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

Percentage Accurate: 85.0% → 91.4%

Time: 30.8s

Alternatives: 16

Speedup: 0.5×

• 50.3% 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: 85.0% 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: 91.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* y (* 18.0 x))))
   (if (<=
        (-
         (- (+ (* c b) (- (* t (* z t_1)) (* (* 4.0 a) t))) (* i (* 4.0 x)))
         (* k (* 27.0 j)))
        INFINITY)
     (fma
      (* k j)
      -27.0
      (fma (* i x) -4.0 (fma (fma z t_1 (* -4.0 a)) t (* c b))))
     (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma 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 = y * (18.0 * x);
	double tmp;
	if (((((c * b) + ((t * (z * t_1)) - ((4.0 * a) * t))) - (i * (4.0 * x))) - (k * (27.0 * j))) <= ((double) INFINITY)) {
		tmp = fma((k * j), -27.0, fma((i * x), -4.0, fma(fma(z, t_1, (-4.0 * a)), t, (c * b))));
	} else {
		tmp = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(y * Float64(18.0 * x))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(z * t_1)) - Float64(Float64(4.0 * a) * t))) - Float64(i * Float64(4.0 * x))) - Float64(k * Float64(27.0 * j))) <= Inf)
		tmp = fma(Float64(k * j), -27.0, fma(Float64(i * x), -4.0, fma(fma(z, t_1, Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, 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[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(z * t$95$1 + 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 + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 96.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. 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. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 96.3

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 96.3%

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

   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 a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 85.0%

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

4. Final simplification 95.4%

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

Alternative 2: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.002:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (fma -4.0 i (* (* (* z y) t) 18.0))
          x
          (fma c b (* -27.0 (* k j)))))
        (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -5e-32)
     t_1
     (if (<= t_2 0.002)
       (fma (fma i x (* a t)) -4.0 (fma c b (* (* (* (* z y) x) t) 18.0)))
       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(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -5e-32) {
		tmp = t_1;
	} else if (t_2 <= 0.002) {
		tmp = fma(fma(i, x, (a * t)), -4.0, fma(c, b, ((((z * y) * x) * t) * 18.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, Float64(-27.0 * Float64(k * j))))
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -5e-32)
		tmp = t_1;
	elseif (t_2 <= 0.002)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, fma(c, b, Float64(Float64(Float64(Float64(z * y) * x) * t) * 18.0)));
	else
		tmp = 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 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-32], t$95$1, If[LessEqual[t$95$2, 0.002], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5e-32 or 2e-3 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 85.5%

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

   if -5e-32 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-3

   1. Initial program 94.8%

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

   3. Taylor expanded in k around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. *-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 91.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 0.002:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;27 \cdot j \leq -5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{elif}\;27 \cdot j \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, \left(t \cdot z\right) \cdot y, \mathsf{fma}\left(x, i, a \cdot t\right) \cdot -4\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* 27.0 j) -5e-9)
   (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b (* -27.0 (* k j))))
   (if (<= (* 27.0 j) 2e-53)
     (fma (fma i x (* a t)) -4.0 (fma c b (* (* (* (* z y) x) t) 18.0)))
     (-
      (fma (* 18.0 x) (* (* t z) y) (* (fma x i (* a t)) -4.0))
      (* k (* 27.0 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 ((27.0 * j) <= -5e-9) {
		tmp = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	} else if ((27.0 * j) <= 2e-53) {
		tmp = fma(fma(i, x, (a * t)), -4.0, fma(c, b, ((((z * y) * x) * t) * 18.0)));
	} else {
		tmp = fma((18.0 * x), ((t * z) * y), (fma(x, i, (a * t)) * -4.0)) - (k * (27.0 * j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(27.0 * j) <= -5e-9)
		tmp = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, Float64(-27.0 * Float64(k * j))));
	elseif (Float64(27.0 * j) <= 2e-53)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, fma(c, b, Float64(Float64(Float64(Float64(z * y) * x) * t) * 18.0)));
	else
		tmp = Float64(fma(Float64(18.0 * x), Float64(Float64(t * z) * y), Float64(fma(x, i, Float64(a * t)) * -4.0)) - Float64(k * Float64(27.0 * j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(27.0 * j), $MachinePrecision], -5e-9], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(27.0 * j), $MachinePrecision], 2e-53], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * x), $MachinePrecision] * N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] + N[(N[(x * i + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 j #s(literal 27 binary64)) < -5.0000000000000001e-9

