, (b * c));
	} else if (t_1 <= 2e+160) {
		tmp = fma(c, b, (fma(i, x, (a * t)) * -4.0));
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+53)
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	elseif (t_1 <= 2e+160)
		tmp = fma(c, b, Float64(fma(i, x, Float64(a * t)) * -4.0));
	else
		tmp = Float64(-27.0 * Float64(k * j));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+53], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+160], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e53

   1. Initial program 81.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 80.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right) \]

   if -2e53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000001e160

   1. Initial program 86.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 67.6%

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

   if 2.00000000000000001e160 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 82.4

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 82.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot t\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, t\_1 \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) t)))
   (if (<= y -4.5e+257)
     (* (fma t_1 18.0 (* -4.0 i)) x)
     (if (<= y 7.5e+24)
       (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))
       (* (fma -4.0 i (* t_1 18.0)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * t;
	double tmp;
	if (y <= -4.5e+257) {
		tmp = fma(t_1, 18.0, (-4.0 * i)) * x;
	} else if (y <= 7.5e+24) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	} else {
		tmp = fma(-4.0, i, (t_1 * 18.0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * t)
	tmp = 0.0
	if (y <= -4.5e+257)
		tmp = Float64(fma(t_1, 18.0, Float64(-4.0 * i)) * x);
	elseif (y <= 7.5e+24)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	else
		tmp = Float64(fma(-4.0, i, Float64(t_1 * 18.0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -4.5e+257], N[(N[(t$95$1 * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 7.5e+24], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999999e257

   1. Initial program 71.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 15.9

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 15.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot i\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(y \cdot z\right), 18, -4 \cdot i\right)} \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot t}, 18, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot t}, 18, -4 \cdot i\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot t, 18, -4 \cdot i\right) \cdot x \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot t, 18, -4 \cdot i\right) \cdot x \]

      13. lower-*.f64 92.8

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, \color{blue}{-4 \cdot i}\right) \cdot x \]

   8. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right) \cdot x} \]

   if -4.4999999999999999e257 < y < 7.50000000000000014e24

   1. Initial program 89.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 85.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   if 7.50000000000000014e24 < y

   1. Initial program 71.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

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

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 56.6

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 37.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+53} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+54}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+53) (not (<= t_1 5e+54))) (* -27.0 (* k j)) (* c b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+53) || !(t_1 <= 5e+54)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+53)) .or. (.not. (t_1 <= 5d+54))) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    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 i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+53) || !(t_1 <= 5e+54)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+53) or not (t_1 <= 5e+54):
		tmp = -27.0 * (k * j)
	else:
		tmp = c * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+53) || !(t_1 <= 5e+54))
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+53) || ~((t_1 <= 5e+54)))
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+53], N[Not[LessEqual[t$95$1, 5e+54]], $MachinePrecision]], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e53 or 5.00000000000000005e54 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 66.4

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 66.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2e53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000005e54

   1. Initial program 86.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 70.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 24.0

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

   8. Applied rewrites 24.0%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+53} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+54}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -200000000000:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+37}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -200000000000.0)
     (* -27.0 (* k j))
     (if (<= t_1 5e+37) (* (* i x) -4.0) (* (* -27.0 k) j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -200000000000.0) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+37) {
		tmp = (i * x) * -4.0;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-200000000000.0d0)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= 5d+37) then
        tmp = (i * x) * (-4.0d0)
    else
        tmp = ((-27.0d0) * k) * j
    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 i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -200000000000.0) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+37) {
		tmp = (i * x) * -4.0;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -200000000000.0:
		tmp = -27.0 * (k * j)
	elif t_1 <= 5e+37:
		tmp = (i * x) * -4.0
	else:
		tmp = (-27.0 * k) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -200000000000.0)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 5e+37)
		tmp = Float64(Float64(i * x) * -4.0);
	else
		tmp = Float64(Float64(-27.0 * k) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -200000000000.0)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 5e+37)
		tmp = (i * x) * -4.0;
	else
		tmp = (-27.0 * k) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -200000000000.0], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+37], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e11