   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 a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 91.2%

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

   if -5.0000000000000001e-9 < (*.f64 j #s(literal 27 binary64)) < 2.00000000000000006e-53

   1. Initial program 95.4%

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

   3. Taylor expanded in k around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. *-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   5. Applied rewrites 91.2%

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

   if 2.00000000000000006e-53 < (*.f64 j #s(literal 27 binary64))

   1. Initial program 83.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. 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 83.5%

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

   5. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 74.9

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

   7. Applied rewrites 74.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;27 \cdot j \leq -5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{elif}\;27 \cdot j \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, \left(t \cdot z\right) \cdot y, \mathsf{fma}\left(x, i, a \cdot t\right) \cdot -4\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-223}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (fma -4.0 i (* (* (* z y) t) 18.0))
          x
          (fma c b (* -27.0 (* k j))))))
   (if (<= x -5.5e-130)
     t_1
     (if (<= x 1.4e-223) (fma c b (fma (* -27.0 k) j (* (* a t) -4.0))) 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(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	double tmp;
	if (x <= -5.5e-130) {
		tmp = t_1;
	} else if (x <= 1.4e-223) {
		tmp = fma(c, b, fma((-27.0 * k), j, ((a * t) * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, Float64(-27.0 * Float64(k * j))))
	tmp = 0.0
	if (x <= -5.5e-130)
		tmp = t_1;
	elseif (x <= 1.4e-223)
		tmp = fma(c, b, fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0)));
	else
		tmp = 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 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e-130], t$95$1, If[LessEqual[x, 1.4e-223], N[(c * b + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000007e-130 or 1.40000000000000007e-223 < x

   1. Initial program 85.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 85.6%

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

   if -5.50000000000000007e-130 < x < 1.40000000000000007e-223

   1. Initial program 98.3%

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

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

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 86.4

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

   5. Applied rewrites 86.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-223}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+126}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq 10^{+99}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* 27.0 j))))
   (if (<= t_1 -2e+126)
     (* (* -27.0 k) j)
     (if (<= t_1 1e+99) (* 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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -2e+126) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= 1e+99) {
		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 = k * (27.0d0 * j)
    if (t_1 <= (-2d+126)) then
        tmp = ((-27.0d0) * k) * j
    else if (t_1 <= 1d+99) 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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -2e+126) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= 1e+99) {
		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 = k * (27.0 * j)
	tmp = 0
	if t_1 <= -2e+126:
		tmp = (-27.0 * k) * j
	elif t_1 <= 1e+99:
		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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -2e+126)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (t_1 <= 1e+99)
		tmp = Float64(c * b);
	else
		tmp = Float64(-27.0 * Float64(k * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (27.0 * j);
	tmp = 0.0;
	if (t_1 <= -2e+126)
		tmp = (-27.0 * k) * j;
	elseif (t_1 <= 1e+99)
		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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+126], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, 1e+99], N[(c * b), $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) < -1.99999999999999985e126

   1. Initial program 80.4%

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

   3. Taylor expanded in k 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 69.4

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

   5. Applied rewrites 69.4%

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

   7. Applied rewrites 69.4%

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

   if -1.99999999999999985e126 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999997e98

   1. Initial program 92.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.2

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

   5. Applied rewrites 35.2%

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

   if 9.9999999999999997e98 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.4%

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

   3. Taylor expanded in k 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 58.7

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

   5. Applied rewrites 58.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+126}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 10^{+99}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+99}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -2e+126) t_1 (if (<= t_2 1e+99) (* c b) 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 = -27.0 * (k * j);
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -2e+126) {
		tmp = t_1;
	} else if (t_2 <= 1e+99) {
		tmp = c * b;
	} else {
		tmp = t_1;
	}
	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 = (-27.0d0) * (k * j)
    t_2 = k * (27.0d0 * j)
    if (t_2 <= (-2d+126)) then
        tmp = t_1
    else if (t_2 <= 1d+99) then
        tmp = c * b
    else
        tmp = t_1
    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 = -27.0 * (k * j);
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -2e+126) {
		tmp = t_1;
	} else if (t_2 <= 1e+99) {
		tmp = c * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	t_2 = k * (27.0 * j)
	tmp = 0
	if t_2 <= -2e+126:
		tmp = t_1
	elif t_2 <= 1e+99:
		tmp = c * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -2e+126)
		tmp = t_1;
	elseif (t_2 <= 1e+99)
		tmp = Float64(c * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	t_2 = k * (27.0 * j);
	tmp = 0.0;
	if (t_2 <= -2e+126)
		tmp = t_1;
	elseif (t_2 <= 1e+99)
		tmp = c * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+126], t$95$1, If[LessEqual[t$95$2, 1e+99], N[(c * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999985e126 or 9.9999999999999997e98 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.3%

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

   3. Taylor expanded in k 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 64.4

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

   5. Applied rewrites 64.4%

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

   if -1.99999999999999985e126 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999997e98

   1. Initial program 92.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.2

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

   5. Applied rewrites 35.2%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+126}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 10^{+99}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z \cdot \left(18 \cdot x\right), y, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 19000000000000:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* z (* 18.0 x)) y (* -4.0 a)) t)))
   (if (<= t -2e+31)
     t_1
     (if (<= t 19000000000000.0)
       (fma (* -4.0 i) x (fma c b (* -27.0 (* k j))))
       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((z * (18.0 * x)), y, (-4.0 * a)) * t;
	double tmp;
	if (t <= -2e+31) {
		tmp = t_1;
	} else if (t <= 19000000000000.0) {
		tmp = fma((-4.0 * i), x, fma(c, b, (-27.0 * (k * j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(z * Float64(18.0 * x)), y, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -2e+31)
		tmp = t_1;
	elseif (t <= 19000000000000.0)
		tmp = fma(Float64(-4.0 * i), x, fma(c, b, Float64(-27.0 * Float64(k * j))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(z * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] * y + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2e+31], t$95$1, If[LessEqual[t, 19000000000000.0], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e31 or 1.9e13 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 66.6%

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

   if -1.9999999999999999e31 < t < 1.9e13

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 86.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(18 \cdot x\right), y, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 19000000000000:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(18 \cdot x\right), y, -4 \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z \cdot \left(18 \cdot x\right), y, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 19000000000000:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* z (* 18.0 x)) y (* -4.0 a)) t)))
   (if (<= t -2e+31)
     t_1
     (if (<= t 19000000000000.0)
       (fma c b (fma (* -4.0 x) i (* -27.0 (* k j))))
       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((z * (18.0 * x)), y, (-4.0 * a)) * t;
	double tmp;
	if (t <= -2e+31) {
		tmp = t_1;
	} else if (t <= 19000000000000.0) {
		tmp = fma(c, b, fma((-4.0 * x), i, (-27.0 * (k * j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(z * Float64(18.0 * x)), y, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -2e+31)
		tmp = t_1;
	elseif (t <= 19000000000000.0)
		tmp = fma(c, b, fma(Float64(-4.0 * x), i, Float64(-27.0 * Float64(k * j))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(z * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] * y + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2e+31], t$95$1, If[LessEqual[t, 19000000000000.0], N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e31 or 1.9e13 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 66.6%