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 58.9

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 58.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2e11 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e37

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      3. lower-*.f64 34.5

         \[\leadsto \color{blue}{\left(i \cdot x\right)} \cdot -4 \]

   5. Applied rewrites 34.5%

      \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

   if 4.99999999999999989e37 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 65.9

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 65.9%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 64.1%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 37.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+54}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+53)
     (* -27.0 (* k j))
     (if (<= t_1 5e+54) (* c b) (* (* -27.0 k) j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+53) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+54) {
		tmp = c * b;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+53)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= 5d+54) then
        tmp = c * b
    else
        tmp = ((-27.0d0) * k) * j
    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 i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+53) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+54) {
		tmp = c * b;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+53:
		tmp = -27.0 * (k * j)
	elif t_1 <= 5e+54:
		tmp = c * b
	else:
		tmp = (-27.0 * k) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+53)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 5e+54)
		tmp = Float64(c * b);
	else
		tmp = Float64(Float64(-27.0 * k) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+53)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 5e+54)
		tmp = c * b;
	else
		tmp = (-27.0 * k) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+53], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+54], N[(c * b), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e53

   1. Initial program 81.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 64.3

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 64.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2e53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000005e54

   1. Initial program 86.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 70.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 24.0

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

   8. Applied rewrites 24.0%

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

   if 5.00000000000000005e54 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 68.7

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 68.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 66.8%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 67.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 30500000:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -8.5e+124)
   (* (fma (* (* z x) y) 18.0 (* -4.0 a)) t)
   (if (<= t 30500000.0)
     (fma c b (fma (* -27.0 j) k (* (* i x) -4.0)))
     (* (fma -4.0 i (* (* (* z y) t) 18.0)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -8.5e+124) {
		tmp = fma(((z * x) * y), 18.0, (-4.0 * a)) * t;
	} else if (t <= 30500000.0) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((i * x) * -4.0)));
	} else {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -8.5e+124)
		tmp = Float64(fma(Float64(Float64(z * x) * y), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 30500000.0)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(i * x) * -4.0)));
	else
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -8.5e+124], N[(N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 30500000.0], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999997e124

   1. Initial program 78.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 17.0

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 17.0%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

      2. metadata-eval N/A

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

      3. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{\left(z \cdot y\right)}, 18, -4 \cdot a\right) \cdot t \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot z\right) \cdot y}, 18, -4 \cdot a\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot z\right) \cdot y}, 18, -4 \cdot a\right) \cdot t \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot x\right)} \cdot y, 18, -4 \cdot a\right) \cdot t \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot x\right)} \cdot y, 18, -4 \cdot a\right) \cdot t \]

      14. lower-*.f64 80.8

          \[\leadsto \mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   8. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right) \cdot t} \]

   if -8.4999999999999997e124 < t < 3.05e7

   1. Initial program 83.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(i \cdot x\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(i \cdot x\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(i \cdot x\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(i \cdot x\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 82.3

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(i \cdot x\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\right)} \]

   if 3.05e7 < t

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

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

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 64.5

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 64.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 72.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot t\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, t\_1 \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, 18, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) t)))
   (if (<= x -2.4e+67)
     (* (fma -4.0 i (* t_1 18.0)) x)
     (if (<= x 9.2e+45)
       (fma c b (fma (* -27.0 j) k (* (* a t) -4.0)))
       (* (fma t_1 18.0 (* -4.0 i)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * t;
	double tmp;
	if (x <= -2.4e+67) {
		tmp = fma(-4.0, i, (t_1 * 18.0)) * x;
	} else if (x <= 9.2e+45) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((a * t) * -4.0)));
	} else {
		tmp = fma(t_1, 18.0, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * t)
	tmp = 0.0
	if (x <= -2.4e+67)
		tmp = Float64(fma(-4.0, i, Float64(t_1 * 18.0)) * x);
	elseif (x <= 9.2e+45)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0)));
	else
		tmp = Float64(fma(t_1, 18.0, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -2.4e+67], N[(N[(-4.0 * i + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 9.2e+45], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.40000000000000002e67