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

   if -1.9999999999999999e31 < t < 1.9e13

   1. Initial program 88.1%

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

   3. Taylor expanded in 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. distribute-neg-in N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 85.4

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

   5. Applied rewrites 85.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(18 \cdot x\right), y, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 19000000000000:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(18 \cdot x\right), y, -4 \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(t \cdot z\right) \cdot y\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 i (* (* (* t z) y) 18.0)) x)))
   (if (<= x -2.6e+163)
     t_1
     (if (<= x 3.5e+64) (fma c b (fma (* -27.0 k) j (* (* a t) -4.0))) 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, i, (((t * z) * y) * 18.0)) * x;
	double tmp;
	if (x <= -2.6e+163) {
		tmp = t_1;
	} else if (x <= 3.5e+64) {
		tmp = fma(c, b, fma((-27.0 * k), j, ((a * t) * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, i, Float64(Float64(Float64(t * z) * y) * 18.0)) * x)
	tmp = 0.0
	if (x <= -2.6e+163)
		tmp = t_1;
	elseif (x <= 3.5e+64)
		tmp = fma(c, b, fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0)));
	else
		tmp = 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 * i + N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.6e+163], t$95$1, If[LessEqual[x, 3.5e+64], N[(c * b + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6000000000000002e163 or 3.4999999999999999e64 < x

   1. Initial program 76.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 74.0

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

   5. Applied rewrites 74.0%

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

   7. Applied rewrites 74.0%

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

   if -2.6000000000000002e163 < x < 3.4999999999999999e64

   1. Initial program 93.5%

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

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

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 73.4

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

   5. Applied rewrites 73.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(t \cdot z\right) \cdot y\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(t \cdot z\right) \cdot y\right) \cdot 18\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(t \cdot z\right) \cdot y\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 i (* (* (* t z) y) 18.0)) x)))
   (if (<= x -2.6e+163)
     t_1
     (if (<= x 1.7e+65) (fma (* k j) -27.0 (* c b)) 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, i, (((t * z) * y) * 18.0)) * x;
	double tmp;
	if (x <= -2.6e+163) {
		tmp = t_1;
	} else if (x <= 1.7e+65) {
		tmp = fma((k * j), -27.0, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, i, Float64(Float64(Float64(t * z) * y) * 18.0)) * x)
	tmp = 0.0
	if (x <= -2.6e+163)
		tmp = t_1;
	elseif (x <= 1.7e+65)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	else
		tmp = 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 * i + N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.6e+163], t$95$1, If[LessEqual[x, 1.7e+65], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6000000000000002e163 or 1.7e65 < x

   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 75.0

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 75.0%

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

   if -2.6000000000000002e163 < x < 1.7e65

   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. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 62.0

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

   7. Applied rewrites 62.0%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(t \cdot z\right) \cdot y\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(t \cdot z\right) \cdot y\right) \cdot 18\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -8 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3600000000000:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -8e-61)
     t_1
     (if (<= t 3600000000000.0) (fma (* k j) -27.0 (* c b)) 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, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -8e-61) {
		tmp = t_1;
	} else if (t <= 3600000000000.0) {
		tmp = fma((k * j), -27.0, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -8e-61)
		tmp = t_1;
	elseif (t <= 3600000000000.0)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	else
		tmp = 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 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8e-61], t$95$1, If[LessEqual[t, 3600000000000.0], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.0000000000000003e-61 or 3.6e12 < t

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if -8.0000000000000003e-61 < t < 3.6e12