   1. Initial program 77.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

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

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 78.0

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]

   if -2.40000000000000002e67 < x < 9.20000000000000049e45

   1. Initial program 92.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 73.9

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   if 9.20000000000000049e45 < x

   1. Initial program 73.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 20.8

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 20.8%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot i\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(y \cdot z\right), 18, -4 \cdot i\right)} \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot t}, 18, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot t}, 18, -4 \cdot i\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot t, 18, -4 \cdot i\right) \cdot x \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot t, 18, -4 \cdot i\right) \cdot x \]

      13. lower-*.f64 73.4

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, \color{blue}{-4 \cdot i}\right) \cdot x \]

   8. Applied rewrites 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 34.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1000000 \lor \neg \left(b \cdot c \leq 10^{+59}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1000000.0) (not (<= (* b c) 1e+59)))
   (* c b)
   (* (* a t) -4.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1000000.0) || !((b * c) <= 1e+59)) {
		tmp = c * b;
	} else {
		tmp = (a * t) * -4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1000000.0d0)) .or. (.not. ((b * c) <= 1d+59))) then
        tmp = c * b
    else
        tmp = (a * t) * (-4.0d0)
    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 i, double j, double k) {
	double tmp;
	if (((b * c) <= -1000000.0) || !((b * c) <= 1e+59)) {
		tmp = c * b;
	} else {
		tmp = (a * t) * -4.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1000000.0) or not ((b * c) <= 1e+59):
		tmp = c * b
	else:
		tmp = (a * t) * -4.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1000000.0) || !(Float64(b * c) <= 1e+59))
		tmp = Float64(c * b);
	else
		tmp = Float64(Float64(a * t) * -4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1000000.0) || ~(((b * c) <= 1e+59)))
		tmp = c * b;
	else
		tmp = (a * t) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+59]], $MachinePrecision]], N[(c * b), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1e6 or 9.99999999999999972e58 < (*.f64 b c)

   1. Initial program 86.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 80.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 40.2

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

   8. Applied rewrites 40.2%

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

   if -1e6 < (*.f64 b c) < 9.99999999999999972e58

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

   5. Applied rewrites 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 18.1%

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

4. Final simplification 26.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1000000 \lor \neg \left(b \cdot c \leq 10^{+59}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+183} \lor \neg \left(x \leq 1.9 \cdot 10^{+73}\right):\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.85e+183) (not (<= x 1.9e+73)))
   (* (* i x) -4.0)
   (fma (* -27.0 j) k (* b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.85e+183) || !(x <= 1.9e+73)) {
		tmp = (i * x) * -4.0;
	} else {
		tmp = fma((-27.0 * j), k, (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.85e+183) || !(x <= 1.9e+73))
		tmp = Float64(Float64(i * x) * -4.0);
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.85e+183], N[Not[LessEqual[x, 1.9e+73]], $MachinePrecision]], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8500000000000001e183 or 1.90000000000000011e73 < x

   1. Initial program 71.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      3. lower-*.f64 54.4

         \[\leadsto \color{blue}{\left(i \cdot x\right)} \cdot -4 \]

   5. Applied rewrites 54.4%

      \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

   if -1.8500000000000001e183 < x < 1.90000000000000011e73

   1. Initial program 91.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.3%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+183} \lor \neg \left(x \leq 1.9 \cdot 10^{+73}\right):\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 23.6% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ c \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = c * b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(c * b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = c * b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 85.0%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

   4. associate-+r+ N/A

      \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

   5. distribute-neg-in N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

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

      \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

   7. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

   8. distribute-lft-out N/A

      \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + -27 \cdot \left(j \cdot k\right)\right) \]

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

       \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + -27 \cdot \left(j \cdot k\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + -27 \cdot \left(j \cdot k\right)\right) \]

   12. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

   13. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

   14. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

   15. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

   16. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

5. Applied rewrites 76.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

6. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 18.7

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

8. Applied rewrites 18.7%

   \[\leadsto \color{blue}{c \cdot b} \]
9. Add Preprocessing

Developer Target 1: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = 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 i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))