   1. Initial program 88.2%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.3

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

   5. Applied rewrites 66.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 66.4

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

   7. Applied rewrites 66.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-61}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t \leq 3600000000000:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+199}:\\ \;\;\;\;\left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot 18\right) \cdot y\right) \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.1e+199)
   (* (* (* (* t 18.0) z) y) x)
   (if (<= y 3.7e-68)
     (fma (* k j) -27.0 (* c b))
     (* (* (* (* t 18.0) y) z) 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 (y <= -1.1e+199) {
		tmp = (((t * 18.0) * z) * y) * x;
	} else if (y <= 3.7e-68) {
		tmp = fma((k * j), -27.0, (c * b));
	} else {
		tmp = (((t * 18.0) * y) * z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.1e+199)
		tmp = Float64(Float64(Float64(Float64(t * 18.0) * z) * y) * x);
	elseif (y <= 3.7e-68)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	else
		tmp = Float64(Float64(Float64(Float64(t * 18.0) * y) * z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.1e+199], N[(N[(N[(N[(t * 18.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 3.7e-68], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1000000000000001e199

   1. Initial program 72.4%

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

   3. Taylor expanded in 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 52.2

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

   5. Applied rewrites 52.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 41.2%

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

   10. Applied rewrites 46.5%

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

   if -1.1000000000000001e199 < y < 3.70000000000000002e-68

   1. Initial program 92.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 59.1

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

   7. Applied rewrites 59.1%

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

   if 3.70000000000000002e-68 < y

   1. Initial program 83.8%

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

   3. Taylor expanded in 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 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 39.3%

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

   10. Applied rewrites 40.7%

       \[\leadsto \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+199}:\\ \;\;\;\;\left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot 18\right) \cdot y\right) \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot y\right) \cdot x\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (* (* t 18.0) z) y) x)))
   (if (<= y -1.1e+199)
     t_1
     (if (<= y 3.7e-68) (fma (* k j) -27.0 (* c b)) 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 = (((t * 18.0) * z) * y) * x;
	double tmp;
	if (y <= -1.1e+199) {
		tmp = t_1;
	} else if (y <= 3.7e-68) {
		tmp = fma((k * j), -27.0, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(t * 18.0) * z) * y) * x)
	tmp = 0.0
	if (y <= -1.1e+199)
		tmp = t_1;
	elseif (y <= 3.7e-68)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(t * 18.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -1.1e+199], t$95$1, If[LessEqual[y, 3.7e-68], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1000000000000001e199 or 3.70000000000000002e-68 < y

   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 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 54.9

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

   5. Applied rewrites 54.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 39.6%

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

   10. Applied rewrites 43.8%

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

   if -1.1000000000000001e199 < y < 3.70000000000000002e-68

   1. Initial program 92.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 59.1

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

   7. Applied rewrites 59.1%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+199}:\\ \;\;\;\;\left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 1.7e+65) (fma (* k j) -27.0 (* c b)) (* (* -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 tmp;
	if (x <= 1.7e+65) {
		tmp = fma((k * j), -27.0, (c * b));
	} else {
		tmp = (-4.0 * i) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 1.7e+65)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	else
		tmp = Float64(Float64(-4.0 * i) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 1.7e+65], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.7e65

   1. Initial program 91.1%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.6

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

   5. Applied rewrites 57.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 57.6

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

   7. Applied rewrites 57.6%

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

   if 1.7e65 < x

   1. Initial program 77.0%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 46.8

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

   5. Applied rewrites 46.8%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 1.7e+65) (fma (* -27.0 j) k (* c b)) (* (* -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 tmp;
	if (x <= 1.7e+65) {
		tmp = fma((-27.0 * j), k, (c * b));
	} else {
		tmp = (-4.0 * i) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 1.7e+65)
		tmp = fma(Float64(-27.0 * j), k, Float64(c * b));
	else
		tmp = Float64(Float64(-4.0 * i) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 1.7e+65], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.7e65

   1. Initial program 91.1%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.6

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

   5. Applied rewrites 57.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-*.f64 57.6

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

   7. Applied rewrites 57.6%

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

   if 1.7e65 < x

   1. Initial program 77.0%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 46.8

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

   5. Applied rewrites 46.8%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 24.7% 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 88.7%

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

3. Taylor expanded in c around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 25.9

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

5. Applied rewrites 25.9%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 89.3% 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 2024236 
(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)))